diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index 0628cec..6cd581b 100644
--- a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ -836,7 +836,8 @@ digraph pic {
--S 1 of 1
)show CoercibleTo
---R CoercibleTo S: Type is a category constructor
+--R
+--R CoercibleTo(S: Type) is a category constructor
--R Abbreviation for CoercibleTo is KOERCE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for KOERCE
@@ -1051,7 +1052,8 @@ digraph pic {
--S 1 of 1
)show ConvertibleTo
---R ConvertibleTo S: Type is a category constructor
+--R
+--R ConvertibleTo(S: Type) is a category constructor
--R Abbreviation for ConvertibleTo is KONVERT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for KONVERT
@@ -1557,13 +1559,14 @@ digraph pic {
--S 1 of 1
)show InnerEvalable
+--R
--R InnerEvalable(A: SetCategory,B: Type) is a category constructor
--R Abbreviation for InnerEvalable is IEVALAB
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for IEVALAB
--R
--R------------------------------- Operations --------------------------------
---R eval : (%,A,B) -> % eval : (%,List A,List B) -> %
+--R eval : (%,A,B) -> % eval : (%,List(A),List(B)) -> %
--R
--E 1
@@ -1810,7 +1813,8 @@ digraph pic {
--S 1 of 1
)show PartialTranscendentalFunctions
---R PartialTranscendentalFunctions K: TranscendentalFunctionCategory is a category constructor
+--R
+--R PartialTranscendentalFunctions(K: TranscendentalFunctionCategory) is a category constructor
--R Abbreviation for PartialTranscendentalFunctions is PTRANFN
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PTRANFN
@@ -2049,14 +2053,15 @@ digraph pic {
--S 1 of 1
)show Patternable
---R Patternable R: Type is a category constructor
+--R
+--R Patternable(R: Type) is a category constructor
--R Abbreviation for Patternable is PATAB
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PATAB
--R
--R------------------------------- Operations --------------------------------
---R convert : % -> Pattern Integer if R has KONVERT PATTERN INT
---R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT
+--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT))
+--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT))
--R
--E 1
@@ -2166,6 +2171,7 @@ digraph pic {
--S 1 of 1
)show PrimitiveFunctionCategory
+--R
--R PrimitiveFunctionCategory is a category constructor
--R Abbreviation for PrimitiveFunctionCategory is PRIMCAT
--R This constructor is exposed in this frame.
@@ -2173,7 +2179,7 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R integral : (%,Symbol) -> %
---R integral : (%,SegmentBinding %) -> %
+--R integral : (%,SegmentBinding(%)) -> %
--R
--E 1
@@ -2262,14 +2268,15 @@ digraph pic {
--S 1 of 1
)show RadicalCategory
+--R
--R RadicalCategory is a category constructor
--R Abbreviation for RadicalCategory is RADCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RADCAT
--R
--R------------------------------- Operations --------------------------------
---R ?**? : (%,Fraction Integer) -> % nthRoot : (%,Integer) -> %
---R sqrt : % -> %
+--R nthRoot : (%,Integer) -> % sqrt : % -> %
+--R ?**? : (%,Fraction(Integer)) -> %
--R
--E 1
@@ -2377,7 +2384,8 @@ digraph pic {
--S 1 of 1
)show RetractableTo
---R RetractableTo S: Type is a category constructor
+--R
+--R RetractableTo(S: Type) is a category constructor
--R Abbreviation for RetractableTo is RETRACT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RETRACT
@@ -3037,6 +3045,7 @@ digraph pic {
--S 1 of 1
)show CombinatorialOpsCategory
+--R
--R CombinatorialOpsCategory is a category constructor
--R Abbreviation for CombinatorialOpsCategory is COMBOPC
--R This constructor is exposed in this frame.
@@ -3047,8 +3056,8 @@ digraph pic {
--R factorials : (%,Symbol) -> % factorials : % -> %
--R permutation : (%,%) -> % product : (%,Symbol) -> %
--R summation : (%,Symbol) -> %
---R product : (%,SegmentBinding %) -> %
---R summation : (%,SegmentBinding %) -> %
+--R product : (%,SegmentBinding(%)) -> %
+--R summation : (%,SegmentBinding(%)) -> %
--R
--E 1
@@ -3328,14 +3337,16 @@ digraph pic {
--S 1 of 1
)show Evalable
---R Evalable R: SetCategory is a category constructor
+--R
+--R Evalable(R: SetCategory) is a category constructor
--R Abbreviation for Evalable is EVALAB
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for EVALAB
--R
--R------------------------------- Operations --------------------------------
---R eval : (%,List Equation R) -> % eval : (%,Equation R) -> %
---R eval : (%,R,R) -> % eval : (%,List R,List R) -> %
+--R eval : (%,Equation(R)) -> % eval : (%,R,R) -> %
+--R eval : (%,List(R),List(R)) -> %
+--R eval : (%,List(Equation(R))) -> %
--R
--E 1
@@ -3593,19 +3604,20 @@ digraph pic {
--S 1 of 1
)show FullyRetractableTo
---R FullyRetractableTo S: Type is a category constructor
+--R
+--R FullyRetractableTo(S: Type) is a category constructor
--R Abbreviation for FullyRetractableTo is FRETRCT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FRETRCT
--R
--R------------------------------- Operations --------------------------------
--R coerce : S -> % retract : % -> S
---R coerce : Integer -> % if S has RETRACT INT
---R coerce : Fraction Integer -> % if S has RETRACT FRAC INT
---R retract : % -> Integer if S has RETRACT INT
---R retract : % -> Fraction Integer if S has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT
+--R coerce : Integer -> % if S has RETRACT(INT)
+--R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT))
+--R retract : % -> Integer if S has RETRACT(INT)
+--R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(S,"failed")
--R
--E 1
@@ -3760,19 +3772,20 @@ digraph pic {
--S 1 of 1
)show FullyPatternMatchable
---R FullyPatternMatchable R: Type is a category constructor
+--R
+--R FullyPatternMatchable(R: Type) is a category constructor
--R Abbreviation for FullyPatternMatchable is FPATMAB
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FPATMAB
--R
--R------------------------------- Operations --------------------------------
---R ?=? : (%,%) -> Boolean if R has PATMAB INT or R has PATMAB FLOAT
---R coerce : % -> OutputForm if R has PATMAB INT or R has PATMAB FLOAT
---R hash : % -> SingleInteger if R has PATMAB INT or R has PATMAB FLOAT
---R latex : % -> String if R has PATMAB INT or R has PATMAB FLOAT
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT
---R ?~=? : (%,%) -> Boolean if R has PATMAB INT or R has PATMAB FLOAT
+--R ?=? : (%,%) -> Boolean if R has PATMAB(INT) or R has PATMAB(FLOAT)
+--R coerce : % -> OutputForm if R has PATMAB(INT) or R has PATMAB(FLOAT)
+--R hash : % -> SingleInteger if R has PATMAB(INT) or R has PATMAB(FLOAT)
+--R latex : % -> String if R has PATMAB(INT) or R has PATMAB(FLOAT)
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT)
+--R ?~=? : (%,%) -> Boolean if R has PATMAB(INT) or R has PATMAB(FLOAT)
--R
--E 1
@@ -4038,15 +4051,17 @@ digraph pic {
--S 1 of 1
)show PlottablePlaneCurveCategory
+--R
--R PlottablePlaneCurveCategory is a category constructor
--R Abbreviation for PlottablePlaneCurveCategory is PPCURVE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PPCURVE
--R
--R------------------------------- Operations --------------------------------
---R coerce : % -> OutputForm xRange : % -> Segment DoubleFloat
---R yRange : % -> Segment DoubleFloat
---R listBranches : % -> List List Point DoubleFloat
+--R coerce : % -> OutputForm
+--R listBranches : % -> List(List(Point(DoubleFloat)))
+--R xRange : % -> Segment(DoubleFloat)
+--R yRange : % -> Segment(DoubleFloat)
--R
--E 1
@@ -4169,15 +4184,18 @@ digraph pic {
--S 1 of 1
)show PlottableSpaceCurveCategory
+--R
--R PlottableSpaceCurveCategory is a category constructor
--R Abbreviation for PlottableSpaceCurveCategory is PSCURVE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PSCURVE
--R
--R------------------------------- Operations --------------------------------
---R coerce : % -> OutputForm xRange : % -> Segment DoubleFloat
---R yRange : % -> Segment DoubleFloat zRange : % -> Segment DoubleFloat
---R listBranches : % -> List List Point DoubleFloat
+--R coerce : % -> OutputForm
+--R listBranches : % -> List(List(Point(DoubleFloat)))
+--R xRange : % -> Segment(DoubleFloat)
+--R yRange : % -> Segment(DoubleFloat)
+--R zRange : % -> Segment(DoubleFloat)
--R
--E 1
@@ -4418,7 +4436,8 @@ digraph pic {
--S 1 of 1
)show SegmentCategory
---R SegmentCategory S: Type is a category constructor
+--R
+--R SegmentCategory(S: Type) is a category constructor
--R Abbreviation for SegmentCategory is SEGCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SEGCAT
@@ -5136,6 +5155,7 @@ digraph pic {
--S 1 of 1
)show BlowUpMethodCategory
+--R
--R BlowUpMethodCategory is a category constructor
--R Abbreviation for BlowUpMethodCategory is BLMETCT
--R This constructor is exposed in this frame.
@@ -5143,7 +5163,7 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean chartCoord : % -> Integer
---R coerce : List Integer -> % coerce : % -> OutputForm
+--R coerce : List(Integer) -> % coerce : % -> OutputForm
--R excepCoord : % -> Integer hash : % -> SingleInteger
--R infClsPt? : % -> Boolean latex : % -> String
--R quotValuation : % -> Integer ramifMult : % -> Integer
@@ -5288,20 +5308,21 @@ digraph pic {
--S 1 of 1
)show DesingTreeCategory
---R DesingTreeCategory S: SetCategory is a category constructor
+--R
+--R DesingTreeCategory(S: SetCategory) is a category constructor
--R Abbreviation for DesingTreeCategory is DSTRCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DSTRCAT
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % copy : % -> %
+--R children : % -> List(%) copy : % -> %
--R cyclic? : % -> Boolean distance : (%,%) -> Integer
--R ?.value : (%,value) -> S empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R leaf? : % -> Boolean leaves : % -> List S
---R map : ((S -> S),%) -> % nodes : % -> List %
---R sample : () -> % tree : List S -> %
---R tree : S -> % tree : (S,List %) -> %
+--R leaf? : % -> Boolean leaves : % -> List(S)
+--R map : ((S -> S),%) -> % nodes : % -> List(%)
+--R sample : () -> % tree : List(S) -> %
+--R tree : S -> % tree : (S,List(%)) -> %
--R value : % -> S
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
@@ -5310,21 +5331,21 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R parts : % -> List(S) if $ has finiteAggregate
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,value,S) -> S if $ has shallowlyMutable
--R setvalue! : (%,S) -> S if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
@@ -5526,25 +5547,27 @@ digraph pic {
--S 1 of 1
)show FortranFunctionCategory
+--R
--R FortranFunctionCategory is a category constructor
--R Abbreviation for FortranFunctionCategory is FORTFN
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FORTFN
--R
--R------------------------------- Operations --------------------------------
---R coerce : FortranCode -> % coerce : List FortranCode -> %
+--R coerce : FortranCode -> % coerce : List(FortranCode) -> %
--R coerce : % -> OutputForm outputAsFortran : % -> Void
---R retract : Polynomial Integer -> % retract : Polynomial Float -> %
---R retract : Expression Integer -> % retract : Expression Float -> %
---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> %
---R retract : Fraction Polynomial Integer -> %
---R retract : Fraction Polynomial Float -> %
---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed")
---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed")
---R retractIfCan : Polynomial Integer -> Union(%,"failed")
---R retractIfCan : Polynomial Float -> Union(%,"failed")
---R retractIfCan : Expression Integer -> Union(%,"failed")
---R retractIfCan : Expression Float -> Union(%,"failed")
+--R retract : Polynomial(Float) -> % retract : Expression(Float) -> %
+--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> %
+--R retract : Fraction(Polynomial(Integer)) -> %
+--R retract : Fraction(Polynomial(Float)) -> %
+--R retract : Polynomial(Integer) -> %
+--R retract : Expression(Integer) -> %
+--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed")
+--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed")
+--R retractIfCan : Polynomial(Integer) -> Union(%,"failed")
+--R retractIfCan : Polynomial(Float) -> Union(%,"failed")
+--R retractIfCan : Expression(Integer) -> Union(%,"failed")
+--R retractIfCan : Expression(Float) -> Union(%,"failed")
--R
--E 1
@@ -5717,16 +5740,17 @@ digraph pic {
--S 1 of 1
)show FortranMatrixCategory
+--R
--R FortranMatrixCategory is a category constructor
--R Abbreviation for FortranMatrixCategory is FMC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FMC
--R
--R------------------------------- Operations --------------------------------
---R coerce : FortranCode -> % coerce : List FortranCode -> %
---R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm
---R outputAsFortran : % -> Void
---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> %
+--R coerce : FortranCode -> % coerce : List(FortranCode) -> %
+--R coerce : % -> OutputForm outputAsFortran : % -> Void
+--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> %
+--R coerce : Matrix(MachineFloat) -> %
--R
--E 1
@@ -5851,27 +5875,28 @@ digraph pic {
--S 1 of 1
)show FortranMatrixFunctionCategory
+--R
--R FortranMatrixFunctionCategory is a category constructor
--R Abbreviation for FortranMatrixFunctionCategory is FMFUN
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FMFUN
--R
--R------------------------------- Operations --------------------------------
---R coerce : FortranCode -> % coerce : List FortranCode -> %
+--R coerce : FortranCode -> % coerce : List(FortranCode) -> %
--R coerce : % -> OutputForm outputAsFortran : % -> Void
---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> %
---R retract : Matrix Fraction Polynomial Integer -> %
---R retract : Matrix Fraction Polynomial Float -> %
---R retract : Matrix Polynomial Integer -> %
---R retract : Matrix Polynomial Float -> %
---R retract : Matrix Expression Integer -> %
---R retract : Matrix Expression Float -> %
---R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed")
---R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed")
---R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed")
---R retractIfCan : Matrix Polynomial Float -> Union(%,"failed")
---R retractIfCan : Matrix Expression Integer -> Union(%,"failed")
---R retractIfCan : Matrix Expression Float -> Union(%,"failed")
+--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> %
+--R retract : Matrix(Fraction(Polynomial(Integer))) -> %
+--R retract : Matrix(Fraction(Polynomial(Float))) -> %
+--R retract : Matrix(Polynomial(Integer)) -> %
+--R retract : Matrix(Polynomial(Float)) -> %
+--R retract : Matrix(Expression(Integer)) -> %
+--R retract : Matrix(Expression(Float)) -> %
+--R retractIfCan : Matrix(Fraction(Polynomial(Integer))) -> Union(%,"failed")
+--R retractIfCan : Matrix(Fraction(Polynomial(Float))) -> Union(%,"failed")
+--R retractIfCan : Matrix(Polynomial(Integer)) -> Union(%,"failed")
+--R retractIfCan : Matrix(Polynomial(Float)) -> Union(%,"failed")
+--R retractIfCan : Matrix(Expression(Integer)) -> Union(%,"failed")
+--R retractIfCan : Matrix(Expression(Float)) -> Union(%,"failed")
--R
--E 1
@@ -6045,16 +6070,17 @@ digraph pic {
--S 1 of 1
)show FortranVectorCategory
+--R
--R FortranVectorCategory is a category constructor
--R Abbreviation for FortranVectorCategory is FVC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FVC
--R
--R------------------------------- Operations --------------------------------
---R coerce : FortranCode -> % coerce : List FortranCode -> %
---R coerce : Vector MachineFloat -> % coerce : % -> OutputForm
---R outputAsFortran : % -> Void
---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> %
+--R coerce : FortranCode -> % coerce : List(FortranCode) -> %
+--R coerce : % -> OutputForm outputAsFortran : % -> Void
+--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> %
+--R coerce : Vector(MachineFloat) -> %
--R
--E 1
@@ -6177,27 +6203,28 @@ digraph pic {
--S 1 of 1
)show FortranVectorFunctionCategory
+--R
--R FortranVectorFunctionCategory is a category constructor
--R Abbreviation for FortranVectorFunctionCategory is FVFUN
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FVFUN
--R
--R------------------------------- Operations --------------------------------
---R coerce : FortranCode -> % coerce : List FortranCode -> %
+--R coerce : FortranCode -> % coerce : List(FortranCode) -> %
--R coerce : % -> OutputForm outputAsFortran : % -> Void
---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> %
---R retract : Vector Fraction Polynomial Integer -> %
---R retract : Vector Fraction Polynomial Float -> %
---R retract : Vector Polynomial Integer -> %
---R retract : Vector Polynomial Float -> %
---R retract : Vector Expression Integer -> %
---R retract : Vector Expression Float -> %
---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed")
---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed")
---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed")
---R retractIfCan : Vector Polynomial Float -> Union(%,"failed")
---R retractIfCan : Vector Expression Integer -> Union(%,"failed")
---R retractIfCan : Vector Expression Float -> Union(%,"failed")
+--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> %
+--R retract : Vector(Fraction(Polynomial(Integer))) -> %
+--R retract : Vector(Fraction(Polynomial(Float))) -> %
+--R retract : Vector(Polynomial(Integer)) -> %
+--R retract : Vector(Polynomial(Float)) -> %
+--R retract : Vector(Expression(Integer)) -> %
+--R retract : Vector(Expression(Float)) -> %
+--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed")
+--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed")
+--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed")
+--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed")
+--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed")
+--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed")
--R
--E 1
@@ -6370,7 +6397,8 @@ digraph pic {
--S 1 of 1
)show FullyEvalableOver
---R FullyEvalableOver R: SetCategory is a category constructor
+--R
+--R FullyEvalableOver(R: SetCategory) is a category constructor
--R Abbreviation for FullyEvalableOver is FEVALAB
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FEVALAB
@@ -6378,11 +6406,11 @@ digraph pic {
--R------------------------------- Operations --------------------------------
--R map : ((R -> R),%) -> %
--R ?.? : (%,R) -> % if R has ELTAB(R,R)
---R eval : (%,List R,List R) -> % if R has EVALAB R
---R eval : (%,R,R) -> % if R has EVALAB R
---R eval : (%,Equation R) -> % if R has EVALAB R
---R eval : (%,List Equation R) -> % if R has EVALAB R
---R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R)
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R)
+--R eval : (%,R,R) -> % if R has EVALAB(R)
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R)
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R)
+--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R)
--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R)
--R
--E 1
@@ -7237,7 +7265,8 @@ digraph pic {
--S 1 of 1
)show HomogeneousAggregate
---R HomogeneousAggregate S: Type is a category constructor
+--R
+--R HomogeneousAggregate(S: Type) is a category constructor
--R Abbreviation for HomogeneousAggregate is HOAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for HOAGG
@@ -7252,19 +7281,19 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
@@ -7693,6 +7722,7 @@ digraph pic {
--S 1 of 1
)show LiouvillianFunctionCategory
+--R
--R LiouvillianFunctionCategory is a category constructor
--R Abbreviation for LiouvillianFunctionCategory is LFCAT
--R This constructor is exposed in this frame.
@@ -7718,7 +7748,7 @@ digraph pic {
--R sech : % -> % sin : % -> %
--R sinh : % -> % tan : % -> %
--R tanh : % -> %
---R integral : (%,SegmentBinding %) -> %
+--R integral : (%,SegmentBinding(%)) -> %
--R
--E 1
@@ -8119,6 +8149,7 @@ digraph pic {
--S 1 of 1
)show NumericalIntegrationCategory
+--R
--R NumericalIntegrationCategory is a category constructor
--R Abbreviation for NumericalIntegrationCategory is NUMINT
--R This constructor is exposed in this frame.
@@ -8128,10 +8159,10 @@ digraph pic {
--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm
--R hash : % -> SingleInteger latex : % -> String
--R ?~=? : (%,%) -> Boolean
---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result)
---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result)
---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result
---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result
+--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result)
+--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result)
+--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result
+--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result
--R
--E 1
@@ -8315,6 +8346,7 @@ digraph pic {
--S 1 of 1
)show NumericalOptimizationCategory
+--R
--R NumericalOptimizationCategory is a category constructor
--R Abbreviation for NumericalOptimizationCategory is OPTCAT
--R This constructor is exposed in this frame.
@@ -8324,10 +8356,10 @@ digraph pic {
--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm
--R hash : % -> SingleInteger latex : % -> String
--R ?~=? : (%,%) -> Boolean
---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String)
---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String)
---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result
---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result
+--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String)
+--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String)
+--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result
+--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result
--R
--E 1
@@ -8505,6 +8537,7 @@ digraph pic {
--S 1 of 1
)show OrdinaryDifferentialEquationsSolverCategory
+--R
--R OrdinaryDifferentialEquationsSolverCategory is a category constructor
--R Abbreviation for OrdinaryDifferentialEquationsSolverCategory is ODECAT
--R This constructor is exposed in this frame.
@@ -8514,8 +8547,8 @@ digraph pic {
--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm
--R hash : % -> SingleInteger latex : % -> String
--R ?~=? : (%,%) -> Boolean
---R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result
---R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String)
+--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> Result
+--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String)
--R
--E 1
@@ -8851,6 +8884,7 @@ digraph pic {
--S 1 of 1
)show PartialDifferentialEquationsSolverCategory
+--R
--R PartialDifferentialEquationsSolverCategory is a category constructor
--R Abbreviation for PartialDifferentialEquationsSolverCategory is PDECAT
--R This constructor is exposed in this frame.
@@ -8860,8 +8894,8 @@ digraph pic {
--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm
--R hash : % -> SingleInteger latex : % -> String
--R ?~=? : (%,%) -> Boolean
---R PDESolve : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> Result
---R measure : (RoutinesTable,Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String)
+--R PDESolve : Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat) -> Result
+--R measure : (RoutinesTable,Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String)
--R
--E 1
@@ -9049,7 +9083,8 @@ digraph pic {
--S 1 of 1
)show PatternMatchable
---R PatternMatchable S: SetCategory is a category constructor
+--R
+--R PatternMatchable(S: SetCategory) is a category constructor
--R Abbreviation for PatternMatchable is PATMAB
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PATMAB
@@ -9058,7 +9093,7 @@ digraph pic {
--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm
--R hash : % -> SingleInteger latex : % -> String
--R ?~=? : (%,%) -> Boolean
---R patternMatch : (%,Pattern S,PatternMatchResult(S,%)) -> PatternMatchResult(S,%)
+--R patternMatch : (%,Pattern(S),PatternMatchResult(S,%)) -> PatternMatchResult(S,%)
--R
--E 1
@@ -9189,13 +9224,14 @@ digraph pic {
--S 1 of 1
)show RealRootCharacterizationCategory
---R RealRootCharacterizationCategory(TheField: Join(OrderedRing,Field),ThePols: UnivariatePolynomialCategory t#1) is a category constructor
+--R
+--R RealRootCharacterizationCategory(TheField: Join(OrderedRing,Field),ThePols: UnivariatePolynomialCategory(t#1)) is a category constructor
--R Abbreviation for RealRootCharacterizationCategory is RRCC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RRCC
--R
--R------------------------------- Operations --------------------------------
---R ?=? : (%,%) -> Boolean allRootsOf : ThePols -> List %
+--R ?=? : (%,%) -> Boolean allRootsOf : ThePols -> List(%)
--R coerce : % -> OutputForm definingPolynomial : % -> ThePols
--R hash : % -> SingleInteger latex : % -> String
--R sign : (ThePols,%) -> Integer zero? : (ThePols,%) -> Boolean
@@ -9417,7 +9453,8 @@ digraph pic {
--S 1 of 1
)show SegmentExpansionCategory
---R SegmentExpansionCategory(S: OrderedRing,L: StreamAggregate t#1) is a category constructor
+--R
+--R SegmentExpansionCategory(S: OrderedRing,L: StreamAggregate(t#1)) is a category constructor
--R Abbreviation for SegmentExpansionCategory is SEGXCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SEGXCAT
@@ -9425,7 +9462,7 @@ digraph pic {
--R------------------------------- Operations --------------------------------
--R BY : (%,Integer) -> % ?..? : (S,S) -> %
--R convert : S -> % expand : % -> L
---R expand : List % -> L hi : % -> S
+--R expand : List(%) -> L hi : % -> S
--R high : % -> S incr : % -> Integer
--R lo : % -> S low : % -> S
--R map : ((S -> S),%) -> L segment : (S,S) -> %
@@ -9868,6 +9905,7 @@ digraph pic {
--S 1 of 1
)show SExpressionCategory
+--R
--R SExpressionCategory(Str: SetCategory,Sym: SetCategory,Int: SetCategory,Flt: SetCategory,Expr: SetCategory) is a category constructor
--R Abbreviation for SExpressionCategory is SEXCAT
--R This constructor is exposed in this frame.
@@ -9879,8 +9917,8 @@ digraph pic {
--R cdr : % -> % coerce : % -> OutputForm
--R convert : Expr -> % convert : Flt -> %
--R convert : Int -> % convert : Sym -> %
---R convert : Str -> % convert : List % -> %
---R destruct : % -> List % ?.? : (%,List Integer) -> %
+--R convert : Str -> % convert : List(%) -> %
+--R destruct : % -> List(%) ?.? : (%,List(Integer)) -> %
--R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean
--R expr : % -> Expr float : % -> Flt
--R float? : % -> Boolean hash : % -> SingleInteger
@@ -10256,48 +10294,49 @@ digraph pic {
--S 1 of 1
)show ThreeSpaceCategory
---R ThreeSpaceCategory R: Ring is a category constructor
+--R
+--R ThreeSpaceCategory(R: Ring) is a category constructor
--R Abbreviation for ThreeSpaceCategory is SPACEC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SPACEC
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean check : % -> %
---R closedCurve : % -> List Point R closedCurve : List Point R -> %
+--R closedCurve : % -> List(Point(R)) closedCurve : List(Point(R)) -> %
--R closedCurve? : % -> Boolean coerce : % -> OutputForm
---R components : % -> List % composite : List % -> %
---R composites : % -> List % copy : % -> %
+--R components : % -> List(%) composite : List(%) -> %
+--R composites : % -> List(%) copy : % -> %
--R create3Space : SubSpace(3,R) -> % create3Space : () -> %
---R curve : % -> List Point R curve : List Point R -> %
---R curve : (%,List List R) -> % curve : (%,List Point R) -> %
+--R curve : % -> List(Point(R)) curve : List(Point(R)) -> %
+--R curve : (%,List(List(R))) -> % curve : (%,List(Point(R))) -> %
--R curve? : % -> Boolean hash : % -> SingleInteger
---R latex : % -> String lp : % -> List Point R
---R merge : (%,%) -> % merge : List % -> %
---R mesh : % -> List List Point R mesh : List List Point R -> %
---R mesh? : % -> Boolean point : % -> Point R
---R point : Point R -> % point : (%,List R) -> %
---R point : (%,Point R) -> % point? : % -> Boolean
---R polygon : % -> List Point R polygon : List Point R -> %
---R polygon : (%,List List R) -> % polygon : (%,List Point R) -> %
---R polygon? : % -> Boolean subspace : % -> SubSpace(3,R)
---R ?~=? : (%,%) -> Boolean
---R closedCurve : (%,List List R) -> %
---R closedCurve : (%,List Point R) -> %
---R enterPointData : (%,List Point R) -> NonNegativeInteger
---R lllip : % -> List List List NonNegativeInteger
---R lllp : % -> List List List Point R
---R llprop : % -> List List SubSpaceComponentProperty
---R lprop : % -> List SubSpaceComponentProperty
---R mesh : (List List Point R,Boolean,Boolean) -> %
---R mesh : (%,List List List R,Boolean,Boolean) -> %
---R mesh : (%,List List Point R,Boolean,Boolean) -> %
---R mesh : (%,List List List R,List SubSpaceComponentProperty,SubSpaceComponentProperty) -> %
---R mesh : (%,List List Point R,List SubSpaceComponentProperty,SubSpaceComponentProperty) -> %
---R modifyPointData : (%,NonNegativeInteger,Point R) -> %
+--R latex : % -> String lp : % -> List(Point(R))
+--R merge : (%,%) -> % merge : List(%) -> %
+--R mesh : % -> List(List(Point(R))) mesh : List(List(Point(R))) -> %
+--R mesh? : % -> Boolean point : % -> Point(R)
+--R point : Point(R) -> % point : (%,List(R)) -> %
+--R point : (%,Point(R)) -> % point? : % -> Boolean
+--R polygon : % -> List(Point(R)) polygon : List(Point(R)) -> %
+--R polygon : (%,List(List(R))) -> % polygon? : % -> Boolean
+--R subspace : % -> SubSpace(3,R) ?~=? : (%,%) -> Boolean
+--R closedCurve : (%,List(List(R))) -> %
+--R closedCurve : (%,List(Point(R))) -> %
+--R enterPointData : (%,List(Point(R))) -> NonNegativeInteger
+--R lllip : % -> List(List(List(NonNegativeInteger)))
+--R lllp : % -> List(List(List(Point(R))))
+--R llprop : % -> List(List(SubSpaceComponentProperty))
+--R lprop : % -> List(SubSpaceComponentProperty)
+--R mesh : (List(List(Point(R))),Boolean,Boolean) -> %
+--R mesh : (%,List(List(List(R))),Boolean,Boolean) -> %
+--R mesh : (%,List(List(Point(R))),Boolean,Boolean) -> %
+--R mesh : (%,List(List(List(R))),List(SubSpaceComponentProperty),SubSpaceComponentProperty) -> %
+--R mesh : (%,List(List(Point(R))),List(SubSpaceComponentProperty),SubSpaceComponentProperty) -> %
+--R modifyPointData : (%,NonNegativeInteger,Point(R)) -> %
--R numberOfComponents : % -> NonNegativeInteger
--R numberOfComposites : % -> NonNegativeInteger
--R objects : % -> Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger)
--R point : (%,NonNegativeInteger) -> %
+--R polygon : (%,List(Point(R))) -> %
--R
--E 1
@@ -10954,26 +10993,27 @@ digraph pic {
--S 1 of 1
)show AffineSpaceCategory
---R AffineSpaceCategory K: Field is a category constructor
+--R
+--R AffineSpaceCategory(K: Field) is a category constructor
--R Abbreviation for AffineSpaceCategory is AFSPCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for AFSPCAT
--R
--R------------------------------- Operations --------------------------------
---R ?=? : (%,%) -> Boolean affinePoint : List K -> %
---R coerce : List K -> % coerce : % -> List K
+--R ?=? : (%,%) -> Boolean affinePoint : List(K) -> %
+--R coerce : List(K) -> % coerce : % -> List(K)
--R coerce : % -> OutputForm conjugate : % -> %
--R definingField : % -> K degree : % -> PositiveInteger
--R ?.? : (%,Integer) -> K hash : % -> SingleInteger
---R latex : % -> String list : % -> List K
---R orbit : % -> List % origin : () -> %
---R pointValue : % -> List K rational? : % -> Boolean
+--R latex : % -> String list : % -> List(K)
+--R orbit : % -> List(%) origin : () -> %
+--R pointValue : % -> List(K) rational? : % -> Boolean
--R setelt : (%,Integer,K) -> K ?~=? : (%,%) -> Boolean
--R conjugate : (%,NonNegativeInteger) -> %
---R orbit : (%,NonNegativeInteger) -> List %
+--R orbit : (%,NonNegativeInteger) -> List(%)
--R rational? : (%,NonNegativeInteger) -> Boolean
---R removeConjugate : List % -> List %
---R removeConjugate : (List %,NonNegativeInteger) -> List %
+--R removeConjugate : List(%) -> List(%)
+--R removeConjugate : (List(%),NonNegativeInteger) -> List(%)
--R
--E 1
@@ -11182,13 +11222,14 @@ digraph pic {
--S 1 of 1
)show BagAggregate
---R BagAggregate S: Type is a category constructor
+--R
+--R BagAggregate(S: Type) is a category constructor
--R Abbreviation for BagAggregate is BGAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BGAGG
--R
--R------------------------------- Operations --------------------------------
---R bag : List S -> % copy : % -> %
+--R bag : List(S) -> % copy : % -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean extract! : % -> S
--R insert! : (S,%) -> % inspect : % -> S
@@ -11199,19 +11240,19 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
@@ -11560,13 +11601,14 @@ digraph pic {
--S 1 of 1
)show Collection
---R Collection S: Type is a category constructor
+--R
+--R Collection(S: Type) is a category constructor
--R Abbreviation for Collection is CLAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for CLAGG
--R
--R------------------------------- Operations --------------------------------
---R construct : List S -> % copy : % -> %
+--R construct : List(S) -> % copy : % -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean map : ((S -> S),%) -> %
--R sample : () -> %
@@ -11574,13 +11616,13 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R hash : % -> SingleInteger if S has SETCAT
@@ -11588,9 +11630,9 @@ digraph pic {
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
@@ -11888,7 +11930,8 @@ digraph pic {
--S 1 of 1
)show DifferentialVariableCategory
---R DifferentialVariableCategory S: OrderedSet is a category constructor
+--R
+--R DifferentialVariableCategory(S: OrderedSet) is a category constructor
--R Abbreviation for DifferentialVariableCategory is DVARCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DVARCAT
@@ -12168,6 +12211,7 @@ digraph pic {
--S 1 of 1
)show ExpressionSpace
+--R
--R ExpressionSpace is a category constructor
--R Abbreviation for ExpressionSpace is ES
--R This constructor is exposed in this frame.
@@ -12177,45 +12221,47 @@ digraph pic {
--R ? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
--R ?>=? : (%,%) -> Boolean belong? : BasicOperator -> Boolean
---R box : List % -> % box : % -> %
---R coerce : Kernel % -> % coerce : % -> OutputForm
+--R box : List(%) -> % box : % -> %
+--R coerce : Kernel(%) -> % coerce : % -> OutputForm
--R distribute : (%,%) -> % distribute : % -> %
--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> %
---R eval : (%,List %,List %) -> % eval : (%,%,%) -> %
---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> %
---R eval : (%,Kernel %,%) -> % freeOf? : (%,Symbol) -> Boolean
+--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> %
+--R eval : (%,Kernel(%),%) -> % freeOf? : (%,Symbol) -> Boolean
--R freeOf? : (%,%) -> Boolean hash : % -> SingleInteger
--R height : % -> NonNegativeInteger is? : (%,Symbol) -> Boolean
---R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel %
---R latex : % -> String map : ((% -> %),Kernel %) -> %
---R max : (%,%) -> % min : (%,%) -> %
---R paren : List % -> % paren : % -> %
---R retract : % -> Kernel % subst : (%,Equation %) -> %
---R tower : % -> List Kernel % ?~=? : (%,%) -> Boolean
+--R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%))
+--R latex : % -> String max : (%,%) -> %
+--R min : (%,%) -> % paren : List(%) -> %
+--R paren : % -> % retract : % -> Kernel(%)
+--R subst : (%,Equation(%)) -> % tower : % -> List(Kernel(%))
+--R ?~=? : (%,%) -> Boolean
--R definingPolynomial : % -> % if $ has RING
---R elt : (BasicOperator,List %) -> %
+--R elt : (BasicOperator,List(%)) -> %
--R elt : (BasicOperator,%,%,%,%) -> %
--R elt : (BasicOperator,%,%,%) -> %
--R eval : (%,BasicOperator,(% -> %)) -> %
---R eval : (%,BasicOperator,(List % -> %)) -> %
---R eval : (%,List BasicOperator,List (List % -> %)) -> %
---R eval : (%,List BasicOperator,List (% -> %)) -> %
+--R eval : (%,BasicOperator,(List(%) -> %)) -> %
+--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> %
+--R eval : (%,List(BasicOperator),List((% -> %))) -> %
--R eval : (%,Symbol,(% -> %)) -> %
---R eval : (%,Symbol,(List % -> %)) -> %
---R eval : (%,List Symbol,List (List % -> %)) -> %
---R eval : (%,List Symbol,List (% -> %)) -> %
---R eval : (%,List Kernel %,List %) -> %
---R even? : % -> Boolean if $ has RETRACT INT
+--R eval : (%,Symbol,(List(%) -> %)) -> %
+--R eval : (%,List(Symbol),List((List(%) -> %))) -> %
+--R eval : (%,List(Symbol),List((% -> %))) -> %
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
+--R eval : (%,List(Kernel(%)),List(%)) -> %
+--R even? : % -> Boolean if $ has RETRACT(INT)
--R is? : (%,BasicOperator) -> Boolean
---R kernel : (BasicOperator,List %) -> %
---R mainKernel : % -> Union(Kernel %,"failed")
---R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING
---R odd? : % -> Boolean if $ has RETRACT INT
+--R kernel : (BasicOperator,List(%)) -> %
+--R mainKernel : % -> Union(Kernel(%),"failed")
+--R map : ((% -> %),Kernel(%)) -> %
+--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING
+--R odd? : % -> Boolean if $ has RETRACT(INT)
--R operator : BasicOperator -> BasicOperator
---R operators : % -> List BasicOperator
---R retractIfCan : % -> Union(Kernel %,"failed")
---R subst : (%,List Kernel %,List %) -> %
---R subst : (%,List Equation %) -> %
+--R operators : % -> List(BasicOperator)
+--R retractIfCan : % -> Union(Kernel(%),"failed")
+--R subst : (%,List(Kernel(%)),List(%)) -> %
+--R subst : (%,List(Equation(%))) -> %
--R
--E 1
@@ -12967,6 +13013,7 @@ digraph pic {
--S 1 of 1
)show IndexedAggregate
+--R
--R IndexedAggregate(Index: SetCategory,Entry: Type) is a category constructor
--R Abbreviation for IndexedAggregate is IXAGG
--R This constructor is exposed in this frame.
@@ -12975,9 +13022,9 @@ digraph pic {
--R------------------------------- Operations --------------------------------
--R copy : % -> % ?.? : (%,Index) -> Entry
--R elt : (%,Index,Entry) -> Entry empty : () -> %
---R empty? : % -> Boolean entries : % -> List Entry
+--R empty? : % -> Boolean entries : % -> List(Entry)
--R eq? : (%,%) -> Boolean index? : (Index,%) -> Boolean
---R indices : % -> List Index map : ((Entry -> Entry),%) -> %
+--R indices : % -> List(Index) map : ((Entry -> Entry),%) -> %
--R qelt : (%,Index) -> Entry sample : () -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if Entry has SETCAT
@@ -12986,10 +13033,10 @@ digraph pic {
--R count : (Entry,%) -> NonNegativeInteger if Entry has SETCAT and $ has finiteAggregate
--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT
---R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
+--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,Entry) -> % if $ has shallowlyMutable
--R first : % -> Entry if Index has ORDSET
@@ -12999,10 +13046,10 @@ digraph pic {
--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable
--R maxIndex : % -> Index if Index has ORDSET
--R member? : (Entry,%) -> Boolean if Entry has SETCAT and $ has finiteAggregate
---R members : % -> List Entry if $ has finiteAggregate
+--R members : % -> List(Entry) if $ has finiteAggregate
--R minIndex : % -> Index if Index has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List Entry if $ has finiteAggregate
+--R parts : % -> List(Entry) if $ has finiteAggregate
--R qsetelt! : (%,Index,Entry) -> Entry if $ has shallowlyMutable
--R setelt : (%,Index,Entry) -> Entry if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
@@ -13890,28 +13937,29 @@ digraph pic {
--S 1 of 1
)show PlacesCategory
---R PlacesCategory(K: Field,PCS: LocalPowerSeriesCategory t#1) is a category constructor
+--R
+--R PlacesCategory(K: Field,PCS: LocalPowerSeriesCategory(t#1)) is a category constructor
--R Abbreviation for PlacesCategory is PLACESC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PLACESC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Integer,%) -> Divisor % ?+? : (%,%) -> Divisor %
---R -? : % -> Divisor % ?-? : (%,%) -> Divisor %
+--R ?*? : (Integer,%) -> Divisor(%) ?+? : (%,%) -> Divisor(%)
+--R -? : % -> Divisor(%) ?-? : (%,%) -> Divisor(%)
--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm
---R create : Symbol -> % create : List K -> %
+--R create : Symbol -> % create : List(K) -> %
--R degree : % -> PositiveInteger ?.? : (%,Integer) -> K
---R foundPlaces : () -> List % hash : % -> SingleInteger
+--R foundPlaces : () -> List(%) hash : % -> SingleInteger
--R itsALeaf! : % -> Void latex : % -> String
---R leaf? : % -> Boolean localParam : % -> List PCS
---R reduce : List % -> Divisor % setParam! : (%,List PCS) -> Void
+--R leaf? : % -> Boolean localParam : % -> List(PCS)
+--R reduce : List(%) -> Divisor(%) setParam! : (%,List(PCS)) -> Void
--R ?~=? : (%,%) -> Boolean
---R ?+? : (%,Divisor %) -> Divisor %
---R ?+? : (Divisor %,%) -> Divisor %
---R ?-? : (%,Divisor %) -> Divisor %
---R ?-? : (Divisor %,%) -> Divisor %
+--R ?+? : (%,Divisor(%)) -> Divisor(%)
+--R ?+? : (Divisor(%),%) -> Divisor(%)
+--R ?-? : (%,Divisor(%)) -> Divisor(%)
+--R ?-? : (Divisor(%),%) -> Divisor(%)
--R setDegree! : (%,PositiveInteger) -> Void
---R setFoundPlacesToEmpty : () -> List %
+--R setFoundPlacesToEmpty : () -> List(%)
--R
--E 1
@@ -14109,28 +14157,29 @@ digraph pic {
--S 1 of 1
)show ProjectiveSpaceCategory
---R ProjectiveSpaceCategory K: Field is a category constructor
+--R
+--R ProjectiveSpaceCategory(K: Field) is a category constructor
--R Abbreviation for ProjectiveSpaceCategory is PRSPCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PRSPCAT
--R
--R------------------------------- Operations --------------------------------
---R ?=? : (%,%) -> Boolean coerce : List K -> %
---R coerce : % -> List K coerce : % -> OutputForm
+--R ?=? : (%,%) -> Boolean coerce : List(K) -> %
+--R coerce : % -> List(K) coerce : % -> OutputForm
--R conjugate : % -> % definingField : % -> K
--R degree : % -> PositiveInteger ?.? : (%,Integer) -> K
--R hash : % -> SingleInteger homogenize : % -> %
--R homogenize : (%,Integer) -> % lastNonNul : % -> Integer
--R lastNonNull : % -> Integer latex : % -> String
---R list : % -> List K orbit : % -> List %
---R pointValue : % -> List K projectivePoint : List K -> %
+--R list : % -> List(K) orbit : % -> List(%)
+--R pointValue : % -> List(K) projectivePoint : List(K) -> %
--R rational? : % -> Boolean setelt : (%,Integer,K) -> K
--R ?~=? : (%,%) -> Boolean
--R conjugate : (%,NonNegativeInteger) -> %
---R orbit : (%,NonNegativeInteger) -> List %
+--R orbit : (%,NonNegativeInteger) -> List(%)
--R rational? : (%,NonNegativeInteger) -> Boolean
---R removeConjugate : List % -> List %
---R removeConjugate : (List %,NonNegativeInteger) -> List %
+--R removeConjugate : List(%) -> List(%)
+--R removeConjugate : (List(%),NonNegativeInteger) -> List(%)
--R
--E 1
@@ -14357,18 +14406,19 @@ digraph pic {
--S 1 of 1
)show RecursiveAggregate
---R RecursiveAggregate S: Type is a category constructor
+--R
+--R RecursiveAggregate(S: Type) is a category constructor
--R Abbreviation for RecursiveAggregate is RCAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RCAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % copy : % -> %
+--R children : % -> List(%) copy : % -> %
--R cyclic? : % -> Boolean distance : (%,%) -> Integer
--R ?.value : (%,value) -> S empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R leaf? : % -> Boolean leaves : % -> List S
---R map : ((S -> S),%) -> % nodes : % -> List %
+--R leaf? : % -> Boolean leaves : % -> List(S)
+--R map : ((S -> S),%) -> % nodes : % -> List(%)
--R sample : () -> % value : % -> S
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
@@ -14377,21 +14427,21 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R parts : % -> List(S) if $ has finiteAggregate
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,value,S) -> S if $ has shallowlyMutable
--R setvalue! : (%,S) -> S if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
@@ -14654,7 +14704,8 @@ first column in an array and vice versa.
--S 1 of 1
)show TwoDimensionalArrayCategory
---R TwoDimensionalArrayCategory(R: Type,Row: FiniteLinearAggregate t#1,Col: FiniteLinearAggregate t#1) is a category constructor
+--R
+--R TwoDimensionalArrayCategory(R: Type,Row: FiniteLinearAggregate(t#1),Col: FiniteLinearAggregate(t#1)) is a category constructor
--R Abbreviation for TwoDimensionalArrayCategory is ARR2CAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ARR2CAT
@@ -14669,7 +14720,7 @@ first column in an array and vice versa.
--R maxColIndex : % -> Integer maxRowIndex : % -> Integer
--R minColIndex : % -> Integer minRowIndex : % -> Integer
--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger
---R parts : % -> List R qelt : (%,Integer,Integer) -> R
+--R parts : % -> List(R) qelt : (%,Integer,Integer) -> R
--R row : (%,Integer) -> Row sample : () -> %
--R setRow! : (%,Integer,Row) -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
@@ -14678,16 +14729,16 @@ first column in an array and vice versa.
--R coerce : % -> OutputForm if R has SETCAT
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if R has SETCAT
--R latex : % -> String if R has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
+--R members : % -> List(R) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,NonNegativeInteger,R) -> %
--R qsetelt! : (%,Integer,Integer,R) -> R
@@ -15264,20 +15315,21 @@ digraph pic {
--S 1 of 1
)show BinaryRecursiveAggregate
---R BinaryRecursiveAggregate S: Type is a category constructor
+--R
+--R BinaryRecursiveAggregate(S: Type) is a category constructor
--R Abbreviation for BinaryRecursiveAggregate is BRAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BRAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % copy : % -> %
+--R children : % -> List(%) copy : % -> %
--R cyclic? : % -> Boolean distance : (%,%) -> Integer
--R ?.right : (%,right) -> % ?.left : (%,left) -> %
--R ?.value : (%,value) -> S empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R leaf? : % -> Boolean leaves : % -> List S
+--R leaf? : % -> Boolean leaves : % -> List(S)
--R left : % -> % map : ((S -> S),%) -> %
---R nodes : % -> List % right : % -> %
+--R nodes : % -> List(%) right : % -> %
--R sample : () -> % value : % -> S
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if S has SETCAT
@@ -15286,21 +15338,21 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R parts : % -> List(S) if $ has finiteAggregate
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,right,%) -> % if $ has shallowlyMutable
--R setelt : (%,left,%) -> % if $ has shallowlyMutable
--R setelt : (%,value,S) -> S if $ has shallowlyMutable
@@ -15792,14 +15844,15 @@ digraph pic {
--S 1 of 1
)show DictionaryOperations
---R DictionaryOperations S: SetCategory is a category constructor
+--R
+--R DictionaryOperations(S: SetCategory) is a category constructor
--R Abbreviation for DictionaryOperations is DIOPS
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIOPS
--R
--R------------------------------- Operations --------------------------------
---R bag : List S -> % construct : List S -> %
---R copy : % -> % dictionary : List S -> %
+--R bag : List(S) -> % construct : List(S) -> %
+--R copy : % -> % dictionary : List(S) -> %
--R dictionary : () -> % empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R extract! : % -> S insert! : (S,%) -> %
@@ -15809,13 +15862,13 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R hash : % -> SingleInteger if S has SETCAT
@@ -15823,9 +15876,9 @@ digraph pic {
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
@@ -16101,20 +16154,21 @@ digraph pic {
--S 1 of 1
)show DoublyLinkedAggregate
---R DoublyLinkedAggregate S: Type is a category constructor
+--R
+--R DoublyLinkedAggregate(S: Type) is a category constructor
--R Abbreviation for DoublyLinkedAggregate is DLAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DLAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % copy : % -> %
+--R children : % -> List(%) copy : % -> %
--R cyclic? : % -> Boolean distance : (%,%) -> Integer
--R ?.value : (%,value) -> S empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R head : % -> % last : % -> S
---R leaf? : % -> Boolean leaves : % -> List S
+--R leaf? : % -> Boolean leaves : % -> List(S)
--R map : ((S -> S),%) -> % next : % -> %
---R nodes : % -> List % previous : % -> %
+--R nodes : % -> List(%) previous : % -> %
--R sample : () -> % tail : % -> %
--R value : % -> S
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
@@ -16125,21 +16179,21 @@ digraph pic {
--R concat! : (%,%) -> % if $ has shallowlyMutable
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R parts : % -> List(S) if $ has finiteAggregate
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,value,S) -> S if $ has shallowlyMutable
--R setnext! : (%,%) -> % if $ has shallowlyMutable
--R setprevious! : (%,%) -> % if $ has shallowlyMutable
@@ -16610,20 +16664,21 @@ digraph pic {
--S 1 of 1
)show LinearAggregate
---R LinearAggregate S: Type is a category constructor
+--R
+--R LinearAggregate(S: Type) is a category constructor
--R Abbreviation for LinearAggregate is LNAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LNAGG
--R
--R------------------------------- Operations --------------------------------
---R concat : List % -> % concat : (%,%) -> %
+--R concat : List(%) -> % concat : (%,%) -> %
--R concat : (S,%) -> % concat : (%,S) -> %
---R construct : List S -> % copy : % -> %
+--R construct : List(S) -> % copy : % -> %
--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S
--R elt : (%,Integer,S) -> S empty : () -> %
---R empty? : % -> Boolean entries : % -> List S
+--R empty? : % -> Boolean entries : % -> List(S)
--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (%,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (%,%,Integer) -> %
--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> %
--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> %
--R qelt : (%,Integer) -> S sample : () -> %
@@ -16631,16 +16686,16 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -16651,10 +16706,10 @@ digraph pic {
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
@@ -16663,7 +16718,7 @@ digraph pic {
--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate
--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
@@ -17039,7 +17094,7 @@ z:Matrix(INT):=zero(3,3)
--R (5) |0 0 0|
--R | |
--R +0 0 0+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 5
--S 6 of 59
@@ -17053,7 +17108,7 @@ matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]]
--R |7 8 9|
--R | |
--R +1 1 1+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 6
--S 7 of 59
@@ -17065,7 +17120,7 @@ z:Matrix(INT):=scalarMatrix(3,5)
--R (7) |0 5 0|
--R | |
--R +0 0 5+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 7
--S 8 of 59
@@ -17077,7 +17132,7 @@ diagonalMatrix [1,2,3]
--R (8) |0 2 0|
--R | |
--R +0 0 3+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 8
--S 9 of 59
@@ -17091,7 +17146,7 @@ diagonalMatrix [matrix [[1,2],[3,4]], matrix [[4,5],[6,7]]]
--R |0 0 4 5|
--R | |
--R +0 0 6 7+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 9
--S 10 of 59
@@ -17103,7 +17158,7 @@ coerce([1,2,3])@Matrix(INT)
--R (10) |2|
--R | |
--R +3+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 10
--S 11 of 59
@@ -17111,7 +17166,7 @@ transpose([1,2,3])@Matrix(INT)
--R
--R
--R (11) [1 2 3]
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 11
--S 12 of 59
@@ -17127,7 +17182,7 @@ transpose matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 8 27 64 125|
--R | |
--R +1 16 81 256 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 12
--S 13 of 59
@@ -17139,7 +17194,7 @@ squareTop matrix [[j**i for i in 0..2] for j in 1..5]
--R (13) |1 2 4|
--R | |
--R +1 3 9+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 13
--S 14 of 59
@@ -17155,7 +17210,7 @@ t1:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 14
--S 15 of 59
@@ -17171,7 +17226,7 @@ horizConcat(t1,t1)
--R |1 4 16 64 256 1 4 16 64 256|
--R | |
--R +1 5 25 125 625 1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 15
--S 16 of 59
@@ -17187,7 +17242,7 @@ t2:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 16
--S 17 of 59
@@ -17213,7 +17268,7 @@ vertConcat(t2,t2)
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 17
--S 18 of 59
@@ -17229,7 +17284,7 @@ t3:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 18
--S 19 of 59
@@ -17238,7 +17293,7 @@ listOfLists t3
--R
--R (19)
--R [[1,1,1,1,1],[1,2,4,8,16],[1,3,9,27,81],[1,4,16,64,256],[1,5,25,125,625]]
---R Type: List List Integer
+--R Type: List(List(Integer))
--E 19
--S 20 of 59
@@ -17254,7 +17309,7 @@ t4:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 20
--S 21 of 59
@@ -17278,7 +17333,7 @@ t5:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 22
--S 23 of 59
@@ -17302,7 +17357,7 @@ t6:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 24
--S 25 of 59
@@ -17318,7 +17373,7 @@ swapRows!(t6,2,4)
--R |1 2 4 8 16 |
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 25
--S 26 of 59
@@ -17334,7 +17389,7 @@ t7:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 26
--S 27 of 59
@@ -17350,7 +17405,7 @@ swapColumns!(t7,2,4)
--R |1 64 16 4 256|
--R | |
--R +1 125 25 5 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 27
--S 28 of 59
@@ -17366,7 +17421,7 @@ t8:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 28
--S 29 of 59
@@ -17378,7 +17433,7 @@ subMatrix(t8,1,3,2,4)
--R (29) |2 4 8 |
--R | |
--R +3 9 27+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 29
--S 30 of 59
@@ -17394,7 +17449,7 @@ t9:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 30
--S 31 of 59
@@ -17410,7 +17465,7 @@ setsubMatrix!(t9,2,2,matrix [[3,3],[3,3]])
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 31
--S 32 of 59
@@ -17426,7 +17481,7 @@ t0:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 32
--S 33 of 59
@@ -17442,7 +17497,7 @@ t0+t0
--R |2 8 32 128 512 |
--R | |
--R +2 10 50 250 1250+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 33
--S 34 of 59
@@ -17458,7 +17513,7 @@ t0-t0
--R |0 0 0 0 0|
--R | |
--R +0 0 0 0 0+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 34
--S 35 of 59
@@ -17474,7 +17529,7 @@ t0-t0
--R |- 1 - 4 - 16 - 64 - 256|
--R | |
--R +- 1 - 5 - 25 - 125 - 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 35
--S 36 of 59
@@ -17490,7 +17545,7 @@ t0*t0
--R |341 1593 7585 36561 177745|
--R | |
--R +781 3711 17871 86841 424731+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 36
--S 37 of 59
@@ -17516,7 +17571,7 @@ t0*t0
--R |1 5 25 125 625|
--R |- - -- --- ---|
--R +3 3 3 3 3 +
---R Type: Matrix Fraction Integer
+--R Type: Matrix(Fraction(Integer))
--E 37
--S 38 of 59
@@ -17532,7 +17587,7 @@ m:=matrix [[j**i for i in 0..4] for j in 1..5]
--R |1 4 16 64 256|
--R | |
--R +1 5 25 125 625+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 38
--S 39 of 59
@@ -17558,7 +17613,7 @@ t0*1/3
--R |1 5 25 125 625|
--R |- - -- --- ---|
--R +3 3 3 3 3 +
---R Type: Matrix Fraction Integer
+--R Type: Matrix(Fraction(Integer))
--E 39
--S 40 of 59
@@ -17574,7 +17629,7 @@ t0*1/3
--R |3 12 48 192 768 |
--R | |
--R +3 15 75 375 1875+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 40
--S 41 of 59
@@ -17590,7 +17645,7 @@ c:=coerce([1,2,3,4,5])@Matrix(INT)
--R |4|
--R | |
--R +5+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 41
--S 42 of 59
@@ -17606,7 +17661,7 @@ t0*c
--R |1593|
--R | |
--R +3711+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 42
--S 43 of 59
@@ -17614,7 +17669,7 @@ r:=transpose([1,2,3,4,5])@Matrix(INT)
--R
--R
--R (43) [1 2 3 4 5]
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 43
--S 44 of 59
@@ -17622,7 +17677,7 @@ r*t0
--R
--R
--R (44) [15 55 225 979 4425]
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 44
--S 45 of 59
@@ -17638,7 +17693,7 @@ t0**3
--R |223825 1061251 5103579 24775909 121090455|
--R | |
--R +533935 2532835 12184195 59162185 289195879+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 45
--S 46 of 59
@@ -17654,7 +17709,7 @@ t10:=matrix [[2**i for i in 2..4] for j in 1..5]
--R |4 8 16|
--R | |
--R +4 8 16+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 46
--S 47 of 59
@@ -17670,7 +17725,7 @@ exquo(t10,2)
--R |2 4 8|
--R | |
--R +2 4 8+
---R Type: Union(Matrix Integer,...)
+--R Type: Union(Matrix(Integer),...)
--E 47
--S 48 of 59
@@ -17686,7 +17741,7 @@ t10/4
--R |1 2 4|
--R | |
--R +1 2 4+
---R Type: Matrix Fraction Integer
+--R Type: Matrix(Fraction(Integer))
--E 48
--S 49 of 59
@@ -17702,7 +17757,7 @@ rowEchelon matrix [[j**i for i in 0..4] for j in 1..5]
--R |0 0 0 6 12|
--R | |
--R +0 0 0 0 24+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 49
--S 50 of 59
@@ -17710,7 +17765,7 @@ columnSpace matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]]
--R
--R
--R (50) [[1,4,7,1],[2,5,8,1]]
---R Type: List Vector Integer
+--R Type: List(Vector(Integer))
--E 50
--S 51 of 59
@@ -17734,7 +17789,7 @@ nullSpace matrix [[1,2,3],[4,5,6],[7,8,9]]
--R
--R
--R (53) [[1,- 2,1]]
---R Type: List Vector Integer
+--R Type: List(Vector(Integer))
--E 53
--S 54 of 59
@@ -17782,7 +17837,7 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5]
--R | 1 1 1 1 1 |
--R | -- - - - - - -- |
--R + 24 6 4 6 24 +
---R Type: Union(Matrix Fraction Integer,...)
+--R Type: Union(Matrix(Fraction(Integer)),...)
--E 57
--S 58 of 59
@@ -17798,13 +17853,13 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5]
--R |341 1593 7585 36561 177745|
--R | |
--R +781 3711 17871 86841 424731+
---R Type: Matrix Integer
+--R Type: Matrix(Integer)
--E 58
--S 59 of 59
)show MatrixCategory
--R
---R MatrixCategory(R: Ring,Row: FiniteLinearAggregate t#1,Col: FiniteLinearAggregate t#1) is a category constructor
+--R MatrixCategory(R: Ring,Row: FiniteLinearAggregate(t#1),Col: FiniteLinearAggregate(t#1)) is a category constructor
--R Abbreviation for MatrixCategory is MATCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MATCAT
@@ -17817,17 +17872,17 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5]
--R ?-? : (%,%) -> % antisymmetric? : % -> Boolean
--R coerce : Col -> % column : (%,Integer) -> Col
--R copy : % -> % diagonal? : % -> Boolean
---R diagonalMatrix : List % -> % diagonalMatrix : List R -> %
+--R diagonalMatrix : List(%) -> % diagonalMatrix : List(R) -> %
--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean fill! : (%,R) -> %
---R horizConcat : (%,%) -> % listOfLists : % -> List List R
+--R horizConcat : (%,%) -> % listOfLists : % -> List(List(R))
--R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> %
--R map : ((R -> R),%) -> % map! : ((R -> R),%) -> %
---R matrix : List List R -> % maxColIndex : % -> Integer
+--R matrix : List(List(R)) -> % maxColIndex : % -> Integer
--R maxRowIndex : % -> Integer minColIndex : % -> Integer
--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger
---R nrows : % -> NonNegativeInteger parts : % -> List R
+--R nrows : % -> NonNegativeInteger parts : % -> List(R)
--R qelt : (%,Integer,Integer) -> R row : (%,Integer) -> Row
--R sample : () -> % setRow! : (%,Integer,Row) -> %
--R square? : % -> Boolean squareTop : % -> %
@@ -17840,15 +17895,15 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5]
--R ?=? : (%,%) -> Boolean if R has SETCAT
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if R has SETCAT
---R columnSpace : % -> List Col if R has EUCDOM
+--R columnSpace : % -> List(Col) if R has EUCDOM
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R determinant : % -> R if R has commutative *
---R elt : (%,List Integer,List Integer) -> %
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+--R determinant : % -> R if R has commutative(*)
+--R elt : (%,List(Integer),List(Integer)) -> %
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R hash : % -> SingleInteger if R has SETCAT
@@ -17856,11 +17911,11 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5]
--R latex : % -> String if R has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
---R minordet : % -> R if R has commutative *
+--R members : % -> List(R) if $ has finiteAggregate
+--R minordet : % -> R if R has commutative(*)
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,NonNegativeInteger,R) -> %
---R nullSpace : % -> List Col if R has INTDOM
+--R nullSpace : % -> List(Col) if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
--R pfaffian : % -> R if R has COMRING
--R qsetelt! : (%,Integer,Integer,R) -> R
@@ -17868,7 +17923,7 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5]
--R rowEchelon : % -> % if R has EUCDOM
--R scalarMatrix : (NonNegativeInteger,R) -> %
--R setColumn! : (%,Integer,Col) -> %
---R setelt : (%,List Integer,List Integer,%) -> %
+--R setelt : (%,List(Integer),List(Integer),%) -> %
--R setelt : (%,Integer,Integer,R) -> R
--R setsubMatrix! : (%,Integer,Integer,%) -> %
--R size? : (%,NonNegativeInteger) -> Boolean
@@ -19574,32 +19629,33 @@ digraph pic {
--S 1 of 1
)show PolynomialSetCategory
+--R
--R PolynomialSetCategory(R: Ring,E: OrderedAbelianMonoidSup,VarSet: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for PolynomialSetCategory is PSETCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PSETCAT
--R
--R------------------------------- Operations --------------------------------
---R ?=? : (%,%) -> Boolean coerce : % -> List P
+--R ?=? : (%,%) -> Boolean coerce : % -> List(P)
--R coerce : % -> OutputForm collect : (%,VarSet) -> %
--R collectUnder : (%,VarSet) -> % collectUpper : (%,VarSet) -> %
---R construct : List P -> % copy : % -> %
+--R construct : List(P) -> % copy : % -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean hash : % -> SingleInteger
---R latex : % -> String mainVariables : % -> List VarSet
+--R latex : % -> String mainVariables : % -> List(VarSet)
--R map : ((P -> P),%) -> % mvar : % -> VarSet
---R retract : List P -> % sample : () -> %
---R trivialIdeal? : % -> Boolean variables : % -> List VarSet
+--R retract : List(P) -> % sample : () -> %
+--R trivialIdeal? : % -> Boolean variables : % -> List(VarSet)
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R convert : % -> InputForm if P has KONVERT INFORM
+--R convert : % -> InputForm if P has KONVERT(INFORM)
--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT
+--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT
--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((P -> Boolean),%) -> Union(P,"failed")
--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM
@@ -19607,9 +19663,9 @@ digraph pic {
--R mainVariable? : (VarSet,%) -> Boolean
--R map! : ((P -> P),%) -> % if $ has shallowlyMutable
--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate
---R members : % -> List P if $ has finiteAggregate
+--R members : % -> List(P) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List P if $ has finiteAggregate
+--R parts : % -> List(P) if $ has finiteAggregate
--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P,P) -> P if P has SETCAT and $ has finiteAggregate
@@ -19617,9 +19673,9 @@ digraph pic {
--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate
---R retractIfCan : List P -> Union(%,"failed")
---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM
+--R retractIfCan : List(P) -> Union(%,"failed")
+--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM
--R roughBase? : % -> Boolean if R has INTDOM
--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM
--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM
@@ -20257,13 +20313,14 @@ digraph pic {
--S 1 of 1
)show PriorityQueueAggregate
---R PriorityQueueAggregate S: OrderedSet is a category constructor
+--R
+--R PriorityQueueAggregate(S: OrderedSet) is a category constructor
--R Abbreviation for PriorityQueueAggregate is PRQAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PRQAGG
--R
--R------------------------------- Operations --------------------------------
---R bag : List S -> % copy : % -> %
+--R bag : List(S) -> % copy : % -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean extract! : % -> S
--R insert! : (S,%) -> % inspect : % -> S
@@ -20276,19 +20333,19 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
@@ -20493,13 +20550,14 @@ digraph pic {
--S 1 of 1
)show QueueAggregate
---R QueueAggregate S: Type is a category constructor
+--R
+--R QueueAggregate(S: Type) is a category constructor
--R Abbreviation for QueueAggregate is QUAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for QUAGG
--R
--R------------------------------- Operations --------------------------------
---R back : % -> S bag : List S -> %
+--R back : % -> S bag : List(S) -> %
--R copy : % -> % dequeue! : % -> S
--R empty : () -> % empty? : % -> Boolean
--R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean
@@ -20513,19 +20571,19 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
@@ -20743,41 +20801,42 @@ digraph pic {
--S 1 of 1
)show SetAggregate
---R SetAggregate S: SetCategory is a category constructor
+--R
+--R SetAggregate(S: SetCategory) is a category constructor
--R Abbreviation for SetAggregate is SETAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SETAGG
--R
--R------------------------------- Operations --------------------------------
--R ? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
---R brace : List S -> % brace : () -> %
---R coerce : % -> OutputForm construct : List S -> %
+--R brace : List(S) -> % brace : () -> %
+--R coerce : % -> OutputForm construct : List(S) -> %
--R copy : % -> % difference : (%,S) -> %
--R difference : (%,%) -> % empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R hash : % -> SingleInteger intersect : (%,%) -> %
--R latex : % -> String map : ((S -> S),%) -> %
---R sample : () -> % set : List S -> %
+--R sample : () -> % set : List(S) -> %
--R set : () -> % subset? : (%,%) -> Boolean
--R union : (S,%) -> % union : (%,S) -> %
--R union : (%,%) -> % ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
@@ -21102,13 +21161,14 @@ digraph pic {
--S 1 of 1
)show StackAggregate
---R StackAggregate S: Type is a category constructor
+--R
+--R StackAggregate(S: Type) is a category constructor
--R Abbreviation for StackAggregate is SKAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SKAGG
--R
--R------------------------------- Operations --------------------------------
---R bag : List S -> % copy : % -> %
+--R bag : List(S) -> % copy : % -> %
--R depth : % -> NonNegativeInteger empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R extract! : % -> S insert! : (S,%) -> %
@@ -21121,19 +21181,19 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
@@ -21354,13 +21414,14 @@ digraph pic {
--S 1 of 1
)show UnaryRecursiveAggregate
---R UnaryRecursiveAggregate S: Type is a category constructor
+--R
+--R UnaryRecursiveAggregate(S: Type) is a category constructor
--R Abbreviation for UnaryRecursiveAggregate is URAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for URAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % concat : (S,%) -> %
+--R children : % -> List(%) concat : (S,%) -> %
--R concat : (%,%) -> % copy : % -> %
--R cycleEntry : % -> % cycleTail : % -> %
--R cyclic? : % -> Boolean distance : (%,%) -> Integer
@@ -21369,8 +21430,8 @@ digraph pic {
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean first : % -> S
--R last : % -> S leaf? : % -> Boolean
---R leaves : % -> List S map : ((S -> S),%) -> %
---R nodes : % -> List % rest : % -> %
+--R leaves : % -> List(S) map : ((S -> S),%) -> %
+--R nodes : % -> List(%) rest : % -> %
--R sample : () -> % second : % -> S
--R tail : % -> % third : % -> S
--R value : % -> S
@@ -21385,10 +21446,10 @@ digraph pic {
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R cycleLength : % -> NonNegativeInteger
--R cycleSplit! : % -> % if $ has shallowlyMutable
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R first : (%,NonNegativeInteger) -> %
--R hash : % -> SingleInteger if S has SETCAT
@@ -21397,12 +21458,12 @@ digraph pic {
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R rest : (%,NonNegativeInteger) -> %
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,last,S) -> S if $ has shallowlyMutable
--R setelt : (%,rest,%) -> % if $ has shallowlyMutable
--R setelt : (%,first,S) -> S if $ has shallowlyMutable
@@ -22101,20 +22162,21 @@ digraph pic {
--S 1 of 1
)show BinaryTreeCategory
---R BinaryTreeCategory S: SetCategory is a category constructor
+--R
+--R BinaryTreeCategory(S: SetCategory) is a category constructor
--R Abbreviation for BinaryTreeCategory is BTCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for BTCAT
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % copy : % -> %
+--R children : % -> List(%) copy : % -> %
--R cyclic? : % -> Boolean distance : (%,%) -> Integer
--R ?.right : (%,right) -> % ?.left : (%,left) -> %
--R ?.value : (%,value) -> S empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R leaf? : % -> Boolean leaves : % -> List S
+--R leaf? : % -> Boolean leaves : % -> List(S)
--R left : % -> % map : ((S -> S),%) -> %
---R node : (%,S,%) -> % nodes : % -> List %
+--R node : (%,S,%) -> % nodes : % -> List(%)
--R right : % -> % sample : () -> %
--R value : % -> S
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
@@ -22124,21 +22186,21 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R parts : % -> List(S) if $ has finiteAggregate
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,right,%) -> % if $ has shallowlyMutable
--R setelt : (%,left,%) -> % if $ has shallowlyMutable
--R setelt : (%,value,S) -> S if $ has shallowlyMutable
@@ -22401,14 +22463,15 @@ digraph pic {
--S 1 of 1
)show Dictionary
---R Dictionary S: SetCategory is a category constructor
+--R
+--R Dictionary(S: SetCategory) is a category constructor
--R Abbreviation for Dictionary is DIAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIAGG
--R
--R------------------------------- Operations --------------------------------
---R bag : List S -> % construct : List S -> %
---R copy : % -> % dictionary : List S -> %
+--R bag : List(S) -> % construct : List(S) -> %
+--R copy : % -> % dictionary : List(S) -> %
--R dictionary : () -> % empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R extract! : % -> S insert! : (S,%) -> %
@@ -22418,13 +22481,13 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R hash : % -> SingleInteger if S has SETCAT
@@ -22432,9 +22495,9 @@ digraph pic {
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
@@ -22702,15 +22765,16 @@ digraph pic {
--S 1 of 1
)show DequeueAggregate
---R DequeueAggregate S: Type is a category constructor
+--R
+--R DequeueAggregate(S: Type) is a category constructor
--R Abbreviation for DequeueAggregate is DQAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DQAGG
--R
--R------------------------------- Operations --------------------------------
---R back : % -> S bag : List S -> %
+--R back : % -> S bag : List(S) -> %
--R bottom! : % -> S copy : % -> %
---R depth : % -> NonNegativeInteger dequeue : List S -> %
+--R depth : % -> NonNegativeInteger dequeue : List(S) -> %
--R dequeue : () -> % dequeue! : % -> S
--R empty : () -> % empty? : % -> Boolean
--R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean
@@ -22729,19 +22793,19 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R hash : % -> SingleInteger if S has SETCAT
--R latex : % -> String if S has SETCAT
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R ?~=? : (%,%) -> Boolean if S has SETCAT
--R
@@ -23005,21 +23069,22 @@ digraph pic {
--S 1 of 1
)show ExtensibleLinearAggregate
---R ExtensibleLinearAggregate S: Type is a category constructor
+--R
+--R ExtensibleLinearAggregate(S: Type) is a category constructor
--R Abbreviation for ExtensibleLinearAggregate is ELAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ELAGG
--R
--R------------------------------- Operations --------------------------------
---R concat : List % -> % concat : (%,%) -> %
+--R concat : List(%) -> % concat : (%,%) -> %
--R concat : (S,%) -> % concat : (%,S) -> %
--R concat! : (%,%) -> % concat! : (%,S) -> %
---R construct : List S -> % copy : % -> %
+--R construct : List(S) -> % copy : % -> %
--R delete : (%,Integer) -> % delete! : (%,Integer) -> %
--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List S eq? : (%,%) -> Boolean
---R index? : (Integer,%) -> Boolean indices : % -> List Integer
+--R entries : % -> List(S) eq? : (%,%) -> Boolean
+--R index? : (Integer,%) -> Boolean indices : % -> List(Integer)
--R insert : (%,%,Integer) -> % insert : (S,%,Integer) -> %
--R insert! : (%,%,Integer) -> % insert! : (S,%,Integer) -> %
--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> %
@@ -23029,17 +23094,17 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
---R delete! : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R delete! : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -23050,12 +23115,12 @@ digraph pic {
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R merge! : (%,%) -> % if S has ORDSET
--R merge! : (((S,S) -> Boolean),%,%) -> %
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
@@ -23068,7 +23133,7 @@ digraph pic {
--R removeDuplicates! : % -> % if S has SETCAT
--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate
--R select! : ((S -> Boolean),%) -> %
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
@@ -23396,20 +23461,21 @@ digraph pic {
--S 1 of 1
)show FiniteLinearAggregate
---R FiniteLinearAggregate S: Type is a category constructor
+--R
+--R FiniteLinearAggregate(S: Type) is a category constructor
--R Abbreviation for FiniteLinearAggregate is FLAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FLAGG
--R
--R------------------------------- Operations --------------------------------
---R concat : List % -> % concat : (%,%) -> %
+--R concat : List(%) -> % concat : (%,%) -> %
--R concat : (S,%) -> % concat : (%,S) -> %
---R construct : List S -> % copy : % -> %
+--R construct : List(S) -> % copy : % -> %
--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S
--R elt : (%,Integer,S) -> S empty : () -> %
---R empty? : % -> Boolean entries : % -> List S
+--R empty? : % -> Boolean entries : % -> List(S)
--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (%,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (%,%,Integer) -> %
--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> %
--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> %
--R qelt : (%,Integer) -> S reverse : % -> %
@@ -23422,17 +23488,17 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if S has ORDSET
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -23444,13 +23510,13 @@ digraph pic {
--R max : (%,%) -> % if S has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R merge : (%,%) -> % if S has ORDSET
--R merge : (((S,S) -> Boolean),%,%) -> %
--R min : (%,%) -> % if S has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R position : (S,%,Integer) -> Integer if S has SETCAT
--R position : (S,%) -> Integer if S has SETCAT
--R position : ((S -> Boolean),%) -> Integer
@@ -23463,7 +23529,7 @@ digraph pic {
--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate
--R reverse! : % -> % if $ has shallowlyMutable
--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : % -> % if S has ORDSET
@@ -23848,6 +23914,7 @@ digraph pic {
--S 1 of 1
)show FreeAbelianMonoidCategory
+--R
--R FreeAbelianMonoidCategory(S: SetCategory,E: CancellationAbelianMonoid) is a category constructor
--R Abbreviation for FreeAbelianMonoidCategory is FAMONC
--R This constructor is exposed in this frame.
@@ -23868,7 +23935,7 @@ digraph pic {
--R highCommonTerms : (%,%) -> % if E has OAMON
--R retractIfCan : % -> Union(S,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R terms : % -> List Record(gen: S,exp: E)
+--R terms : % -> List(Record(gen: S,exp: E))
--R
--E 1
@@ -24081,14 +24148,15 @@ digraph pic {
--S 1 of 1
)show MultiDictionary
---R MultiDictionary S: SetCategory is a category constructor
+--R
+--R MultiDictionary(S: SetCategory) is a category constructor
--R Abbreviation for MultiDictionary is MDAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MDAGG
--R
--R------------------------------- Operations --------------------------------
---R bag : List S -> % construct : List S -> %
---R copy : % -> % dictionary : List S -> %
+--R bag : List(S) -> % construct : List(S) -> %
+--R copy : % -> % dictionary : List(S) -> %
--R dictionary : () -> % empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R extract! : % -> S insert! : (S,%) -> %
@@ -24098,14 +24166,14 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if S has SETCAT
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R duplicates : % -> List Record(entry: S,count: NonNegativeInteger)
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R duplicates : % -> List(Record(entry: S,count: NonNegativeInteger))
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R hash : % -> SingleInteger if S has SETCAT
@@ -24114,9 +24182,9 @@ digraph pic {
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
@@ -24514,7 +24582,8 @@ digraph pic {
--S 1 of 1
)show PermutationCategory
---R PermutationCategory S: SetCategory is a category constructor
+--R
+--R PermutationCategory(S: SetCategory) is a category constructor
--R Abbreviation for PermutationCategory is PERMCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PERMCAT
@@ -24526,11 +24595,11 @@ digraph pic {
--R 1 : () -> % ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm
--R commutator : (%,%) -> % conjugate : (%,%) -> %
---R cycle : List S -> % cycles : List List S -> %
+--R cycle : List(S) -> % cycles : List(List(S)) -> %
--R ?.? : (%,S) -> S eval : (%,S) -> S
--R hash : % -> SingleInteger inv : % -> %
--R latex : % -> String one? : % -> Boolean
---R orbit : (%,S) -> Set S recip : % -> Union(%,"failed")
+--R orbit : (%,S) -> Set(S) recip : % -> Union(%,"failed")
--R sample : () -> % ?~=? : (%,%) -> Boolean
--R ?**? : (%,NonNegativeInteger) -> %
--R ?<=? : (%,%) -> Boolean if S has ORDSET or S has FINITE
@@ -24762,15 +24831,16 @@ digraph pic {
--S 1 of 1
)show StreamAggregate
---R StreamAggregate S: Type is a category constructor
+--R
+--R StreamAggregate(S: Type) is a category constructor
--R Abbreviation for StreamAggregate is STAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for STAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % concat : (%,S) -> %
---R concat : List % -> % concat : (S,%) -> %
---R concat : (%,%) -> % construct : List S -> %
+--R children : % -> List(%) concat : (%,S) -> %
+--R concat : List(%) -> % concat : (S,%) -> %
+--R concat : (%,%) -> % construct : List(S) -> %
--R copy : % -> % cycleEntry : % -> %
--R cycleTail : % -> % cyclic? : % -> Boolean
--R delete : (%,Integer) -> % distance : (%,%) -> Integer
@@ -24778,14 +24848,14 @@ digraph pic {
--R ?.last : (%,last) -> S ?.rest : (%,rest) -> %
--R ?.first : (%,first) -> S ?.value : (%,value) -> S
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List S eq? : (%,%) -> Boolean
+--R entries : % -> List(S) eq? : (%,%) -> Boolean
--R explicitlyFinite? : % -> Boolean first : % -> S
---R index? : (Integer,%) -> Boolean indices : % -> List Integer
+--R index? : (Integer,%) -> Boolean indices : % -> List(Integer)
--R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> %
--R last : % -> S leaf? : % -> Boolean
---R leaves : % -> List S map : (((S,S) -> S),%,%) -> %
+--R leaves : % -> List(S) map : (((S,S) -> S),%,%) -> %
--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> %
---R nodes : % -> List % possiblyInfinite? : % -> Boolean
+--R nodes : % -> List(%) possiblyInfinite? : % -> Boolean
--R qelt : (%,Integer) -> S rest : % -> %
--R sample : () -> % second : % -> S
--R tail : % -> % third : % -> S
@@ -24797,18 +24867,18 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R concat! : (%,S) -> % if $ has shallowlyMutable
--R concat! : (%,%) -> % if $ has shallowlyMutable
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R cycleLength : % -> NonNegativeInteger
--R cycleSplit! : % -> % if $ has shallowlyMutable
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -24820,11 +24890,11 @@ digraph pic {
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
@@ -24834,9 +24904,9 @@ digraph pic {
--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate
--R rest : (%,NonNegativeInteger) -> %
--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,last,S) -> S if $ has shallowlyMutable
--R setelt : (%,rest,%) -> % if $ has shallowlyMutable
--R setelt : (%,first,S) -> S if $ has shallowlyMutable
@@ -25272,6 +25342,7 @@ digraph pic {
--S 1 of 1
)show TriangularSetCategory
+--R
--R TriangularSetCategory(R: IntegralDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for TriangularSetCategory is TSETCAT
--R This constructor is exposed in this frame.
@@ -25279,10 +25350,10 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean
---R algebraicVariables : % -> List V coerce : % -> List P
+--R algebraicVariables : % -> List(V) coerce : % -> List(P)
--R coerce : % -> OutputForm collect : (%,V) -> %
--R collectQuasiMonic : % -> % collectUnder : (%,V) -> %
---R collectUpper : (%,V) -> % construct : List P -> %
+--R collectUpper : (%,V) -> % construct : List(P) -> %
--R copy : % -> % degree : % -> NonNegativeInteger
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean extend : (%,P) -> %
@@ -25290,29 +25361,29 @@ digraph pic {
--R headReduce : (P,%) -> P headReduced? : % -> Boolean
--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean
--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean
---R initials : % -> List P last : % -> Union(P,"failed")
+--R initials : % -> List(P) last : % -> Union(P,"failed")
--R latex : % -> String mainVariable? : (V,%) -> Boolean
---R mainVariables : % -> List V map : ((P -> P),%) -> %
+--R mainVariables : % -> List(V) map : ((P -> P),%) -> %
--R mvar : % -> V normalized? : % -> Boolean
--R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P
--R removeZero : (P,%) -> P rest : % -> Union(%,"failed")
---R retract : List P -> % sample : () -> %
+--R retract : List(P) -> % sample : () -> %
--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean
---R trivialIdeal? : % -> Boolean variables : % -> List V
---R zeroSetSplit : List P -> List % ?~=? : (%,%) -> Boolean
+--R trivialIdeal? : % -> Boolean variables : % -> List(V)
+--R zeroSetSplit : List(P) -> List(%) ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean
---R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
---R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
+--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean
+--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
+--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
--R coHeight : % -> NonNegativeInteger if V has FINITE
---R convert : % -> InputForm if P has KONVERT INFORM
+--R convert : % -> InputForm if P has KONVERT(INFORM)
--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT
+--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT
--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
--R extendIfCan : (%,P) -> Union(%,"failed")
--R find : ((P -> Boolean),%) -> Union(P,"failed")
@@ -25321,10 +25392,10 @@ digraph pic {
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((P -> P),%) -> % if $ has shallowlyMutable
--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate
---R members : % -> List P if $ has finiteAggregate
+--R members : % -> List(P) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List P if $ has finiteAggregate
---R quasiComponent : % -> Record(close: List P,open: List P)
+--R parts : % -> List(P) if $ has finiteAggregate
+--R quasiComponent : % -> Record(close: List(P),open: List(P))
--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P
--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate
@@ -25334,10 +25405,10 @@ digraph pic {
--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate
---R retractIfCan : List P -> Union(%,"failed")
---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P
+--R retractIfCan : List(P) -> Union(%,"failed")
+--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P)
--R roughBase? : % -> Boolean if R has INTDOM
--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM
--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM
@@ -25348,7 +25419,7 @@ digraph pic {
--R sort : (%,V) -> Record(under: %,floor: %,upper: %)
--R stronglyReduced? : (P,%) -> Boolean
--R triangular? : % -> Boolean if R has INTDOM
---R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P)
+--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P)))
--R
--E 1
@@ -26188,7 +26259,8 @@ digraph pic {
--S 1 of 1
)show FiniteDivisorCategory
---R FiniteDivisorCategory(F: Field,UP: UnivariatePolynomialCategory t#1,UPUP: UnivariatePolynomialCategory Fraction t#2,R: FunctionFieldCategory(t#1,t#2,t#3)) is a category constructor
+--R
+--R FiniteDivisorCategory(F: Field,UP: UnivariatePolynomialCategory(t#1),UPUP: UnivariatePolynomialCategory(Fraction(t#2)),R: FunctionFieldCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for FiniteDivisorCategory is FDIVCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FDIVCAT
@@ -26205,10 +26277,10 @@ digraph pic {
--R sample : () -> % zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
---R decompose : % -> Record(id: FractionalIdeal(UP,Fraction UP,UPUP,R),principalPart: R)
---R divisor : FractionalIdeal(UP,Fraction UP,UPUP,R) -> %
+--R decompose : % -> Record(id: FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart: R)
+--R divisor : FractionalIdeal(UP,Fraction(UP),UPUP,R) -> %
--R generator : % -> Union(R,"failed")
---R ideal : % -> FractionalIdeal(UP,Fraction UP,UPUP,R)
+--R ideal : % -> FractionalIdeal(UP,Fraction(UP),UPUP,R)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 1
@@ -26410,17 +26482,18 @@ digraph pic {
--S 1 of 1
)show FiniteSetAggregate
---R FiniteSetAggregate S: SetCategory is a category constructor
+--R
+--R FiniteSetAggregate(S: SetCategory) is a category constructor
--R Abbreviation for FiniteSetAggregate is FSAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FSAGG
--R
--R------------------------------- Operations --------------------------------
--R ? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
---R bag : List S -> % brace : () -> %
---R brace : List S -> % coerce : % -> OutputForm
---R construct : List S -> % copy : % -> %
---R dictionary : List S -> % dictionary : () -> %
+--R bag : List(S) -> % brace : () -> %
+--R brace : List(S) -> % coerce : % -> OutputForm
+--R construct : List(S) -> % copy : % -> %
+--R dictionary : List(S) -> % dictionary : () -> %
--R difference : (%,%) -> % difference : (%,S) -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean extract! : % -> S
@@ -26429,20 +26502,20 @@ digraph pic {
--R latex : % -> String map : ((S -> S),%) -> %
--R max : % -> S if S has ORDSET min : % -> S if S has ORDSET
--R sample : () -> % set : () -> %
---R set : List S -> % subset? : (%,%) -> Boolean
+--R set : List(S) -> % subset? : (%,%) -> Boolean
--R union : (%,%) -> % union : (%,S) -> %
--R union : (S,%) -> % ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R cardinality : % -> NonNegativeInteger
--R complement : % -> % if S has FINITE
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R index : PositiveInteger -> % if S has FINITE
@@ -26450,9 +26523,9 @@ digraph pic {
--R lookup : % -> PositiveInteger if S has FINITE
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R random : () -> % if S has FINITE
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
@@ -26822,6 +26895,7 @@ digraph pic {
--S 1 of 1
)show KeyedDictionary
+--R
--R KeyedDictionary(Key: SetCategory,Entry: SetCategory) is a category constructor
--R Abbreviation for KeyedDictionary is KDAGG
--R This constructor is exposed in this frame.
@@ -26831,21 +26905,21 @@ digraph pic {
--R copy : % -> % dictionary : () -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean key? : (Key,%) -> Boolean
---R keys : % -> List Key sample : () -> %
+--R keys : % -> List(Key) sample : () -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT
--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
---R bag : List Record(key: Key,entry: Entry) -> %
+--R bag : List(Record(key: Key,entry: Entry)) -> %
--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT
---R construct : List Record(key: Key,entry: Entry) -> %
---R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM
+--R construct : List(Record(key: Key,entry: Entry)) -> %
+--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM)
--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R dictionary : List Record(key: Key,entry: Entry) -> %
---R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
+--R dictionary : List(Record(key: Key,entry: Entry)) -> %
+--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
--R extract! : % -> Record(key: Key,entry: Entry)
--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed")
@@ -26857,9 +26931,9 @@ digraph pic {
--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> %
--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable
--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
---R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
+--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
+--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate
--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate
--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
@@ -27143,33 +27217,34 @@ digraph pic {
--S 1 of 1
)show LazyStreamAggregate
---R LazyStreamAggregate S: Type is a category constructor
+--R
+--R LazyStreamAggregate(S: Type) is a category constructor
--R Abbreviation for LazyStreamAggregate is LZSTAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LZSTAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % complete : % -> %
---R concat : (%,S) -> % concat : List % -> %
+--R children : % -> List(%) complete : % -> %
+--R concat : (%,S) -> % concat : List(%) -> %
--R concat : (S,%) -> % concat : (%,%) -> %
---R construct : List S -> % copy : % -> %
+--R construct : List(S) -> % copy : % -> %
--R cycleEntry : % -> % cycleTail : % -> %
--R cyclic? : % -> Boolean delete : (%,Integer) -> %
--R distance : (%,%) -> Integer elt : (%,Integer,S) -> S
--R ?.? : (%,Integer) -> S ?.last : (%,last) -> S
--R ?.rest : (%,rest) -> % ?.first : (%,first) -> S
--R ?.value : (%,value) -> S empty : () -> %
---R empty? : % -> Boolean entries : % -> List S
+--R empty? : % -> Boolean entries : % -> List(S)
--R eq? : (%,%) -> Boolean explicitEntries? : % -> Boolean
--R explicitlyEmpty? : % -> Boolean explicitlyFinite? : % -> Boolean
--R extend : (%,Integer) -> % first : % -> S
--R frst : % -> S index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (S,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (S,%,Integer) -> %
--R insert : (%,%,Integer) -> % last : % -> S
--R lazy? : % -> Boolean lazyEvaluate : % -> %
---R leaf? : % -> Boolean leaves : % -> List S
+--R leaf? : % -> Boolean leaves : % -> List(S)
--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> %
---R new : (NonNegativeInteger,S) -> % nodes : % -> List %
+--R new : (NonNegativeInteger,S) -> % nodes : % -> List(%)
--R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S
--R remove : ((S -> Boolean),%) -> % rest : % -> %
--R rst : % -> % sample : () -> %
@@ -27183,18 +27258,18 @@ digraph pic {
--R coerce : % -> OutputForm if S has SETCAT
--R concat! : (%,S) -> % if $ has shallowlyMutable
--R concat! : (%,%) -> % if $ has shallowlyMutable
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R cycleLength : % -> NonNegativeInteger
--R cycleSplit! : % -> % if $ has shallowlyMutable
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -27206,12 +27281,12 @@ digraph pic {
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
--R numberOfComputedEntries : % -> NonNegativeInteger
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
@@ -27219,9 +27294,9 @@ digraph pic {
--R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate
--R rest : (%,NonNegativeInteger) -> %
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,last,S) -> S if $ has shallowlyMutable
--R setelt : (%,rest,%) -> % if $ has shallowlyMutable
--R setelt : (%,first,S) -> S if $ has shallowlyMutable
@@ -28081,7 +28156,8 @@ digraph pic {
--S 1 of 1
)show LeftModule
---R LeftModule R: Rng is a category constructor
+--R
+--R LeftModule(R: Rng) is a category constructor
--R Abbreviation for LeftModule is LMODULE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LMODULE
@@ -28245,16 +28321,17 @@ digraph pic {
--S 1 of 1
)show ListAggregate
---R ListAggregate S: Type is a category constructor
+--R
+--R ListAggregate(S: Type) is a category constructor
--R Abbreviation for ListAggregate is LSAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LSAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % concat : (%,S) -> %
---R concat : List % -> % concat : (S,%) -> %
+--R children : % -> List(%) concat : (%,S) -> %
+--R concat : List(%) -> % concat : (S,%) -> %
--R concat : (%,%) -> % concat! : (%,S) -> %
---R concat! : (%,%) -> % construct : List S -> %
+--R concat! : (%,%) -> % construct : List(S) -> %
--R copy : % -> % cycleEntry : % -> %
--R cycleTail : % -> % cyclic? : % -> Boolean
--R delete : (%,Integer) -> % delete! : (%,Integer) -> %
@@ -28262,16 +28339,16 @@ digraph pic {
--R ?.? : (%,Integer) -> S ?.last : (%,last) -> S
--R ?.rest : (%,rest) -> % ?.first : (%,first) -> S
--R ?.value : (%,value) -> S empty : () -> %
---R empty? : % -> Boolean entries : % -> List S
+--R empty? : % -> Boolean entries : % -> List(S)
--R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean
--R first : % -> S index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (S,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (S,%,Integer) -> %
--R insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> %
--R insert! : (%,%,Integer) -> % last : % -> S
---R leaf? : % -> Boolean leaves : % -> List S
+--R leaf? : % -> Boolean leaves : % -> List(S)
--R list : S -> % map : (((S,S) -> S),%,%) -> %
--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> %
---R nodes : % -> List % possiblyInfinite? : % -> Boolean
+--R nodes : % -> List(%) possiblyInfinite? : % -> Boolean
--R qelt : (%,Integer) -> S rest : % -> %
--R reverse : % -> % sample : () -> %
--R second : % -> S tail : % -> %
@@ -28285,20 +28362,20 @@ digraph pic {
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R child? : (%,%) -> Boolean if S has SETCAT
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R cycleLength : % -> NonNegativeInteger
--R cycleSplit! : % -> % if $ has shallowlyMutable
---R delete : (%,UniversalSegment Integer) -> %
---R delete! : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R delete! : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -28311,7 +28388,7 @@ digraph pic {
--R max : (%,%) -> % if S has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R merge : (((S,S) -> Boolean),%,%) -> %
--R merge : (%,%) -> % if S has ORDSET
--R merge! : (((S,S) -> Boolean),%,%) -> %
@@ -28320,7 +28397,7 @@ digraph pic {
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R node? : (%,%) -> Boolean if S has SETCAT
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R position : ((S -> Boolean),%) -> Integer
--R position : (S,%) -> Integer if S has SETCAT
--R position : (S,%,Integer) -> Integer if S has SETCAT
@@ -28338,9 +28415,9 @@ digraph pic {
--R reverse! : % -> % if $ has shallowlyMutable
--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate
--R select! : ((S -> Boolean),%) -> %
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,last,S) -> S if $ has shallowlyMutable
--R setelt : (%,rest,%) -> % if $ has shallowlyMutable
--R setelt : (%,first,S) -> S if $ has shallowlyMutable
@@ -28961,17 +29038,18 @@ digraph pic {
--S 1 of 1
)show MultisetAggregate
---R MultisetAggregate S: SetCategory is a category constructor
+--R
+--R MultisetAggregate(S: SetCategory) is a category constructor
--R Abbreviation for MultisetAggregate is MSETAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MSETAGG
--R
--R------------------------------- Operations --------------------------------
--R ? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
---R bag : List S -> % brace : () -> %
---R brace : List S -> % coerce : % -> OutputForm
---R construct : List S -> % copy : % -> %
---R dictionary : List S -> % dictionary : () -> %
+--R bag : List(S) -> % brace : () -> %
+--R brace : List(S) -> % coerce : % -> OutputForm
+--R construct : List(S) -> % copy : % -> %
+--R dictionary : List(S) -> % dictionary : () -> %
--R difference : (%,%) -> % difference : (%,S) -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean extract! : % -> S
@@ -28979,29 +29057,29 @@ digraph pic {
--R inspect : % -> S intersect : (%,%) -> %
--R latex : % -> String map : ((S -> S),%) -> %
--R removeDuplicates! : % -> % sample : () -> %
---R set : () -> % set : List S -> %
+--R set : () -> % set : List(S) -> %
--R subset? : (%,%) -> Boolean union : (%,%) -> %
--R union : (%,S) -> % union : (S,%) -> %
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R duplicates : % -> List Record(entry: S,count: NonNegativeInteger)
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R duplicates : % -> List(Record(entry: S,count: NonNegativeInteger))
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R insert! : (S,%,NonNegativeInteger) -> %
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
@@ -29452,20 +29530,21 @@ digraph pic {
--S 1 of 1
)show OneDimensionalArrayAggregate
---R OneDimensionalArrayAggregate S: Type is a category constructor
+--R
+--R OneDimensionalArrayAggregate(S: Type) is a category constructor
--R Abbreviation for OneDimensionalArrayAggregate is A1AGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for A1AGG
--R
--R------------------------------- Operations --------------------------------
---R concat : List % -> % concat : (%,%) -> %
+--R concat : List(%) -> % concat : (%,%) -> %
--R concat : (S,%) -> % concat : (%,S) -> %
---R construct : List S -> % copy : % -> %
+--R construct : List(S) -> % copy : % -> %
--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S
--R elt : (%,Integer,S) -> S empty : () -> %
---R empty? : % -> Boolean entries : % -> List S
+--R empty? : % -> Boolean entries : % -> List(S)
--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (%,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (%,%,Integer) -> %
--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> %
--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> %
--R qelt : (%,Integer) -> S reverse : % -> %
@@ -29478,17 +29557,17 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if S has ORDSET
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if S has SETCAT
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,S) -> % if $ has shallowlyMutable
--R find : ((S -> Boolean),%) -> Union(S,"failed")
@@ -29500,13 +29579,13 @@ digraph pic {
--R max : (%,%) -> % if S has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R merge : (%,%) -> % if S has ORDSET
--R merge : (((S,S) -> Boolean),%,%) -> %
--R min : (%,%) -> % if S has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R position : (S,%,Integer) -> Integer if S has SETCAT
--R position : (S,%) -> Integer if S has SETCAT
--R position : ((S -> Boolean),%) -> Integer
@@ -29519,7 +29598,7 @@ digraph pic {
--R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate
--R reverse! : % -> % if $ has shallowlyMutable
--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable
--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : % -> % if S has ORDSET
@@ -30218,6 +30297,7 @@ digraph pic {
--S 1 of 1
)show RegularTriangularSetCategory
+--R
--R RegularTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for RegularTriangularSetCategory is RSETCAT
--R This constructor is exposed in this frame.
@@ -30225,71 +30305,72 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean
---R algebraicVariables : % -> List V augment : (List P,%) -> List %
---R augment : (P,List %) -> List % augment : (P,%) -> List %
---R coerce : % -> List P coerce : % -> OutputForm
+--R algebraicVariables : % -> List(V) augment : (List(P),%) -> List(%)
+--R augment : (P,List(%)) -> List(%) augment : (P,%) -> List(%)
+--R coerce : % -> List(P) coerce : % -> OutputForm
--R collect : (%,V) -> % collectQuasiMonic : % -> %
--R collectUnder : (%,V) -> % collectUpper : (%,V) -> %
---R construct : List P -> % copy : % -> %
+--R construct : List(P) -> % copy : % -> %
--R degree : % -> NonNegativeInteger empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R extend : (List P,%) -> List % extend : (P,List %) -> List %
---R extend : (P,%) -> List % extend : (%,P) -> %
+--R extend : (List(P),%) -> List(%) extend : (P,List(%)) -> List(%)
+--R extend : (P,%) -> List(%) extend : (%,P) -> %
--R first : % -> Union(P,"failed") hash : % -> SingleInteger
--R headReduce : (P,%) -> P headReduced? : % -> Boolean
--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean
--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean
---R initials : % -> List P internalAugment : (P,%) -> %
---R intersect : (P,List %) -> List % intersect : (List P,%) -> List %
---R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean
---R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed")
+--R initials : % -> List(P) internalAugment : (P,%) -> %
+--R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean
+--R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed")
--R latex : % -> String mainVariable? : (V,%) -> Boolean
---R mainVariables : % -> List V map : ((P -> P),%) -> %
+--R mainVariables : % -> List(V) map : ((P -> P),%) -> %
--R mvar : % -> V normalized? : % -> Boolean
--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean
--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P
---R rest : % -> Union(%,"failed") retract : List P -> %
+--R rest : % -> Union(%,"failed") retract : List(P) -> %
--R sample : () -> % stronglyReduce : (P,%) -> P
--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean
---R variables : % -> List V zeroSetSplit : List P -> List %
+--R variables : % -> List(V) zeroSetSplit : List(P) -> List(%)
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R algebraicCoefficients? : (P,%) -> Boolean
--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R augment : (List P,List %) -> List %
---R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean
---R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
---R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
+--R augment : (List(P),List(%)) -> List(%)
+--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean
+--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
+--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
--R coHeight : % -> NonNegativeInteger if V has FINITE
---R convert : % -> InputForm if P has KONVERT INFORM
+--R convert : % -> InputForm if P has KONVERT(INFORM)
--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT
+--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT
--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R extend : (List P,List %) -> List %
+--R extend : (List(P),List(%)) -> List(%)
--R extendIfCan : (%,P) -> Union(%,"failed")
--R find : ((P -> Boolean),%) -> Union(P,"failed")
--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM
--R initiallyReduced? : (P,%) -> Boolean
---R internalAugment : (List P,%) -> %
---R intersect : (List P,List %) -> List %
---R invertible? : (P,%) -> List Record(val: Boolean,tower: %)
---R invertibleElseSplit? : (P,%) -> Union(Boolean,List %)
---R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %)
---R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %)
+--R internalAugment : (List(P),%) -> %
+--R intersect : (P,List(%)) -> List(%)
+--R intersect : (List(P),List(%)) -> List(%)
+--R intersect : (List(P),%) -> List(%)
+--R invertible? : (P,%) -> List(Record(val: Boolean,tower: %))
+--R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%))
+--R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %))
+--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List(%))
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((P -> P),%) -> % if $ has shallowlyMutable
--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate
---R members : % -> List P if $ has finiteAggregate
+--R members : % -> List(P) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List P if $ has finiteAggregate
+--R parts : % -> List(P) if $ has finiteAggregate
--R purelyAlgebraic? : (P,%) -> Boolean
--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean
--R purelyTranscendental? : (P,%) -> Boolean
---R quasiComponent : % -> Record(close: List P,open: List P)
+--R quasiComponent : % -> Record(close: List(P),open: List(P))
--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P
--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate
@@ -30299,10 +30380,10 @@ digraph pic {
--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate
---R retractIfCan : List P -> Union(%,"failed")
---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P
+--R retractIfCan : List(P) -> Union(%,"failed")
+--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P)
--R roughBase? : % -> Boolean if R has INTDOM
--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM
--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM
@@ -30311,11 +30392,11 @@ digraph pic {
--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : (%,V) -> Record(under: %,floor: %,upper: %)
---R squareFreePart : (P,%) -> List Record(val: P,tower: %)
+--R squareFreePart : (P,%) -> List(Record(val: P,tower: %))
--R stronglyReduced? : (P,%) -> Boolean
--R triangular? : % -> Boolean if R has INTDOM
---R zeroSetSplit : (List P,Boolean) -> List %
---R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P)
+--R zeroSetSplit : (List(P),Boolean) -> List(%)
+--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P)))
--R
--E 1
@@ -31001,7 +31082,8 @@ digraph pic {
--S 1 of 1
)show RightModule
---R RightModule R: Rng is a category constructor
+--R
+--R RightModule(R: Rng) is a category constructor
--R Abbreviation for RightModule is RMODULE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RMODULE
@@ -31523,6 +31605,7 @@ digraph pic {
--S 1 of 1
)show BitAggregate
+--R
--R BitAggregate is a category constructor
--R Abbreviation for BitAggregate is BTAGG
--R This constructor is exposed in this frame.
@@ -31535,13 +31618,13 @@ digraph pic {
--R ?\/? : (%,%) -> % ^? : % -> %
--R ?and? : (%,%) -> % coerce : % -> OutputForm
--R concat : (%,Boolean) -> % concat : (Boolean,%) -> %
---R concat : (%,%) -> % concat : List % -> %
---R construct : List Boolean -> % copy : % -> %
+--R concat : (%,%) -> % concat : List(%) -> %
+--R construct : List(Boolean) -> % copy : % -> %
--R delete : (%,Integer) -> % ?.? : (%,Integer) -> Boolean
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List Boolean eq? : (%,%) -> Boolean
+--R entries : % -> List(Boolean) eq? : (%,%) -> Boolean
--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (%,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (%,%,Integer) -> %
--R latex : % -> String max : (%,%) -> %
--R min : (%,%) -> % nand : (%,%) -> %
--R nor : (%,%) -> % not? : % -> %
@@ -31551,18 +31634,18 @@ digraph pic {
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate
---R convert : % -> InputForm if Boolean has KONVERT INFORM
+--R convert : % -> InputForm if Boolean has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : ((Boolean -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (Boolean,%) -> NonNegativeInteger if Boolean has SETCAT and $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
--R elt : (%,Integer,Boolean) -> Boolean
---R ?.? : (%,UniversalSegment Integer) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT
---R eval : (%,List Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
---R eval : (%,Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
---R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
---R eval : (%,List Boolean,List Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT
+--R eval : (%,List(Equation(Boolean))) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT
+--R eval : (%,Equation(Boolean)) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT
+--R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT
+--R eval : (%,List(Boolean),List(Boolean)) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT
--R every? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,Boolean) -> % if $ has shallowlyMutable
--R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed")
@@ -31574,13 +31657,13 @@ digraph pic {
--R map! : ((Boolean -> Boolean),%) -> % if $ has shallowlyMutable
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (Boolean,%) -> Boolean if Boolean has SETCAT and $ has finiteAggregate
---R members : % -> List Boolean if $ has finiteAggregate
+--R members : % -> List(Boolean) if $ has finiteAggregate
--R merge : (((Boolean,Boolean) -> Boolean),%,%) -> %
--R merge : (%,%) -> % if Boolean has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,Boolean) -> %
---R parts : % -> List Boolean if $ has finiteAggregate
+--R parts : % -> List(Boolean) if $ has finiteAggregate
--R position : ((Boolean -> Boolean),%) -> Integer
--R position : (Boolean,%) -> Integer if Boolean has SETCAT
--R position : (Boolean,%,Integer) -> Integer if Boolean has SETCAT
@@ -31594,7 +31677,7 @@ digraph pic {
--R reverse! : % -> % if $ has shallowlyMutable
--R select : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate
--R setelt : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable
---R setelt : (%,UniversalSegment Integer,Boolean) -> Boolean if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),Boolean) -> Boolean if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : (((Boolean,Boolean) -> Boolean),%) -> %
--R sort : % -> % if Boolean has ORDSET
@@ -32207,6 +32290,7 @@ digraph pic {
--S 1 of 1
)show NormalizedTriangularSetCategory
+--R
--R NormalizedTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for NormalizedTriangularSetCategory is NTSCAT
--R This constructor is exposed in this frame.
@@ -32214,71 +32298,72 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean
---R algebraicVariables : % -> List V augment : (List P,%) -> List %
---R augment : (P,List %) -> List % augment : (P,%) -> List %
---R coerce : % -> List P coerce : % -> OutputForm
+--R algebraicVariables : % -> List(V) augment : (List(P),%) -> List(%)
+--R augment : (P,List(%)) -> List(%) augment : (P,%) -> List(%)
+--R coerce : % -> List(P) coerce : % -> OutputForm
--R collect : (%,V) -> % collectQuasiMonic : % -> %
--R collectUnder : (%,V) -> % collectUpper : (%,V) -> %
---R construct : List P -> % copy : % -> %
+--R construct : List(P) -> % copy : % -> %
--R degree : % -> NonNegativeInteger empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R extend : (List P,%) -> List % extend : (P,List %) -> List %
---R extend : (P,%) -> List % extend : (%,P) -> %
+--R extend : (List(P),%) -> List(%) extend : (P,List(%)) -> List(%)
+--R extend : (P,%) -> List(%) extend : (%,P) -> %
--R first : % -> Union(P,"failed") hash : % -> SingleInteger
--R headReduce : (P,%) -> P headReduced? : % -> Boolean
--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean
--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean
---R initials : % -> List P internalAugment : (P,%) -> %
---R intersect : (P,List %) -> List % intersect : (List P,%) -> List %
---R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean
---R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed")
+--R initials : % -> List(P) internalAugment : (P,%) -> %
+--R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean
+--R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed")
--R latex : % -> String mainVariable? : (V,%) -> Boolean
---R mainVariables : % -> List V map : ((P -> P),%) -> %
+--R mainVariables : % -> List(V) map : ((P -> P),%) -> %
--R mvar : % -> V normalized? : % -> Boolean
--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean
--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P
---R rest : % -> Union(%,"failed") retract : List P -> %
+--R rest : % -> Union(%,"failed") retract : List(P) -> %
--R sample : () -> % stronglyReduce : (P,%) -> P
--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean
---R variables : % -> List V zeroSetSplit : List P -> List %
+--R variables : % -> List(V) zeroSetSplit : List(P) -> List(%)
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R algebraicCoefficients? : (P,%) -> Boolean
--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R augment : (List P,List %) -> List %
---R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean
---R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
---R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
+--R augment : (List(P),List(%)) -> List(%)
+--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean
+--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
+--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
--R coHeight : % -> NonNegativeInteger if V has FINITE
---R convert : % -> InputForm if P has KONVERT INFORM
+--R convert : % -> InputForm if P has KONVERT(INFORM)
--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT
+--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT
--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R extend : (List P,List %) -> List %
+--R extend : (List(P),List(%)) -> List(%)
--R extendIfCan : (%,P) -> Union(%,"failed")
--R find : ((P -> Boolean),%) -> Union(P,"failed")
--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM
--R initiallyReduced? : (P,%) -> Boolean
---R internalAugment : (List P,%) -> %
---R intersect : (List P,List %) -> List %
---R invertible? : (P,%) -> List Record(val: Boolean,tower: %)
---R invertibleElseSplit? : (P,%) -> Union(Boolean,List %)
---R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %)
---R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %)
+--R internalAugment : (List(P),%) -> %
+--R intersect : (P,List(%)) -> List(%)
+--R intersect : (List(P),List(%)) -> List(%)
+--R intersect : (List(P),%) -> List(%)
+--R invertible? : (P,%) -> List(Record(val: Boolean,tower: %))
+--R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%))
+--R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %))
+--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List(%))
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((P -> P),%) -> % if $ has shallowlyMutable
--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate
---R members : % -> List P if $ has finiteAggregate
+--R members : % -> List(P) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List P if $ has finiteAggregate
+--R parts : % -> List(P) if $ has finiteAggregate
--R purelyAlgebraic? : (P,%) -> Boolean
--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean
--R purelyTranscendental? : (P,%) -> Boolean
---R quasiComponent : % -> Record(close: List P,open: List P)
+--R quasiComponent : % -> Record(close: List(P),open: List(P))
--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P
--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate
@@ -32288,10 +32373,10 @@ digraph pic {
--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate
---R retractIfCan : List P -> Union(%,"failed")
---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P
+--R retractIfCan : List(P) -> Union(%,"failed")
+--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P)
--R roughBase? : % -> Boolean if R has INTDOM
--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM
--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM
@@ -32300,11 +32385,11 @@ digraph pic {
--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : (%,V) -> Record(under: %,floor: %,upper: %)
---R squareFreePart : (P,%) -> List Record(val: P,tower: %)
+--R squareFreePart : (P,%) -> List(Record(val: P,tower: %))
--R stronglyReduced? : (P,%) -> Boolean
--R triangular? : % -> Boolean if R has INTDOM
---R zeroSetSplit : (List P,Boolean) -> List %
---R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P)
+--R zeroSetSplit : (List(P),Boolean) -> List(%)
+--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P)))
--R
--E 1
@@ -33023,17 +33108,18 @@ digraph pic {
--S 1 of 1
)show OrderedMultisetAggregate
---R OrderedMultisetAggregate S: OrderedSet is a category constructor
+--R
+--R OrderedMultisetAggregate(S: OrderedSet) is a category constructor
--R Abbreviation for OrderedMultisetAggregate is OMSAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OMSAGG
--R
--R------------------------------- Operations --------------------------------
--R ? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
---R bag : List S -> % brace : () -> %
---R brace : List S -> % coerce : % -> OutputForm
---R construct : List S -> % copy : % -> %
---R dictionary : List S -> % dictionary : () -> %
+--R bag : List(S) -> % brace : () -> %
+--R brace : List(S) -> % coerce : % -> OutputForm
+--R construct : List(S) -> % copy : % -> %
+--R dictionary : List(S) -> % dictionary : () -> %
--R difference : (%,%) -> % difference : (%,S) -> %
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean extract! : % -> S
@@ -33043,29 +33129,29 @@ digraph pic {
--R max : % -> S merge : (%,%) -> %
--R merge! : (%,%) -> % min : % -> S
--R removeDuplicates! : % -> % sample : () -> %
---R set : () -> % set : List S -> %
+--R set : () -> % set : List(S) -> %
--R subset? : (%,%) -> Boolean union : (%,%) -> %
--R union : (%,S) -> % union : (S,%) -> %
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
---R convert : % -> InputForm if S has KONVERT INFORM
+--R convert : % -> InputForm if S has KONVERT(INFORM)
--R count : (S,%) -> NonNegativeInteger if S has SETCAT and $ has finiteAggregate
--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R duplicates : % -> List Record(entry: S,count: NonNegativeInteger)
---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT
---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT
+--R duplicates : % -> List(Record(entry: S,count: NonNegativeInteger))
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT
--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate
--R find : ((S -> Boolean),%) -> Union(S,"failed")
--R insert! : (S,%,NonNegativeInteger) -> %
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((S -> S),%) -> % if $ has shallowlyMutable
--R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate
---R members : % -> List S if $ has finiteAggregate
+--R members : % -> List(S) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List S if $ has finiteAggregate
+--R parts : % -> List(S) if $ has finiteAggregate
--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate
--R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate
@@ -33593,6 +33679,7 @@ digraph pic {
--S 1 of 1
)show SquareFreeRegularTriangularSetCategory
+--R
--R SquareFreeRegularTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for SquareFreeRegularTriangularSetCategory is SFRTCAT
--R This constructor is exposed in this frame.
@@ -33600,71 +33687,72 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean
---R algebraicVariables : % -> List V augment : (List P,%) -> List %
---R augment : (P,List %) -> List % augment : (P,%) -> List %
---R coerce : % -> List P coerce : % -> OutputForm
+--R algebraicVariables : % -> List(V) augment : (List(P),%) -> List(%)
+--R augment : (P,List(%)) -> List(%) augment : (P,%) -> List(%)
+--R coerce : % -> List(P) coerce : % -> OutputForm
--R collect : (%,V) -> % collectQuasiMonic : % -> %
--R collectUnder : (%,V) -> % collectUpper : (%,V) -> %
---R construct : List P -> % copy : % -> %
+--R construct : List(P) -> % copy : % -> %
--R degree : % -> NonNegativeInteger empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R extend : (List P,%) -> List % extend : (P,List %) -> List %
---R extend : (P,%) -> List % extend : (%,P) -> %
+--R extend : (List(P),%) -> List(%) extend : (P,List(%)) -> List(%)
+--R extend : (P,%) -> List(%) extend : (%,P) -> %
--R first : % -> Union(P,"failed") hash : % -> SingleInteger
--R headReduce : (P,%) -> P headReduced? : % -> Boolean
--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean
--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean
---R initials : % -> List P internalAugment : (P,%) -> %
---R intersect : (P,List %) -> List % intersect : (List P,%) -> List %
---R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean
---R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed")
+--R initials : % -> List(P) internalAugment : (P,%) -> %
+--R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean
+--R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed")
--R latex : % -> String mainVariable? : (V,%) -> Boolean
---R mainVariables : % -> List V map : ((P -> P),%) -> %
+--R mainVariables : % -> List(V) map : ((P -> P),%) -> %
--R mvar : % -> V normalized? : % -> Boolean
--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean
--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P
---R rest : % -> Union(%,"failed") retract : List P -> %
+--R rest : % -> Union(%,"failed") retract : List(P) -> %
--R sample : () -> % stronglyReduce : (P,%) -> P
--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean
---R variables : % -> List V zeroSetSplit : List P -> List %
+--R variables : % -> List(V) zeroSetSplit : List(P) -> List(%)
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R algebraicCoefficients? : (P,%) -> Boolean
--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R augment : (List P,List %) -> List %
---R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean
---R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
---R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
+--R augment : (List(P),List(%)) -> List(%)
+--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean
+--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
+--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
--R coHeight : % -> NonNegativeInteger if V has FINITE
---R convert : % -> InputForm if P has KONVERT INFORM
+--R convert : % -> InputForm if P has KONVERT(INFORM)
--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT
+--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT
--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R extend : (List P,List %) -> List %
+--R extend : (List(P),List(%)) -> List(%)
--R extendIfCan : (%,P) -> Union(%,"failed")
--R find : ((P -> Boolean),%) -> Union(P,"failed")
--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM
--R initiallyReduced? : (P,%) -> Boolean
---R internalAugment : (List P,%) -> %
---R intersect : (List P,List %) -> List %
---R invertible? : (P,%) -> List Record(val: Boolean,tower: %)
---R invertibleElseSplit? : (P,%) -> Union(Boolean,List %)
---R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %)
---R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %)
+--R internalAugment : (List(P),%) -> %
+--R intersect : (P,List(%)) -> List(%)
+--R intersect : (List(P),List(%)) -> List(%)
+--R intersect : (List(P),%) -> List(%)
+--R invertible? : (P,%) -> List(Record(val: Boolean,tower: %))
+--R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%))
+--R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %))
+--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List(%))
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((P -> P),%) -> % if $ has shallowlyMutable
--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate
---R members : % -> List P if $ has finiteAggregate
+--R members : % -> List(P) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List P if $ has finiteAggregate
+--R parts : % -> List(P) if $ has finiteAggregate
--R purelyAlgebraic? : (P,%) -> Boolean
--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean
--R purelyTranscendental? : (P,%) -> Boolean
---R quasiComponent : % -> Record(close: List P,open: List P)
+--R quasiComponent : % -> Record(close: List(P),open: List(P))
--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P
--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate
@@ -33674,10 +33762,10 @@ digraph pic {
--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate
---R retractIfCan : List P -> Union(%,"failed")
---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P
+--R retractIfCan : List(P) -> Union(%,"failed")
+--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P)
--R roughBase? : % -> Boolean if R has INTDOM
--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM
--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM
@@ -33686,11 +33774,11 @@ digraph pic {
--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : (%,V) -> Record(under: %,floor: %,upper: %)
---R squareFreePart : (P,%) -> List Record(val: P,tower: %)
+--R squareFreePart : (P,%) -> List(Record(val: P,tower: %))
--R stronglyReduced? : (P,%) -> Boolean
--R triangular? : % -> Boolean if R has INTDOM
---R zeroSetSplit : (List P,Boolean) -> List %
---R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P)
+--R zeroSetSplit : (List(P),Boolean) -> List(%)
+--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P)))
--R
--E 1
@@ -34063,25 +34151,26 @@ digraph pic {
--S 1 of 1
)show StringAggregate
+--R
--R StringAggregate is a category constructor
--R Abbreviation for StringAggregate is SRAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for SRAGG
--R
--R------------------------------- Operations --------------------------------
---R coerce : Character -> % concat : List % -> %
+--R coerce : Character -> % concat : List(%) -> %
--R concat : (%,%) -> % concat : (Character,%) -> %
---R concat : (%,Character) -> % construct : List Character -> %
+--R concat : (%,Character) -> % construct : List(Character) -> %
--R copy : % -> % delete : (%,Integer) -> %
--R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List Character eq? : (%,%) -> Boolean
---R index? : (Integer,%) -> Boolean indices : % -> List Integer
+--R entries : % -> List(Character) eq? : (%,%) -> Boolean
+--R index? : (Integer,%) -> Boolean indices : % -> List(Integer)
--R insert : (%,%,Integer) -> % leftTrim : (%,Character) -> %
--R lowerCase : % -> % lowerCase! : % -> %
--R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character
--R reverse : % -> % rightTrim : (%,Character) -> %
---R sample : () -> % split : (%,Character) -> List %
+--R sample : () -> % split : (%,Character) -> List(%)
--R suffix? : (%,%) -> Boolean trim : (%,CharacterClass) -> %
--R trim : (%,Character) -> % upperCase : % -> %
--R upperCase! : % -> %
@@ -34093,18 +34182,18 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if Character has ORDSET
--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if Character has SETCAT
---R convert : % -> InputForm if Character has KONVERT INFORM
+--R convert : % -> InputForm if Character has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (Character,%) -> NonNegativeInteger if Character has SETCAT and $ has finiteAggregate
--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R elt : (%,Integer,Character) -> Character
--R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT
---R eval : (%,List Character,List Character) -> % if Character has EVALAB CHAR and Character has SETCAT
---R eval : (%,Character,Character) -> % if Character has EVALAB CHAR and Character has SETCAT
---R eval : (%,Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT
---R eval : (%,List Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT
+--R eval : (%,List(Character),List(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT
+--R eval : (%,Character,Character) -> % if Character has EVALAB(CHAR) and Character has SETCAT
+--R eval : (%,Equation(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT
+--R eval : (%,List(Equation(Character))) -> % if Character has EVALAB(CHAR) and Character has SETCAT
--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,Character) -> % if $ has shallowlyMutable
--R find : ((Character -> Boolean),%) -> Union(Character,"failed")
@@ -34122,14 +34211,14 @@ digraph pic {
--R max : (%,%) -> % if Character has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (Character,%) -> Boolean if Character has SETCAT and $ has finiteAggregate
---R members : % -> List Character if $ has finiteAggregate
+--R members : % -> List(Character) if $ has finiteAggregate
--R merge : (%,%) -> % if Character has ORDSET
--R merge : (((Character,Character) -> Boolean),%,%) -> %
--R min : (%,%) -> % if Character has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,Character) -> %
---R parts : % -> List Character if $ has finiteAggregate
+--R parts : % -> List(Character) if $ has finiteAggregate
--R position : (CharacterClass,%,Integer) -> Integer
--R position : (%,%,Integer) -> Integer
--R position : (Character,%,Integer) -> Integer if Character has SETCAT
@@ -34142,11 +34231,11 @@ digraph pic {
--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (Character,%) -> % if Character has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if Character has SETCAT and $ has finiteAggregate
---R replace : (%,UniversalSegment Integer,%) -> %
+--R replace : (%,UniversalSegment(Integer),%) -> %
--R reverse! : % -> % if $ has shallowlyMutable
--R rightTrim : (%,CharacterClass) -> %
--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,Character) -> Character if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),Character) -> Character if $ has shallowlyMutable
--R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : % -> % if Character has ORDSET
@@ -34155,7 +34244,7 @@ digraph pic {
--R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable
--R sorted? : % -> Boolean if Character has ORDSET
--R sorted? : (((Character,Character) -> Boolean),%) -> Boolean
---R split : (%,CharacterClass) -> List %
+--R split : (%,CharacterClass) -> List(%)
--R substring? : (%,%,Integer) -> Boolean
--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
--R ?~=? : (%,%) -> Boolean if Character has SETCAT
@@ -34598,6 +34687,7 @@ digraph pic {
--S 1 of 1
)show TableAggregate
+--R
--R TableAggregate(Key: SetCategory,Entry: SetCategory) is a category constructor
--R Abbreviation for TableAggregate is TBAGG
--R This constructor is exposed in this frame.
@@ -34607,9 +34697,9 @@ digraph pic {
--R copy : % -> % dictionary : () -> %
--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List Entry eq? : (%,%) -> Boolean
---R index? : (Key,%) -> Boolean indices : % -> List Key
---R key? : (Key,%) -> Boolean keys : % -> List Key
+--R entries : % -> List(Entry) eq? : (%,%) -> Boolean
+--R index? : (Key,%) -> Boolean indices : % -> List(Key)
+--R key? : (Key,%) -> Boolean keys : % -> List(Key)
--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry
--R sample : () -> % setelt : (%,Key,Entry) -> Entry
--R table : () -> %
@@ -34617,24 +34707,24 @@ digraph pic {
--R ?=? : (%,%) -> Boolean if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT
--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate
--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
---R bag : List Record(key: Key,entry: Entry) -> %
+--R bag : List(Record(key: Key,entry: Entry)) -> %
--R coerce : % -> OutputForm if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT
---R construct : List Record(key: Key,entry: Entry) -> %
---R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM
+--R construct : List(Record(key: Key,entry: Entry)) -> %
+--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM)
--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (Entry,%) -> NonNegativeInteger if Entry has SETCAT and $ has finiteAggregate
--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R dictionary : List Record(key: Key,entry: Entry) -> %
+--R dictionary : List(Record(key: Key,entry: Entry)) -> %
--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT
---R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate
--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
--R extract! : % -> Record(key: Key,entry: Entry)
@@ -34653,12 +34743,12 @@ digraph pic {
--R maxIndex : % -> Key if Key has ORDSET
--R member? : (Entry,%) -> Boolean if Entry has SETCAT and $ has finiteAggregate
--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
---R members : % -> List Entry if $ has finiteAggregate
---R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
+--R members : % -> List(Entry) if $ has finiteAggregate
+--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
--R minIndex : % -> Key if Key has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List Entry if $ has finiteAggregate
---R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
+--R parts : % -> List(Entry) if $ has finiteAggregate
+--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable
--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate
--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate
@@ -34674,7 +34764,7 @@ digraph pic {
--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable
---R table : List Record(key: Key,entry: Entry) -> %
+--R table : List(Record(key: Key,entry: Entry)) -> %
--R ?~=? : (%,%) -> Boolean if Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT
--R
--E 1
@@ -35150,20 +35240,21 @@ digraph pic {
--S 1 of 1
)show VectorCategory
---R VectorCategory R: Type is a category constructor
+--R
+--R VectorCategory(R: Type) is a category constructor
--R Abbreviation for VectorCategory is VECTCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for VECTCAT
--R
--R------------------------------- Operations --------------------------------
---R -? : % -> % if R has ABELGRP concat : List % -> %
+--R -? : % -> % if R has ABELGRP concat : List(%) -> %
--R concat : (%,%) -> % concat : (R,%) -> %
---R concat : (%,R) -> % construct : List R -> %
+--R concat : (%,R) -> % construct : List(R) -> %
--R copy : % -> % delete : (%,Integer) -> %
--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List R eq? : (%,%) -> Boolean
---R index? : (Integer,%) -> Boolean indices : % -> List Integer
+--R entries : % -> List(R) eq? : (%,%) -> Boolean
+--R index? : (Integer,%) -> Boolean indices : % -> List(Integer)
--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> %
--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> %
--R new : (NonNegativeInteger,R) -> % qelt : (%,Integer) -> R
@@ -35181,19 +35272,19 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if R has ORDSET
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if R has SETCAT
---R convert : % -> InputForm if R has KONVERT INFORM
+--R convert : % -> InputForm if R has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R cross : (%,%) -> % if R has RING
---R delete : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
--R dot : (%,%) -> R if R has RING
---R ?.? : (%,UniversalSegment Integer) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,R) -> % if $ has shallowlyMutable
--R find : ((R -> Boolean),%) -> Union(R,"failed")
@@ -35207,14 +35298,14 @@ digraph pic {
--R max : (%,%) -> % if R has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
+--R members : % -> List(R) if $ has finiteAggregate
--R merge : (%,%) -> % if R has ORDSET
--R merge : (((R,R) -> Boolean),%,%) -> %
--R min : (%,%) -> % if R has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R outerProduct : (%,%) -> Matrix R if R has RING
---R parts : % -> List R if $ has finiteAggregate
+--R outerProduct : (%,%) -> Matrix(R) if R has RING
+--R parts : % -> List(R) if $ has finiteAggregate
--R position : (R,%,Integer) -> Integer if R has SETCAT
--R position : (R,%) -> Integer if R has SETCAT
--R position : ((R -> Boolean),%) -> Integer
@@ -35227,7 +35318,7 @@ digraph pic {
--R removeDuplicates : % -> % if R has SETCAT and $ has finiteAggregate
--R reverse! : % -> % if $ has shallowlyMutable
--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable
--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : % -> % if R has ORDSET
@@ -35607,28 +35698,29 @@ digraph pic {
--S 1 of 1
)show AssociationListAggregate
+--R
--R AssociationListAggregate(Key: SetCategory,Entry: SetCategory) is a category constructor
--R Abbreviation for AssociationListAggregate is ALAGG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ALAGG
--R
--R------------------------------- Operations --------------------------------
---R children : % -> List % concat : (%,%) -> %
---R concat : List % -> % concat! : (%,%) -> %
+--R children : % -> List(%) concat : (%,%) -> %
+--R concat : List(%) -> % concat! : (%,%) -> %
--R copy : % -> % cycleEntry : % -> %
--R cycleTail : % -> % cyclic? : % -> Boolean
--R delete : (%,Integer) -> % delete! : (%,Integer) -> %
--R dictionary : () -> % distance : (%,%) -> Integer
--R ?.rest : (%,rest) -> % elt : (%,Key,Entry) -> Entry
--R ?.? : (%,Key) -> Entry empty : () -> %
---R empty? : % -> Boolean entries : % -> List Entry
+--R empty? : % -> Boolean entries : % -> List(Entry)
--R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean
--R index? : (Integer,%) -> Boolean index? : (Key,%) -> Boolean
---R indices : % -> List Integer indices : % -> List Key
+--R indices : % -> List(Integer) indices : % -> List(Key)
--R insert : (%,%,Integer) -> % insert! : (%,%,Integer) -> %
---R key? : (Key,%) -> Boolean keys : % -> List Key
+--R key? : (Key,%) -> Boolean keys : % -> List(Key)
--R leaf? : % -> Boolean map : ((Entry -> Entry),%) -> %
---R nodes : % -> List % possiblyInfinite? : % -> Boolean
+--R nodes : % -> List(%) possiblyInfinite? : % -> Boolean
--R qelt : (%,Key) -> Entry rest : % -> %
--R reverse : % -> % sample : () -> %
--R setelt : (%,Key,Entry) -> Entry table : () -> %
@@ -35643,15 +35735,15 @@ digraph pic {
--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate
--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
--R assoc : (Key,%) -> Union(Record(key: Key,entry: Entry),"failed")
---R bag : List Record(key: Key,entry: Entry) -> %
+--R bag : List(Record(key: Key,entry: Entry)) -> %
--R child? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT
--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT
--R concat : (Record(key: Key,entry: Entry),%) -> %
--R concat : (%,Record(key: Key,entry: Entry)) -> %
--R concat! : (%,Record(key: Key,entry: Entry)) -> %
---R construct : List Record(key: Key,entry: Entry) -> %
---R construct : List Record(key: Key,entry: Entry) -> %
---R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM or Record(key: Key,entry: Entry) has KONVERT INFORM
+--R construct : List(Record(key: Key,entry: Entry)) -> %
+--R construct : List(Record(key: Key,entry: Entry)) -> %
+--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) or Record(key: Key,entry: Entry) has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
@@ -35661,30 +35753,30 @@ digraph pic {
--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R cycleLength : % -> NonNegativeInteger
--R cycleSplit! : % -> % if $ has shallowlyMutable
---R delete : (%,UniversalSegment Integer) -> %
---R delete! : (%,UniversalSegment Integer) -> %
---R dictionary : List Record(key: Key,entry: Entry) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R delete! : (%,UniversalSegment(Integer)) -> %
+--R dictionary : List(Record(key: Key,entry: Entry)) -> %
--R ?.value : (%,value) -> Record(key: Key,entry: Entry)
--R ?.first : (%,first) -> Record(key: Key,entry: Entry)
--R ?.last : (%,last) -> Record(key: Key,entry: Entry)
---R ?.? : (%,UniversalSegment Integer) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R ?.? : (%,Integer) -> Record(key: Key,entry: Entry)
--R elt : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)
---R entries : % -> List Record(key: Key,entry: Entry)
+--R entries : % -> List(Record(key: Key,entry: Entry))
--R entry? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT
--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT
---R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT
---R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
---R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT
+--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
+--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT
--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate
--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate
@@ -35704,7 +35796,7 @@ digraph pic {
--R last : % -> Record(key: Key,entry: Entry)
--R last : (%,NonNegativeInteger) -> %
--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT
---R leaves : % -> List Record(key: Key,entry: Entry)
+--R leaves : % -> List(Record(key: Key,entry: Entry))
--R less? : (%,NonNegativeInteger) -> Boolean
--R list : Record(key: Key,entry: Entry) -> %
--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> %
@@ -35720,9 +35812,9 @@ digraph pic {
--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
--R member? : (Entry,%) -> Boolean if Entry has SETCAT and $ has finiteAggregate
--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate
---R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
---R members : % -> List Entry if $ has finiteAggregate
---R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
+--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
+--R members : % -> List(Entry) if $ has finiteAggregate
+--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
--R merge : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET
--R merge : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%,%) -> %
--R merge! : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET
@@ -35733,9 +35825,9 @@ digraph pic {
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,Record(key: Key,entry: Entry)) -> %
--R node? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT
---R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
---R parts : % -> List Entry if $ has finiteAggregate
---R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate
+--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
+--R parts : % -> List(Entry) if $ has finiteAggregate
+--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate
--R position : (Record(key: Key,entry: Entry),%,Integer) -> Integer if Record(key: Key,entry: Entry) has SETCAT
--R position : (Record(key: Key,entry: Entry),%) -> Integer if Record(key: Key,entry: Entry) has SETCAT
--R position : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Integer
@@ -35767,12 +35859,12 @@ digraph pic {
--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate
--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> %
--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate
---R setchildren! : (%,List %) -> % if $ has shallowlyMutable
+--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable
--R setelt : (%,value,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
--R setelt : (%,first,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
--R setelt : (%,rest,%) -> % if $ has shallowlyMutable
--R setelt : (%,last,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
---R setelt : (%,UniversalSegment Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
--R setelt : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
--R setfirst! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
--R setlast! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable
@@ -35788,7 +35880,7 @@ digraph pic {
--R split! : (%,Integer) -> % if $ has shallowlyMutable
--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable
---R table : List Record(key: Key,entry: Entry) -> %
+--R table : List(Record(key: Key,entry: Entry)) -> %
--R third : % -> Record(key: Key,entry: Entry)
--R value : % -> Record(key: Key,entry: Entry)
--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT
@@ -37386,6 +37478,7 @@ digraph pic {
--S 1 of 1
)show FreeModuleCat
+--R
--R FreeModuleCat(R: Ring,Basis: SetCategory) is a category constructor
--R Abbreviation for FreeModuleCat is FMCAT
--R This constructor is exposed in this frame.
@@ -37397,18 +37490,18 @@ digraph pic {
--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> %
--R ?-? : (%,%) -> % -? : % -> %
--R ?=? : (%,%) -> Boolean 0 : () -> %
---R coefficient : (%,Basis) -> R coefficients : % -> List R
+--R coefficient : (%,Basis) -> R coefficients : % -> List(R)
--R coerce : Basis -> % coerce : % -> OutputForm
--R hash : % -> SingleInteger latex : % -> String
--R leadingCoefficient : % -> R leadingMonomial : % -> Basis
--R map : ((R -> R),%) -> % monom : (Basis,R) -> %
---R monomial? : % -> Boolean monomials : % -> List %
+--R monomial? : % -> Boolean monomials : % -> List(%)
--R reductum : % -> % retract : % -> Basis
--R sample : () -> % zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R leadingTerm : % -> Record(k: Basis,c: R)
---R listOfTerms : % -> List Record(k: Basis,c: R)
+--R listOfTerms : % -> List(Record(k: Basis,c: R))
--R numberOfMonomials : % -> NonNegativeInteger
--R retractIfCan : % -> Union(Basis,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
@@ -37655,7 +37748,8 @@ digraph pic {
--S 1 of 1
)show LeftAlgebra
---R LeftAlgebra R: Ring is a category constructor
+--R
+--R LeftAlgebra(R: Ring) is a category constructor
--R Abbreviation for LeftAlgebra is LALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LALG
@@ -37844,7 +37938,8 @@ digraph pic {
--S 1 of 1
)show LinearlyExplicitRingOver
---R LinearlyExplicitRingOver R: Ring is a category constructor
+--R
+--R LinearlyExplicitRingOver(R: Ring) is a category constructor
--R Abbreviation for LinearlyExplicitRingOver is LINEXP
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LINEXP
@@ -37864,8 +37959,8 @@ digraph pic {
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : Matrix % -> Matrix R
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : Matrix(%) -> Matrix(R)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 1
@@ -38057,7 +38152,8 @@ digraph pic {
--S 1 of 1
)show Module
---R Module R: CommutativeRing is a category constructor
+--R
+--R Module(R: CommutativeRing) is a category constructor
--R Abbreviation for Module is MODULE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MODULE
@@ -38494,7 +38590,8 @@ digraph pic {
--S 1 of 1
)show PartialDifferentialRing
---R PartialDifferentialRing S: SetCategory is a category constructor
+--R
+--R PartialDifferentialRing(S: SetCategory) is a category constructor
--R Abbreviation for PartialDifferentialRing is PDRING
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PDRING
@@ -38504,21 +38601,21 @@ digraph pic {
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
---R D : (%,List S) -> % D : (%,S) -> %
+--R D : (%,List(S)) -> % D : (%,S) -> %
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> %
---R coerce : % -> OutputForm differentiate : (%,List S) -> %
+--R coerce : % -> OutputForm differentiate : (%,List(S)) -> %
--R differentiate : (%,S) -> % hash : % -> SingleInteger
--R latex : % -> String one? : % -> Boolean
--R recip : % -> Union(%,"failed") sample : () -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
---R D : (%,List S,List NonNegativeInteger) -> %
+--R D : (%,List(S),List(NonNegativeInteger)) -> %
--R D : (%,S,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R differentiate : (%,List S,List NonNegativeInteger) -> %
+--R differentiate : (%,List(S),List(NonNegativeInteger)) -> %
--R differentiate : (%,S,NonNegativeInteger) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
@@ -38766,25 +38863,26 @@ digraph pic {
--S 1 of 1
)show PointCategory
---R PointCategory R: Ring is a category constructor
+--R
+--R PointCategory(R: Ring) is a category constructor
--R Abbreviation for PointCategory is PTCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PTCAT
--R
--R------------------------------- Operations --------------------------------
---R -? : % -> % if R has ABELGRP concat : List % -> %
+--R -? : % -> % if R has ABELGRP concat : List(%) -> %
--R concat : (%,%) -> % concat : (R,%) -> %
---R concat : (%,R) -> % construct : List R -> %
---R convert : List R -> % copy : % -> %
+--R concat : (%,R) -> % construct : List(R) -> %
+--R convert : List(R) -> % copy : % -> %
--R cross : (%,%) -> % delete : (%,Integer) -> %
--R dimension : % -> PositiveInteger ?.? : (%,Integer) -> R
--R elt : (%,Integer,R) -> R empty : () -> %
---R empty? : % -> Boolean entries : % -> List R
---R eq? : (%,%) -> Boolean extend : (%,List R) -> %
---R index? : (Integer,%) -> Boolean indices : % -> List Integer
+--R empty? : % -> Boolean entries : % -> List(R)
+--R eq? : (%,%) -> Boolean extend : (%,List(R)) -> %
+--R index? : (Integer,%) -> Boolean indices : % -> List(Integer)
--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> %
--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> %
---R new : (NonNegativeInteger,R) -> % point : List R -> %
+--R new : (NonNegativeInteger,R) -> % point : List(R) -> %
--R qelt : (%,Integer) -> R reverse : % -> %
--R sample : () -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
@@ -38800,18 +38898,18 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if R has ORDSET
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R coerce : % -> OutputForm if R has SETCAT
---R convert : % -> InputForm if R has KONVERT INFORM
+--R convert : % -> InputForm if R has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
--R dot : (%,%) -> R if R has RING
---R ?.? : (%,UniversalSegment Integer) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,R) -> % if $ has shallowlyMutable
--R find : ((R -> Boolean),%) -> Union(R,"failed")
@@ -38825,14 +38923,14 @@ digraph pic {
--R max : (%,%) -> % if R has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
+--R members : % -> List(R) if $ has finiteAggregate
--R merge : (%,%) -> % if R has ORDSET
--R merge : (((R,R) -> Boolean),%,%) -> %
--R min : (%,%) -> % if R has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
---R outerProduct : (%,%) -> Matrix R if R has RING
---R parts : % -> List R if $ has finiteAggregate
+--R outerProduct : (%,%) -> Matrix(R) if R has RING
+--R parts : % -> List(R) if $ has finiteAggregate
--R position : (R,%,Integer) -> Integer if R has SETCAT
--R position : (R,%) -> Integer if R has SETCAT
--R position : ((R -> Boolean),%) -> Integer
@@ -38845,7 +38943,7 @@ digraph pic {
--R removeDuplicates : % -> % if R has SETCAT and $ has finiteAggregate
--R reverse! : % -> % if $ has shallowlyMutable
--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable
--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : % -> % if R has ORDSET
@@ -39182,6 +39280,7 @@ The RectangularMatrix domain is matrices of fixed dimension.
--S 1 of 1
)show RectangularMatrixCategory
+--R
--R RectangularMatrixCategory(m: NonNegativeInteger,n: NonNegativeInteger,R: Ring,Row: DirectProductCategory(t#2,t#3),Col: DirectProductCategory(t#1,t#3)) is a category constructor
--R Abbreviation for RectangularMatrixCategory is RMATCAT
--R This constructor is exposed in this frame.
@@ -39198,9 +39297,9 @@ The RectangularMatrix domain is matrices of fixed dimension.
--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R
--R empty : () -> % empty? : % -> Boolean
--R eq? : (%,%) -> Boolean hash : % -> SingleInteger
---R latex : % -> String listOfLists : % -> List List R
+--R latex : % -> String listOfLists : % -> List(List(R))
--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> %
---R matrix : List List R -> % maxColIndex : % -> Integer
+--R matrix : List(List(R)) -> % maxColIndex : % -> Integer
--R maxRowIndex : % -> Integer minColIndex : % -> Integer
--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger
--R nrows : % -> NonNegativeInteger qelt : (%,Integer,Integer) -> R
@@ -39213,20 +39312,20 @@ The RectangularMatrix domain is matrices of fixed dimension.
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((R -> R),%) -> % if $ has shallowlyMutable
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
+--R members : % -> List(R) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R nullSpace : % -> List Col if R has INTDOM
+--R nullSpace : % -> List(Col) if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
---R parts : % -> List R if $ has finiteAggregate
+--R parts : % -> List(R) if $ has finiteAggregate
--R rank : % -> NonNegativeInteger if R has INTDOM
--R rowEchelon : % -> % if R has EUCDOM
--R size? : (%,NonNegativeInteger) -> Boolean
@@ -39629,6 +39728,7 @@ digraph pic {
--S 1 of 1
)show SquareFreeNormalizedTriangularSetCategory
+--R
--R SquareFreeNormalizedTriangularSetCategory(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(t#1,t#2,t#3)) is a category constructor
--R Abbreviation for SquareFreeNormalizedTriangularSetCategory is SNTSCAT
--R This constructor is exposed in this frame.
@@ -39636,71 +39736,72 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean
---R algebraicVariables : % -> List V augment : (List P,%) -> List %
---R augment : (P,List %) -> List % augment : (P,%) -> List %
---R coerce : % -> List P coerce : % -> OutputForm
+--R algebraicVariables : % -> List(V) augment : (List(P),%) -> List(%)
+--R augment : (P,List(%)) -> List(%) augment : (P,%) -> List(%)
+--R coerce : % -> List(P) coerce : % -> OutputForm
--R collect : (%,V) -> % collectQuasiMonic : % -> %
--R collectUnder : (%,V) -> % collectUpper : (%,V) -> %
---R construct : List P -> % copy : % -> %
+--R construct : List(P) -> % copy : % -> %
--R degree : % -> NonNegativeInteger empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
---R extend : (List P,%) -> List % extend : (P,List %) -> List %
---R extend : (P,%) -> List % extend : (%,P) -> %
+--R extend : (List(P),%) -> List(%) extend : (P,List(%)) -> List(%)
+--R extend : (P,%) -> List(%) extend : (%,P) -> %
--R first : % -> Union(P,"failed") hash : % -> SingleInteger
--R headReduce : (P,%) -> P headReduced? : % -> Boolean
--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean
--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean
---R initials : % -> List P internalAugment : (P,%) -> %
---R intersect : (P,List %) -> List % intersect : (List P,%) -> List %
---R intersect : (P,%) -> List % invertible? : (P,%) -> Boolean
---R invertibleSet : (P,%) -> List % last : % -> Union(P,"failed")
+--R initials : % -> List(P) internalAugment : (P,%) -> %
+--R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean
+--R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed")
--R latex : % -> String mainVariable? : (V,%) -> Boolean
---R mainVariables : % -> List V map : ((P -> P),%) -> %
+--R mainVariables : % -> List(V) map : ((P -> P),%) -> %
--R mvar : % -> V normalized? : % -> Boolean
--R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean
--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P
---R rest : % -> Union(%,"failed") retract : List P -> %
+--R rest : % -> Union(%,"failed") retract : List(P) -> %
--R sample : () -> % stronglyReduce : (P,%) -> P
--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean
---R variables : % -> List V zeroSetSplit : List P -> List %
+--R variables : % -> List(V) zeroSetSplit : List(P) -> List(%)
--R ?~=? : (%,%) -> Boolean
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
--R algebraicCoefficients? : (P,%) -> Boolean
--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R augment : (List P,List %) -> List %
---R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean
---R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
---R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed")
+--R augment : (List(P),List(%)) -> List(%)
+--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean
+--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
+--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed")
--R coHeight : % -> NonNegativeInteger if V has FINITE
---R convert : % -> InputForm if P has KONVERT INFORM
+--R convert : % -> InputForm if P has KONVERT(INFORM)
--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R count : (P,%) -> NonNegativeInteger if P has SETCAT and $ has finiteAggregate
---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT
---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT
+--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT
+--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT
--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate
---R extend : (List P,List %) -> List %
+--R extend : (List(P),List(%)) -> List(%)
--R extendIfCan : (%,P) -> Union(%,"failed")
--R find : ((P -> Boolean),%) -> Union(P,"failed")
--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM
--R initiallyReduced? : (P,%) -> Boolean
---R internalAugment : (List P,%) -> %
---R intersect : (List P,List %) -> List %
---R invertible? : (P,%) -> List Record(val: Boolean,tower: %)
---R invertibleElseSplit? : (P,%) -> Union(Boolean,List %)
---R lastSubResultant : (P,P,%) -> List Record(val: P,tower: %)
---R lastSubResultantElseSplit : (P,P,%) -> Union(P,List %)
+--R internalAugment : (List(P),%) -> %
+--R intersect : (P,List(%)) -> List(%)
+--R intersect : (List(P),List(%)) -> List(%)
+--R intersect : (List(P),%) -> List(%)
+--R invertible? : (P,%) -> List(Record(val: Boolean,tower: %))
+--R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%))
+--R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %))
+--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List(%))
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((P -> P),%) -> % if $ has shallowlyMutable
--R member? : (P,%) -> Boolean if P has SETCAT and $ has finiteAggregate
---R members : % -> List P if $ has finiteAggregate
+--R members : % -> List(P) if $ has finiteAggregate
--R more? : (%,NonNegativeInteger) -> Boolean
---R parts : % -> List P if $ has finiteAggregate
+--R parts : % -> List(P) if $ has finiteAggregate
--R purelyAlgebraic? : (P,%) -> Boolean
--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean
--R purelyTranscendental? : (P,%) -> Boolean
---R quasiComponent : % -> Record(close: List P,open: List P)
+--R quasiComponent : % -> Record(close: List(P),open: List(P))
--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P
--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate
--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate
@@ -39710,10 +39811,10 @@ digraph pic {
--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (P,%) -> % if P has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if P has SETCAT and $ has finiteAggregate
---R retractIfCan : List P -> Union(%,"failed")
---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM
---R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P
+--R retractIfCan : List(P) -> Union(%,"failed")
+--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM
+--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P)
--R roughBase? : % -> Boolean if R has INTDOM
--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM
--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM
@@ -39722,11 +39823,11 @@ digraph pic {
--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : (%,V) -> Record(under: %,floor: %,upper: %)
---R squareFreePart : (P,%) -> List Record(val: P,tower: %)
+--R squareFreePart : (P,%) -> List(Record(val: P,tower: %))
--R stronglyReduced? : (P,%) -> Boolean
--R triangular? : % -> Boolean if R has INTDOM
---R zeroSetSplit : (List P,Boolean) -> List %
---R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P)
+--R zeroSetSplit : (List(P),Boolean) -> List(%)
+--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P)))
--R
--E 1
@@ -40072,6 +40173,7 @@ digraph pic {
--S 1 of 1
)show StringCategory
+--R
--R StringCategory is a category constructor
--R Abbreviation for StringCategory is STRICAT
--R This constructor is exposed in this frame.
@@ -40080,20 +40182,20 @@ digraph pic {
--R------------------------------- Operations --------------------------------
--R ?=? : (%,%) -> Boolean OMwrite : (%,Boolean) -> String
--R OMwrite : % -> String coerce : % -> OutputForm
---R coerce : Character -> % concat : List % -> %
+--R coerce : Character -> % concat : List(%) -> %
--R concat : (%,%) -> % concat : (Character,%) -> %
---R concat : (%,Character) -> % construct : List Character -> %
+--R concat : (%,Character) -> % construct : List(Character) -> %
--R copy : % -> % delete : (%,Integer) -> %
--R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List Character eq? : (%,%) -> Boolean
+--R entries : % -> List(Character) eq? : (%,%) -> Boolean
--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean
---R indices : % -> List Integer insert : (%,%,Integer) -> %
+--R indices : % -> List(Integer) insert : (%,%,Integer) -> %
--R latex : % -> String leftTrim : (%,Character) -> %
--R lowerCase : % -> % lowerCase! : % -> %
--R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character
--R reverse : % -> % rightTrim : (%,Character) -> %
---R sample : () -> % split : (%,Character) -> List %
+--R sample : () -> % split : (%,Character) -> List(%)
--R string : Integer -> % suffix? : (%,%) -> Boolean
--R trim : (%,CharacterClass) -> % trim : (%,Character) -> %
--R upperCase : % -> % upperCase! : % -> %
@@ -40106,18 +40208,18 @@ digraph pic {
--R OMwrite : (OpenMathDevice,%,Boolean) -> Void
--R OMwrite : (OpenMathDevice,%) -> Void
--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate
---R convert : % -> InputForm if Character has KONVERT INFORM
+--R convert : % -> InputForm if Character has KONVERT(INFORM)
--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable
--R count : (Character,%) -> NonNegativeInteger if Character has SETCAT and $ has finiteAggregate
--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R delete : (%,UniversalSegment Integer) -> %
---R ?.? : (%,UniversalSegment Integer) -> %
+--R delete : (%,UniversalSegment(Integer)) -> %
+--R ?.? : (%,UniversalSegment(Integer)) -> %
--R elt : (%,Integer,Character) -> Character
--R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT
---R eval : (%,List Character,List Character) -> % if Character has EVALAB CHAR and Character has SETCAT
---R eval : (%,Character,Character) -> % if Character has EVALAB CHAR and Character has SETCAT
---R eval : (%,Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT
---R eval : (%,List Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT
+--R eval : (%,List(Character),List(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT
+--R eval : (%,Character,Character) -> % if Character has EVALAB(CHAR) and Character has SETCAT
+--R eval : (%,Equation(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT
+--R eval : (%,List(Equation(Character))) -> % if Character has EVALAB(CHAR) and Character has SETCAT
--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,Character) -> % if $ has shallowlyMutable
--R find : ((Character -> Boolean),%) -> Union(Character,"failed")
@@ -40133,14 +40235,14 @@ digraph pic {
--R max : (%,%) -> % if Character has ORDSET
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (Character,%) -> Boolean if Character has SETCAT and $ has finiteAggregate
---R members : % -> List Character if $ has finiteAggregate
+--R members : % -> List(Character) if $ has finiteAggregate
--R merge : (%,%) -> % if Character has ORDSET
--R merge : (((Character,Character) -> Boolean),%,%) -> %
--R min : (%,%) -> % if Character has ORDSET
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R new : (NonNegativeInteger,Character) -> %
---R parts : % -> List Character if $ has finiteAggregate
+--R parts : % -> List(Character) if $ has finiteAggregate
--R position : (CharacterClass,%,Integer) -> Integer
--R position : (%,%,Integer) -> Integer
--R position : (Character,%,Integer) -> Integer if Character has SETCAT
@@ -40153,11 +40255,11 @@ digraph pic {
--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate
--R remove : (Character,%) -> % if Character has SETCAT and $ has finiteAggregate
--R removeDuplicates : % -> % if Character has SETCAT and $ has finiteAggregate
---R replace : (%,UniversalSegment Integer,%) -> %
+--R replace : (%,UniversalSegment(Integer),%) -> %
--R reverse! : % -> % if $ has shallowlyMutable
--R rightTrim : (%,CharacterClass) -> %
--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate
---R setelt : (%,UniversalSegment Integer,Character) -> Character if $ has shallowlyMutable
+--R setelt : (%,UniversalSegment(Integer),Character) -> Character if $ has shallowlyMutable
--R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable
--R size? : (%,NonNegativeInteger) -> Boolean
--R sort : % -> % if Character has ORDSET
@@ -40166,7 +40268,7 @@ digraph pic {
--R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable
--R sorted? : % -> Boolean if Character has ORDSET
--R sorted? : (((Character,Character) -> Boolean),%) -> Boolean
---R split : (%,CharacterClass) -> List %
+--R split : (%,CharacterClass) -> List(%)
--R substring? : (%,%,Integer) -> Boolean
--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable
--R
@@ -40537,7 +40639,8 @@ digraph pic {
--S 1 of 1
)show UnivariateSkewPolynomialCategory
---R UnivariateSkewPolynomialCategory R: Ring is a category constructor
+--R
+--R UnivariateSkewPolynomialCategory(R: Ring) is a category constructor
--R Abbreviation for UnivariateSkewPolynomialCategory is OREPCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OREPCAT
@@ -40550,7 +40653,7 @@ digraph pic {
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % apply : (%,R,R) -> R
---R coefficients : % -> List R coerce : R -> %
+--R coefficients : % -> List(R) coerce : R -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R degree : % -> NonNegativeInteger hash : % -> SingleInteger
--R latex : % -> String leadingCoefficient : % -> R
@@ -40563,7 +40666,7 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R coefficient : (%,NonNegativeInteger) -> R
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT))
--R content : % -> R if R has GCDDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
@@ -40578,11 +40681,11 @@ digraph pic {
--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM
--R monomial : (R,NonNegativeInteger) -> %
--R primitivePart : % -> % if R has GCDDOM
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
--R rightExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD
--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
@@ -41112,7 +41215,8 @@ digraph pic {
--S 1 of 1
)show XAlgebra
---R XAlgebra R: Ring is a category constructor
+--R
+--R XAlgebra(R: Ring) is a category constructor
--R Abbreviation for XAlgebra is XALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for XALG
@@ -41336,7 +41440,8 @@ digraph pic {
--S 1 of 1
)show Algebra
---R Algebra R: CommutativeRing is a category constructor
+--R
+--R Algebra(R: CommutativeRing) is a category constructor
--R Abbreviation for Algebra is ALGEBRA
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ALGEBRA
@@ -41596,7 +41701,8 @@ digraph pic {
--S 1 of 1
)show DifferentialExtension
---R DifferentialExtension R: Ring is a category constructor
+--R
+--R DifferentialExtension(R: Ring) is a category constructor
--R Abbreviation for DifferentialExtension is DIFEXT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIFEXT
@@ -41616,19 +41722,19 @@ digraph pic {
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
---R D : (%,Symbol) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol) -> % if R has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
+--R D : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
--R D : (%,(R -> R),NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R differentiate : % -> % if R has DIFRING
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
+--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
--R differentiate : (%,(R -> R)) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
@@ -41890,7 +41996,8 @@ digraph pic {
--S 1 of 1
)show FullyLinearlyExplicitRingOver
---R FullyLinearlyExplicitRingOver R: Ring is a category constructor
+--R
+--R FullyLinearlyExplicitRingOver(R: Ring) is a category constructor
--R Abbreviation for FullyLinearlyExplicitRingOver is FLINEXP
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FLINEXP
@@ -41910,10 +42017,10 @@ digraph pic {
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : Matrix % -> Matrix R
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : Matrix(%) -> Matrix(R)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 1
@@ -42131,7 +42238,8 @@ digraph pic {
--S 1 of 1
)show LieAlgebra
---R LieAlgebra R: CommutativeRing is a category constructor
+--R
+--R LieAlgebra(R: CommutativeRing) is a category constructor
--R Abbreviation for LieAlgebra is LIECAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LIECAT
@@ -42322,7 +42430,8 @@ digraph pic {
--S 1 of 1
)show LinearOrdinaryDifferentialOperatorCategory
---R LinearOrdinaryDifferentialOperatorCategory A: Ring is a category constructor
+--R
+--R LinearOrdinaryDifferentialOperatorCategory(A: Ring) is a category constructor
--R Abbreviation for LinearOrdinaryDifferentialOperatorCategory is LODOCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LODOCAT
@@ -42336,7 +42445,7 @@ digraph pic {
--R D : () -> % 1 : () -> %
--R 0 : () -> % ?^? : (%,PositiveInteger) -> %
--R adjoint : % -> % apply : (%,A,A) -> A
---R coefficients : % -> List A coerce : A -> %
+--R coefficients : % -> List(A) coerce : A -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R degree : % -> NonNegativeInteger ?.? : (%,A) -> A
--R hash : % -> SingleInteger latex : % -> String
@@ -42349,7 +42458,7 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R coefficient : (%,NonNegativeInteger) -> A
---R coerce : Fraction Integer -> % if A has RETRACT FRAC INT
+--R coerce : Fraction(Integer) -> % if A has RETRACT(FRAC(INT))
--R content : % -> A if A has GCDDOM
--R directSum : (%,%) -> % if A has FIELD
--R exquo : (%,A) -> Union(%,"failed") if A has INTDOM
@@ -42365,11 +42474,11 @@ digraph pic {
--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM
--R monomial : (A,NonNegativeInteger) -> %
--R primitivePart : % -> % if A has GCDDOM
---R retract : % -> Fraction Integer if A has RETRACT FRAC INT
---R retract : % -> Integer if A has RETRACT INT
+--R retract : % -> Fraction(Integer) if A has RETRACT(FRAC(INT))
+--R retract : % -> Integer if A has RETRACT(INT)
--R retractIfCan : % -> Union(A,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if A has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if A has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if A has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if A has RETRACT(INT)
--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD
--R rightExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD
--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD
@@ -42737,7 +42846,8 @@ digraph pic {
--S 1 of 1
)show NonAssociativeAlgebra
---R NonAssociativeAlgebra R: CommutativeRing is a category constructor
+--R
+--R NonAssociativeAlgebra(R: CommutativeRing) is a category constructor
--R Abbreviation for NonAssociativeAlgebra is NAALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for NAALG
@@ -42958,7 +43068,8 @@ digraph pic {
--S 1 of 1
)show VectorSpace
---R VectorSpace S: Field is a category constructor
+--R
+--R VectorSpace(S: Field) is a category constructor
--R Abbreviation for VectorSpace is VSPACE
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for VSPACE
@@ -43142,6 +43253,7 @@ digraph pic {
--S 1 of 1
)show XFreeAlgebra
+--R
--R XFreeAlgebra(vl: OrderedSet,R: Ring) is a category constructor
--R Abbreviation for XFreeAlgebra is XFALG
--R This constructor is exposed in this frame.
@@ -43165,21 +43277,21 @@ digraph pic {
--R one? : % -> Boolean quasiRegular : % -> %
--R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed")
--R rquo : (%,%) -> % rquo : (%,vl) -> %
---R sample : () -> % varList : % -> List vl
+--R sample : () -> % varList : % -> List(vl)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R coef : (%,OrderedFreeMonoid vl) -> R
---R coerce : OrderedFreeMonoid vl -> %
---R lquo : (%,OrderedFreeMonoid vl) -> %
---R mindeg : % -> OrderedFreeMonoid vl
---R mindegTerm : % -> Record(k: OrderedFreeMonoid vl,c: R)
---R monom : (OrderedFreeMonoid vl,R) -> %
---R retract : % -> OrderedFreeMonoid vl
---R retractIfCan : % -> Union(OrderedFreeMonoid vl,"failed")
---R rquo : (%,OrderedFreeMonoid vl) -> %
+--R coef : (%,OrderedFreeMonoid(vl)) -> R
+--R coerce : OrderedFreeMonoid(vl) -> %
+--R lquo : (%,OrderedFreeMonoid(vl)) -> %
+--R mindeg : % -> OrderedFreeMonoid(vl)
+--R mindegTerm : % -> Record(k: OrderedFreeMonoid(vl),c: R)
+--R monom : (OrderedFreeMonoid(vl),R) -> %
+--R retract : % -> OrderedFreeMonoid(vl)
+--R retractIfCan : % -> Union(OrderedFreeMonoid(vl),"failed")
+--R rquo : (%,OrderedFreeMonoid(vl)) -> %
--R sh : (%,NonNegativeInteger) -> % if R has COMRING
--R sh : (%,%) -> % if R has COMRING
--R subtractIfCan : (%,%) -> Union(%,"failed")
@@ -43529,6 +43641,7 @@ digraph pic {
--S 1 of 1
)show DirectProductCategory
+--R
--R DirectProductCategory(dim: NonNegativeInteger,R: Type) is a category constructor
--R Abbreviation for DirectProductCategory is DIRPCAT
--R This constructor is exposed in this frame.
@@ -43536,12 +43649,12 @@ digraph pic {
--R
--R------------------------------- Operations --------------------------------
--R -? : % -> % if R has RING 1 : () -> % if R has MONOID
---R 0 : () -> % if R has CABMON coerce : % -> Vector R
---R copy : % -> % directProduct : Vector R -> %
+--R 0 : () -> % if R has CABMON coerce : % -> Vector(R)
+--R copy : % -> % directProduct : Vector(R) -> %
--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R
--R empty : () -> % empty? : % -> Boolean
---R entries : % -> List R eq? : (%,%) -> Boolean
---R index? : (Integer,%) -> Boolean indices : % -> List Integer
+--R entries : % -> List(R) eq? : (%,%) -> Boolean
+--R index? : (Integer,%) -> Boolean indices : % -> List(Integer)
--R map : ((R -> R),%) -> % qelt : (%,Integer) -> R
--R sample : () -> %
--R #? : % -> NonNegativeInteger if $ has finiteAggregate
@@ -43563,10 +43676,10 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if R has ORDRING or R has OAMONS
--R D : (%,(R -> R)) -> % if R has RING
--R D : (%,(R -> R),NonNegativeInteger) -> % if R has RING
---R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
---R D : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
---R D : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
---R D : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
+--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
+--R D : (%,List(Symbol)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
+--R D : (%,Symbol) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
--R D : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Ring))
--R D : % -> % if and(has(R,DifferentialRing),has(R,Ring))
--R ?^? : (%,PositiveInteger) -> % if R has MONOID
@@ -43575,26 +43688,26 @@ digraph pic {
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R characteristic : () -> NonNegativeInteger if R has RING
--R coerce : R -> % if R has SETCAT
---R coerce : Fraction Integer -> % if and(has(R,RetractableTo Fraction Integer),has(R,SetCategory))
---R coerce : Integer -> % if and(has(R,RetractableTo Integer),has(R,SetCategory)) or R has RING
+--R coerce : Fraction(Integer) -> % if and(has(R,RetractableTo(Fraction(Integer))),has(R,SetCategory))
+--R coerce : Integer -> % if and(has(R,RetractableTo(Integer)),has(R,SetCategory)) or R has RING
--R coerce : % -> OutputForm if R has SETCAT
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
--R differentiate : (%,(R -> R)) -> % if R has RING
--R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has RING
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
---R differentiate : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
---R differentiate : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Ring))
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
+--R differentiate : (%,List(Symbol)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
+--R differentiate : (%,Symbol) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Ring))
--R differentiate : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Ring))
--R differentiate : % -> % if and(has(R,DifferentialRing),has(R,Ring))
--R dimension : () -> CardinalNumber if R has FIELD
--R dot : (%,%) -> R if R has RING
--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R fill! : (%,R) -> % if $ has shallowlyMutable
--R first : % -> R if Integer has ORDSET
@@ -43607,27 +43720,27 @@ digraph pic {
--R max : (%,%) -> % if R has ORDRING or R has OAMONS
--R maxIndex : % -> Integer if Integer has ORDSET
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
+--R members : % -> List(R) if $ has finiteAggregate
--R min : (%,%) -> % if R has ORDRING or R has OAMONS
--R minIndex : % -> Integer if Integer has ORDSET
--R more? : (%,NonNegativeInteger) -> Boolean
--R negative? : % -> Boolean if R has ORDRING
--R one? : % -> Boolean if R has MONOID
---R parts : % -> List R if $ has finiteAggregate
+--R parts : % -> List(R) if $ has finiteAggregate
--R positive? : % -> Boolean if R has ORDRING
--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable
--R random : () -> % if R has FINITE
--R recip : % -> Union(%,"failed") if R has MONOID
---R reducedSystem : Matrix % -> Matrix R if R has RING
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring))
---R reducedSystem : Matrix % -> Matrix Integer if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring))
+--R reducedSystem : Matrix(%) -> Matrix(R) if R has RING
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring))
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring))
--R retract : % -> R if R has SETCAT
---R retract : % -> Fraction Integer if and(has(R,RetractableTo Fraction Integer),has(R,SetCategory))
---R retract : % -> Integer if and(has(R,RetractableTo Integer),has(R,SetCategory))
+--R retract : % -> Fraction(Integer) if and(has(R,RetractableTo(Fraction(Integer))),has(R,SetCategory))
+--R retract : % -> Integer if and(has(R,RetractableTo(Integer)),has(R,SetCategory))
--R retractIfCan : % -> Union(R,"failed") if R has SETCAT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if and(has(R,RetractableTo Fraction Integer),has(R,SetCategory))
---R retractIfCan : % -> Union(Integer,"failed") if and(has(R,RetractableTo Integer),has(R,SetCategory))
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if and(has(R,RetractableTo(Fraction(Integer))),has(R,SetCategory))
+--R retractIfCan : % -> Union(Integer,"failed") if and(has(R,RetractableTo(Integer)),has(R,SetCategory))
--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable
--R sign : % -> Integer if R has ORDRING
--R size : () -> NonNegativeInteger if R has FINITE
@@ -44145,20 +44258,21 @@ digraph pic {
--S 1 of 1
)show DivisionRing
+--R
--R DivisionRing is a category constructor
--R Abbreviation for DivisionRing is DIVRING
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIVRING
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> %
+--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
--R ?-? : (%,%) -> % -? : % -> %
--R ?=? : (%,%) -> Boolean 1 : () -> %
--R 0 : () -> % ?^? : (%,Integer) -> %
---R ?^? : (%,PositiveInteger) -> % coerce : Fraction Integer -> %
+--R ?^? : (%,PositiveInteger) -> % coerce : Fraction(Integer) -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R hash : % -> SingleInteger inv : % -> %
--R latex : % -> String one? : % -> Boolean
@@ -44393,7 +44507,8 @@ digraph pic {
--S 1 of 1
)show FiniteRankNonAssociativeAlgebra
---R FiniteRankNonAssociativeAlgebra R: CommutativeRing is a category constructor
+--R
+--R FiniteRankNonAssociativeAlgebra(R: CommutativeRing) is a category constructor
--R Abbreviation for FiniteRankNonAssociativeAlgebra is FINAALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FINAALG
@@ -44412,40 +44527,41 @@ digraph pic {
--R flexible? : () -> Boolean hash : % -> SingleInteger
--R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean
--R jordanAlgebra? : () -> Boolean latex : % -> String
---R leftAlternative? : () -> Boolean leftDiscriminant : Vector % -> R
+--R leftAlternative? : () -> Boolean leftDiscriminant : Vector(%) -> R
--R leftNorm : % -> R leftTrace : % -> R
--R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean
--R powerAssociative? : () -> Boolean rank : () -> PositiveInteger
---R rightAlternative? : () -> Boolean rightDiscriminant : Vector % -> R
---R rightNorm : % -> R rightTrace : % -> R
---R sample : () -> % someBasis : () -> Vector %
---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
+--R rightAlternative? : () -> Boolean rightNorm : % -> R
+--R rightTrace : % -> R sample : () -> %
+--R someBasis : () -> Vector(%) zero? : % -> Boolean
+--R ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
---R associatorDependence : () -> List Vector R if R has INTDOM
---R conditionsForIdempotents : Vector % -> List Polynomial R
---R coordinates : (Vector %,Vector %) -> Matrix R
---R coordinates : (%,Vector %) -> Vector R
---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R
---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM
+--R associatorDependence : () -> List(Vector(R)) if R has INTDOM
+--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R))
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(R)
+--R coordinates : (%,Vector(%)) -> Vector(R)
+--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R)
+--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM
--R leftPower : (%,PositiveInteger) -> %
--R leftRecip : % -> Union(%,"failed") if R has INTDOM
---R leftRegularRepresentation : (%,Vector %) -> Matrix R
---R leftTraceMatrix : Vector % -> Matrix R
+--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R)
+--R leftTraceMatrix : Vector(%) -> Matrix(R)
--R leftUnit : () -> Union(%,"failed") if R has INTDOM
---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM
+--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM
--R noncommutativeJordanAlgebra? : () -> Boolean
--R plenaryPower : (%,PositiveInteger) -> %
--R recip : % -> Union(%,"failed") if R has INTDOM
---R represents : (Vector R,Vector %) -> %
---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R
---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM
+--R represents : (Vector(R),Vector(%)) -> %
+--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R)
+--R rightDiscriminant : Vector(%) -> R
+--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM
--R rightPower : (%,PositiveInteger) -> %
--R rightRecip : % -> Union(%,"failed") if R has INTDOM
---R rightRegularRepresentation : (%,Vector %) -> Matrix R
---R rightTraceMatrix : Vector % -> Matrix R
+--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R)
+--R rightTraceMatrix : Vector(%) -> Matrix(R)
--R rightUnit : () -> Union(%,"failed") if R has INTDOM
---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM
---R structuralConstants : Vector % -> Vector Matrix R
+--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM
+--R structuralConstants : Vector(%) -> Vector(Matrix(R))
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unit : () -> Union(%,"failed") if R has INTDOM
--R
@@ -45375,6 +45491,7 @@ digraph pic {
--S 1 of 1
)show FreeLieAlgebra
+--R
--R FreeLieAlgebra(VarSet: OrderedSet,R: CommutativeRing) is a category constructor
--R Abbreviation for FreeLieAlgebra is FLALG
--R This constructor is exposed in this frame.
@@ -45385,19 +45502,19 @@ digraph pic {
--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> %
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
---R LiePoly : LyndonWord VarSet -> % 0 : () -> %
+--R LiePoly : LyndonWord(VarSet) -> % 0 : () -> %
--R coerce : VarSet -> % coerce : % -> OutputForm
--R construct : (%,%) -> % degree : % -> NonNegativeInteger
--R eval : (%,VarSet,%) -> % hash : % -> SingleInteger
--R latex : % -> String mirror : % -> %
---R sample : () -> % varList : % -> List VarSet
+--R sample : () -> % varList : % -> List(VarSet)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?/? : (%,R) -> % if R has FIELD
--R coef : (XRecursivePolynomial(VarSet,R),%) -> R
--R coerce : % -> XRecursivePolynomial(VarSet,R)
--R coerce : % -> XDistributedPolynomial(VarSet,R)
---R eval : (%,List VarSet,List %) -> %
+--R eval : (%,List(VarSet),List(%)) -> %
--R lquo : (XRecursivePolynomial(VarSet,R),%) -> XRecursivePolynomial(VarSet,R)
--R rquo : (XRecursivePolynomial(VarSet,R),%) -> XRecursivePolynomial(VarSet,R)
--R subtractIfCan : (%,%) -> Union(%,"failed")
@@ -45922,7 +46039,8 @@ digraph pic {
--S 1 of 1
)show MonogenicLinearOperator
---R MonogenicLinearOperator R: Ring is a category constructor
+--R
+--R MonogenicLinearOperator(R: Ring) is a category constructor
--R Abbreviation for MonogenicLinearOperator is MLO
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MLO
@@ -46210,7 +46328,8 @@ digraph pic {
--S 1 of 1
)show OctonionCategory
---R OctonionCategory R: CommutativeRing is a category constructor
+--R
+--R OctonionCategory(R: CommutativeRing) is a category constructor
--R Abbreviation for OctonionCategory is OC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for OC
@@ -46244,28 +46363,28 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
---R convert : % -> InputForm if R has KONVERT INFORM
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT))
+--R convert : % -> InputForm if R has KONVERT(INFORM)
--R ?.? : (%,R) -> % if R has ELTAB(R,R)
--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R)
---R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R)
---R eval : (%,List Equation R) -> % if R has EVALAB R
---R eval : (%,Equation R) -> % if R has EVALAB R
---R eval : (%,R,R) -> % if R has EVALAB R
---R eval : (%,List R,List R) -> % if R has EVALAB R
+--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R)
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R)
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R)
+--R eval : (%,R,R) -> % if R has EVALAB(R)
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R)
--R index : PositiveInteger -> % if R has FINITE
--R lookup : % -> PositiveInteger if R has FINITE
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
--R random : () -> % if R has FINITE
---R rational : % -> Fraction Integer if R has INS
+--R rational : % -> Fraction(Integer) if R has INS
--R rational? : % -> Boolean if R has INS
---R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R size : () -> NonNegativeInteger if R has FINITE
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
@@ -46781,7 +46900,8 @@ digraph pic {
--S 1 of 1
)show QuaternionCategory
---R QuaternionCategory R: CommutativeRing is a category constructor
+--R
+--R QuaternionCategory(R: CommutativeRing) is a category constructor
--R Abbreviation for QuaternionCategory is QUATCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for QUATCAT
@@ -46805,8 +46925,8 @@ digraph pic {
--R real : % -> R recip : % -> Union(%,"failed")
--R retract : % -> R sample : () -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (Fraction Integer,%) -> % if R has FIELD
---R ?*? : (%,Fraction Integer) -> % if R has FIELD
+--R ?*? : (Fraction(Integer),%) -> % if R has FIELD
+--R ?*? : (%,Fraction(Integer)) -> % if R has FIELD
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
@@ -46815,46 +46935,46 @@ digraph pic {
--R ?>? : (%,%) -> Boolean if R has ORDSET
--R ?>=? : (%,%) -> Boolean if R has ORDSET
--R D : (%,(R -> R),NonNegativeInteger) -> %
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol) -> % if R has PDRING SYMBOL
---R D : (%,Symbol) -> % if R has PDRING SYMBOL
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol) -> % if R has PDRING(SYMBOL)
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
--R ?^? : (%,Integer) -> % if R has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT
---R convert : % -> InputForm if R has KONVERT INFORM
+--R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT))
+--R convert : % -> InputForm if R has KONVERT(INFORM)
--R differentiate : (%,(R -> R)) -> %
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL)
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
--R differentiate : % -> % if R has DIFRING
--R ?.? : (%,R) -> % if R has ELTAB(R,R)
--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R)
---R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R)
---R eval : (%,List Equation R) -> % if R has EVALAB R
---R eval : (%,Equation R) -> % if R has EVALAB R
---R eval : (%,R,R) -> % if R has EVALAB R
---R eval : (%,List R,List R) -> % if R has EVALAB R
+--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R)
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R)
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R)
+--R eval : (%,R,R) -> % if R has EVALAB(R)
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R)
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
---R rational : % -> Fraction Integer if R has INS
+--R rational : % -> Fraction(Integer) if R has INS
--R rational? : % -> Boolean if R has INS
---R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R
--E 1
@@ -47350,6 +47470,7 @@ The SquareMatrix domain is for square matrices of fixed dimension.
--S 1 of 1
)show SquareMatrixCategory
+--R
--R SquareMatrixCategory(ndim: NonNegativeInteger,R: Ring,Row: DirectProductCategory(t#1,t#2),Col: DirectProductCategory(t#1,t#2)) is a category constructor
--R Abbreviation for SquareMatrixCategory is SMATCAT
--R This constructor is exposed in this frame.
@@ -47368,13 +47489,13 @@ The SquareMatrix domain is for square matrices of fixed dimension.
--R coerce : R -> % coerce : Integer -> %
--R coerce : % -> OutputForm column : (%,Integer) -> Col
--R copy : % -> % diagonal : % -> Row
---R diagonal? : % -> Boolean diagonalMatrix : List R -> %
+--R diagonal? : % -> Boolean diagonalMatrix : List(R) -> %
--R diagonalProduct : % -> R elt : (%,Integer,Integer) -> R
--R elt : (%,Integer,Integer,R) -> R empty : () -> %
--R empty? : % -> Boolean eq? : (%,%) -> Boolean
--R hash : % -> SingleInteger latex : % -> String
---R listOfLists : % -> List List R map : ((R -> R),%) -> %
---R map : (((R,R) -> R),%,%) -> % matrix : List List R -> %
+--R listOfLists : % -> List(List(R)) map : ((R -> R),%) -> %
+--R map : (((R,R) -> R),%,%) -> % matrix : List(List(R)) -> %
--R maxColIndex : % -> Integer maxRowIndex : % -> Integer
--R minColIndex : % -> Integer minRowIndex : % -> Integer
--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger
@@ -47390,52 +47511,52 @@ The SquareMatrix domain is for square matrices of fixed dimension.
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
---R D : (%,Symbol) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol) -> % if R has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
+--R D : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
--R D : (%,(R -> R),NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R characteristic : () -> NonNegativeInteger
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT))
--R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate
--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate
---R determinant : % -> R if R has commutative *
+--R determinant : % -> R if R has commutative(*)
--R differentiate : % -> % if R has DIFRING
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
+--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
--R differentiate : (%,(R -> R)) -> %
---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT
---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT
--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R inverse : % -> Union(%,"failed") if R has FIELD
--R less? : (%,NonNegativeInteger) -> Boolean
--R map! : ((R -> R),%) -> % if $ has shallowlyMutable
--R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate
---R members : % -> List R if $ has finiteAggregate
---R minordet : % -> R if R has commutative *
+--R members : % -> List(R) if $ has finiteAggregate
+--R minordet : % -> R if R has commutative(*)
--R more? : (%,NonNegativeInteger) -> Boolean
---R nullSpace : % -> List Col if R has INTDOM
+--R nullSpace : % -> List(Col) if R has INTDOM
--R nullity : % -> NonNegativeInteger if R has INTDOM
---R parts : % -> List R if $ has finiteAggregate
+--R parts : % -> List(R) if $ has finiteAggregate
--R rank : % -> NonNegativeInteger if R has INTDOM
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R rowEchelon : % -> % if R has EUCDOM
--R size? : (%,NonNegativeInteger) -> Boolean
--R subtractIfCan : (%,%) -> Union(%,"failed")
@@ -47976,6 +48097,7 @@ digraph pic {
--S 1 of 1
)show XPolynomialsCat
+--R
--R XPolynomialsCat(vl: OrderedSet,R: Ring) is a category constructor
--R Abbreviation for XPolynomialsCat is XPOLYC
--R This constructor is exposed in this frame.
@@ -48000,22 +48122,22 @@ digraph pic {
--R quasiRegular : % -> % quasiRegular? : % -> Boolean
--R recip : % -> Union(%,"failed") rquo : (%,%) -> %
--R rquo : (%,vl) -> % sample : () -> %
---R varList : % -> List vl zero? : % -> Boolean
+--R varList : % -> List(vl) zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R coef : (%,OrderedFreeMonoid vl) -> R
---R coerce : OrderedFreeMonoid vl -> %
---R lquo : (%,OrderedFreeMonoid vl) -> %
---R maxdeg : % -> OrderedFreeMonoid vl
---R mindeg : % -> OrderedFreeMonoid vl
---R mindegTerm : % -> Record(k: OrderedFreeMonoid vl,c: R)
---R monom : (OrderedFreeMonoid vl,R) -> %
---R retract : % -> OrderedFreeMonoid vl
---R retractIfCan : % -> Union(OrderedFreeMonoid vl,"failed")
---R rquo : (%,OrderedFreeMonoid vl) -> %
+--R coef : (%,OrderedFreeMonoid(vl)) -> R
+--R coerce : OrderedFreeMonoid(vl) -> %
+--R lquo : (%,OrderedFreeMonoid(vl)) -> %
+--R maxdeg : % -> OrderedFreeMonoid(vl)
+--R mindeg : % -> OrderedFreeMonoid(vl)
+--R mindegTerm : % -> Record(k: OrderedFreeMonoid(vl),c: R)
+--R monom : (OrderedFreeMonoid(vl),R) -> %
+--R retract : % -> OrderedFreeMonoid(vl)
+--R retractIfCan : % -> Union(OrderedFreeMonoid(vl),"failed")
+--R rquo : (%,OrderedFreeMonoid(vl)) -> %
--R sh : (%,NonNegativeInteger) -> % if R has COMRING
--R sh : (%,%) -> % if R has COMRING
--R subtractIfCan : (%,%) -> Union(%,"failed")
@@ -48301,6 +48423,7 @@ digraph pic {
--S 1 of 1
)show AbelianMonoidRing
+--R
--R AbelianMonoidRing(R: Ring,E: OrderedAbelianMonoid) is a category constructor
--R Abbreviation for AbelianMonoidRing is AMR
--R This constructor is exposed in this frame.
@@ -48322,8 +48445,8 @@ digraph pic {
--R one? : % -> Boolean recip : % -> Union(%,"failed")
--R reductum : % -> % sample : () -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
@@ -48333,7 +48456,7 @@ digraph pic {
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
--R coerce : R -> % if R has COMRING
--R coerce : % -> % if R has INTDOM
---R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT))
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unit? : % -> Boolean if R has INTDOM
@@ -48933,7 +49056,8 @@ digraph pic {
--S 1 of 1
)show FramedNonAssociativeAlgebra
---R FramedNonAssociativeAlgebra R: CommutativeRing is a category constructor
+--R
+--R FramedNonAssociativeAlgebra(R: CommutativeRing) is a category constructor
--R Abbreviation for FramedNonAssociativeAlgebra is FRNAALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FRNAALG
@@ -48946,59 +49070,59 @@ digraph pic {
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 0 : () -> % alternative? : () -> Boolean
--R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean
---R antiCommutator : (%,%) -> % apply : (Matrix R,%) -> %
+--R antiCommutator : (%,%) -> % apply : (Matrix(R),%) -> %
--R associative? : () -> Boolean associator : (%,%,%) -> %
---R basis : () -> Vector % coerce : % -> OutputForm
+--R basis : () -> Vector(%) coerce : % -> OutputForm
--R commutative? : () -> Boolean commutator : (%,%) -> %
---R convert : Vector R -> % convert : % -> Vector R
---R coordinates : % -> Vector R ?.? : (%,Integer) -> R
+--R convert : Vector(R) -> % convert : % -> Vector(R)
+--R coordinates : % -> Vector(R) ?.? : (%,Integer) -> R
--R flexible? : () -> Boolean hash : % -> SingleInteger
--R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean
--R jordanAlgebra? : () -> Boolean latex : % -> String
--R leftAlternative? : () -> Boolean leftDiscriminant : () -> R
---R leftDiscriminant : Vector % -> R leftNorm : % -> R
---R leftTrace : % -> R leftTraceMatrix : () -> Matrix R
+--R leftDiscriminant : Vector(%) -> R leftNorm : % -> R
+--R leftTrace : % -> R leftTraceMatrix : () -> Matrix(R)
--R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean
--R powerAssociative? : () -> Boolean rank : () -> PositiveInteger
---R represents : Vector R -> % rightAlternative? : () -> Boolean
---R rightDiscriminant : () -> R rightDiscriminant : Vector % -> R
---R rightNorm : % -> R rightTrace : % -> R
---R rightTraceMatrix : () -> Matrix R sample : () -> %
---R someBasis : () -> Vector % zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
+--R represents : Vector(R) -> % rightAlternative? : () -> Boolean
+--R rightDiscriminant : () -> R rightNorm : % -> R
+--R rightTrace : % -> R rightTraceMatrix : () -> Matrix(R)
+--R sample : () -> % someBasis : () -> Vector(%)
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
---R associatorDependence : () -> List Vector R if R has INTDOM
---R conditionsForIdempotents : () -> List Polynomial R
---R conditionsForIdempotents : Vector % -> List Polynomial R
---R coordinates : Vector % -> Matrix R
---R coordinates : (Vector %,Vector %) -> Matrix R
---R coordinates : (%,Vector %) -> Vector R
---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R
---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM
+--R associatorDependence : () -> List(Vector(R)) if R has INTDOM
+--R conditionsForIdempotents : () -> List(Polynomial(R))
+--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R))
+--R coordinates : Vector(%) -> Matrix(R)
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(R)
+--R coordinates : (%,Vector(%)) -> Vector(R)
+--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R)
+--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM
--R leftPower : (%,PositiveInteger) -> %
---R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD
+--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD
--R leftRecip : % -> Union(%,"failed") if R has INTDOM
---R leftRegularRepresentation : % -> Matrix R
---R leftRegularRepresentation : (%,Vector %) -> Matrix R
---R leftTraceMatrix : Vector % -> Matrix R
+--R leftRegularRepresentation : % -> Matrix(R)
+--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R)
+--R leftTraceMatrix : Vector(%) -> Matrix(R)
--R leftUnit : () -> Union(%,"failed") if R has INTDOM
---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM
+--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM
--R noncommutativeJordanAlgebra? : () -> Boolean
--R plenaryPower : (%,PositiveInteger) -> %
--R recip : % -> Union(%,"failed") if R has INTDOM
---R represents : (Vector R,Vector %) -> %
---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R
---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM
+--R represents : (Vector(R),Vector(%)) -> %
+--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R)
+--R rightDiscriminant : Vector(%) -> R
+--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM
--R rightPower : (%,PositiveInteger) -> %
---R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD
+--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD
--R rightRecip : % -> Union(%,"failed") if R has INTDOM
---R rightRegularRepresentation : % -> Matrix R
---R rightRegularRepresentation : (%,Vector %) -> Matrix R
---R rightTraceMatrix : Vector % -> Matrix R
+--R rightRegularRepresentation : % -> Matrix(R)
+--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R)
+--R rightTraceMatrix : Vector(%) -> Matrix(R)
--R rightUnit : () -> Union(%,"failed") if R has INTDOM
---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM
---R structuralConstants : () -> Vector Matrix R
---R structuralConstants : Vector % -> Vector Matrix R
+--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM
+--R structuralConstants : () -> Vector(Matrix(R))
+--R structuralConstants : Vector(%) -> Vector(Matrix(R))
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unit : () -> Union(%,"failed") if R has INTDOM
--R
@@ -49622,6 +49746,7 @@ digraph pic {
--S 1 of 1
)show GcdDomain
+--R
--R GcdDomain is a category constructor
--R Abbreviation for GcdDomain is GCDDOM
--R This constructor is exposed in this frame.
@@ -49635,9 +49760,9 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm gcd : List % -> %
+--R coerce : % -> OutputForm gcd : List(%) -> %
--R gcd : (%,%) -> % hash : % -> SingleInteger
---R latex : % -> String lcm : List % -> %
+--R latex : % -> String lcm : List(%) -> %
--R lcm : (%,%) -> % one? : % -> Boolean
--R recip : % -> Union(%,"failed") sample : () -> %
--R unit? : % -> Boolean unitCanonical : % -> %
@@ -49647,7 +49772,7 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R exquo : (%,%) -> Union(%,"failed")
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -50155,6 +50280,7 @@ digraph pic {
--S 1 of 1
)show FiniteAbelianMonoidRing
+--R
--R FiniteAbelianMonoidRing(R: Ring,E: OrderedAbelianMonoid) is a category constructor
--R Abbreviation for FiniteAbelianMonoidRing is FAMR
--R This constructor is exposed in this frame.
@@ -50168,7 +50294,7 @@ digraph pic {
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R
---R coefficients : % -> List R coerce : R -> %
+--R coefficients : % -> List(R) coerce : R -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R degree : % -> E ground : % -> R
--R ground? : % -> Boolean hash : % -> SingleInteger
@@ -50180,8 +50306,8 @@ digraph pic {
--R recip : % -> Union(%,"failed") reductum : % -> %
--R retract : % -> R sample : () -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
@@ -50190,18 +50316,18 @@ digraph pic {
--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT))
--R coerce : % -> % if R has INTDOM
--R content : % -> R if R has GCDDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R numberOfMonomials : % -> NonNegativeInteger
--R primitivePart : % -> % if R has GCDDOM
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unit? : % -> Boolean if R has INTDOM
--R unitCanonical : % -> % if R has INTDOM
@@ -50607,57 +50733,58 @@ digraph pic {
--S 1 of 1
)show IntervalCategory
---R IntervalCategory R: Join(FloatingPointSystem,TranscendentalFunctionCategory) is a category constructor
+--R
+--R IntervalCategory(R: Join(FloatingPointSystem,TranscendentalFunctionCategory)) is a category constructor
--R Abbreviation for IntervalCategory is INTCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for INTCAT
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> %
---R ?**? : (%,%) -> % ?**? : (%,PositiveInteger) -> %
---R ?+? : (%,%) -> % ?-? : (%,%) -> %
---R -? : % -> % ? : (%,%) -> Boolean
---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean
---R 1 : () -> % 0 : () -> %
---R ?^? : (%,PositiveInteger) -> % acos : % -> %
---R acosh : % -> % acot : % -> %
---R acoth : % -> % acsc : % -> %
---R acsch : % -> % asec : % -> %
---R asech : % -> % asin : % -> %
---R asinh : % -> % associates? : (%,%) -> Boolean
---R atan : % -> % atanh : % -> %
---R coerce : Integer -> % coerce : % -> %
---R coerce : Integer -> % coerce : % -> OutputForm
---R contains? : (%,R) -> Boolean cos : % -> %
---R cosh : % -> % cot : % -> %
---R coth : % -> % csc : % -> %
---R csch : % -> % exp : % -> %
---R gcd : List % -> % gcd : (%,%) -> %
---R hash : % -> SingleInteger inf : % -> R
---R interval : Fraction Integer -> % interval : R -> %
---R interval : (R,R) -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
---R log : % -> % max : (%,%) -> %
---R min : (%,%) -> % negative? : % -> Boolean
---R nthRoot : (%,Integer) -> % one? : % -> Boolean
---R pi : () -> % positive? : % -> Boolean
---R qinterval : (R,R) -> % recip : % -> Union(%,"failed")
---R retract : % -> Integer sample : () -> %
---R sec : % -> % sech : % -> %
---R sin : % -> % sinh : % -> %
---R sqrt : % -> % sup : % -> R
---R tan : % -> % tanh : % -> %
---R unit? : % -> Boolean unitCanonical : % -> %
---R width : % -> R zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
+--R ?*? : (PositiveInteger,%) -> % ?**? : (%,%) -> %
+--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
+--R ?-? : (%,%) -> % -? : % -> %
+--R ? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
+--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
+--R ?>=? : (%,%) -> Boolean 1 : () -> %
+--R 0 : () -> % ?^? : (%,PositiveInteger) -> %
+--R acos : % -> % acosh : % -> %
+--R acot : % -> % acoth : % -> %
+--R acsc : % -> % acsch : % -> %
+--R asec : % -> % asech : % -> %
+--R asin : % -> % asinh : % -> %
+--R associates? : (%,%) -> Boolean atan : % -> %
+--R atanh : % -> % coerce : Integer -> %
+--R coerce : % -> % coerce : Integer -> %
+--R coerce : % -> OutputForm contains? : (%,R) -> Boolean
+--R cos : % -> % cosh : % -> %
+--R cot : % -> % coth : % -> %
+--R csc : % -> % csch : % -> %
+--R exp : % -> % gcd : List(%) -> %
+--R gcd : (%,%) -> % hash : % -> SingleInteger
+--R inf : % -> R interval : Fraction(Integer) -> %
+--R interval : R -> % interval : (R,R) -> %
+--R latex : % -> String lcm : List(%) -> %
+--R lcm : (%,%) -> % log : % -> %
+--R max : (%,%) -> % min : (%,%) -> %
+--R negative? : % -> Boolean nthRoot : (%,Integer) -> %
+--R one? : % -> Boolean pi : () -> %
+--R positive? : % -> Boolean qinterval : (R,R) -> %
+--R recip : % -> Union(%,"failed") retract : % -> Integer
+--R sample : () -> % sec : % -> %
+--R sech : % -> % sin : % -> %
+--R sinh : % -> % sqrt : % -> %
+--R sup : % -> R tan : % -> %
+--R tanh : % -> % unit? : % -> Boolean
+--R unitCanonical : % -> % width : % -> R
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
+--R ?**? : (%,Fraction(Integer)) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R exquo : (%,%) -> Union(%,"failed")
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R retractIfCan : % -> Union(Integer,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
@@ -51037,6 +51164,7 @@ digraph pic {
--S 1 of 1
)show PowerSeriesCategory
+--R
--R PowerSeriesCategory(Coef: Ring,Expon: OrderedAbelianMonoid,Var: OrderedSet) is a category constructor
--R Abbreviation for PowerSeriesCategory is PSCAT
--R This constructor is exposed in this frame.
@@ -51058,10 +51186,10 @@ digraph pic {
--R monomial : (Coef,Expon) -> % monomial? : % -> Boolean
--R one? : % -> Boolean pole? : % -> Boolean
--R recip : % -> Union(%,"failed") reductum : % -> %
---R sample : () -> % variables : % -> List Var
+--R sample : () -> % variables : % -> List(Var)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,Coef) -> % if Coef has FIELD
@@ -51071,9 +51199,9 @@ digraph pic {
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
--R coerce : Coef -> % if Coef has COMRING
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
---R monomial : (%,List Var,List Expon) -> %
+--R monomial : (%,List(Var),List(Expon)) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
@@ -51383,6 +51511,7 @@ digraph pic {
--S 1 of 1
)show PrincipalIdealDomain
+--R
--R PrincipalIdealDomain is a category constructor
--R Abbreviation for PrincipalIdealDomain is PID
--R This constructor is exposed in this frame.
@@ -51396,9 +51525,9 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm gcd : List % -> %
+--R coerce : % -> OutputForm gcd : List(%) -> %
--R gcd : (%,%) -> % hash : % -> SingleInteger
---R latex : % -> String lcm : List % -> %
+--R latex : % -> String lcm : List(%) -> %
--R lcm : (%,%) -> % one? : % -> Boolean
--R recip : % -> Union(%,"failed") sample : () -> %
--R unit? : % -> Boolean unitCanonical : % -> %
@@ -51407,10 +51536,10 @@ digraph pic {
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -51635,6 +51764,7 @@ digraph pic {
--S 1 of 1
)show UniqueFactorizationDomain
+--R
--R UniqueFactorizationDomain is a category constructor
--R Abbreviation for UniqueFactorizationDomain is UFD
--R This constructor is exposed in this frame.
@@ -51648,13 +51778,13 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm factor : % -> Factored %
---R gcd : List % -> % gcd : (%,%) -> %
+--R coerce : % -> OutputForm factor : % -> Factored(%)
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R one? : % -> Boolean prime? : % -> Boolean
--R recip : % -> Union(%,"failed") sample : () -> %
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R unit? : % -> Boolean unitCanonical : % -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
@@ -51662,7 +51792,7 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R exquo : (%,%) -> Union(%,"failed")
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -51904,7 +52034,8 @@ digraph pic {
--S 1 of 1
)show DivisorCategory
---R DivisorCategory S: SetCategory is a category constructor
+--R
+--R DivisorCategory(S: SetCategory) is a category constructor
--R Abbreviation for DivisorCategory is DIVCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIVCAT
@@ -51925,15 +52056,15 @@ digraph pic {
--R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> Integer
--R nthFactor : (%,Integer) -> S retract : % -> S
--R sample : () -> % size : % -> NonNegativeInteger
---R split : % -> List % supp : % -> List S
---R suppOfPole : % -> List S suppOfZero : % -> List S
+--R split : % -> List(%) supp : % -> List(S)
+--R suppOfPole : % -> List(S) suppOfZero : % -> List(S)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R highCommonTerms : (%,%) -> % if Integer has OAMON
--R mapCoef : ((Integer -> Integer),%) -> %
--R retractIfCan : % -> Union(S,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R terms : % -> List Record(gen: S,exp: Integer)
+--R terms : % -> List(Record(gen: S,exp: Integer))
--R
--E 1
@@ -52159,6 +52290,7 @@ digraph pic {
--S 1 of 1
)show EuclideanDomain
+--R
--R EuclideanDomain is a category constructor
--R Abbreviation for EuclideanDomain is EUCDOM
--R This constructor is exposed in this frame.
@@ -52172,9 +52304,9 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm gcd : List % -> %
+--R coerce : % -> OutputForm gcd : List(%) -> %
--R gcd : (%,%) -> % hash : % -> SingleInteger
---R latex : % -> String lcm : List % -> %
+--R latex : % -> String lcm : List(%) -> %
--R lcm : (%,%) -> % one? : % -> Boolean
--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
--R ?rem? : (%,%) -> % sample : () -> %
@@ -52187,13 +52319,13 @@ digraph pic {
--R characteristic : () -> NonNegativeInteger
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -52558,6 +52690,7 @@ digraph pic {
--S 1 of 1
)show MultivariateTaylorSeriesCategory
+--R
--R MultivariateTaylorSeriesCategory(Coef: Ring,Var: OrderedSet) is a category constructor
--R Abbreviation for MultivariateTaylorSeriesCategory is MTSCAT
--R This constructor is exposed in this frame.
@@ -52569,86 +52702,87 @@ digraph pic {
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
---R D : (%,List Var) -> % D : (%,Var) -> %
+--R D : (%,List(Var)) -> % D : (%,Var) -> %
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> %
--R coerce : % -> OutputForm complete : % -> %
---R differentiate : (%,Var) -> % eval : (%,List %,List %) -> %
---R eval : (%,%,%) -> % eval : (%,Equation %) -> %
---R eval : (%,List Equation %) -> % eval : (%,List Var,List %) -> %
---R eval : (%,Var,%) -> % hash : % -> SingleInteger
---R latex : % -> String leadingCoefficient : % -> Coef
---R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> %
---R monomial? : % -> Boolean one? : % -> Boolean
---R pole? : % -> Boolean recip : % -> Union(%,"failed")
---R reductum : % -> % sample : () -> %
---R variables : % -> List Var zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
+--R differentiate : (%,Var) -> % eval : (%,%,%) -> %
+--R eval : (%,Equation(%)) -> % eval : (%,Var,%) -> %
+--R hash : % -> SingleInteger latex : % -> String
+--R leadingCoefficient : % -> Coef leadingMonomial : % -> %
+--R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean
+--R one? : % -> Boolean pole? : % -> Boolean
+--R recip : % -> Union(%,"failed") reductum : % -> %
+--R sample : () -> % variables : % -> List(Var)
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,Coef) -> % if Coef has FIELD
---R D : (%,List Var,List NonNegativeInteger) -> %
+--R D : (%,List(Var),List(NonNegativeInteger)) -> %
--R D : (%,Var,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
---R acos : % -> % if Coef has ALGEBRA FRAC INT
---R acosh : % -> % if Coef has ALGEBRA FRAC INT
---R acot : % -> % if Coef has ALGEBRA FRAC INT
---R acoth : % -> % if Coef has ALGEBRA FRAC INT
---R acsc : % -> % if Coef has ALGEBRA FRAC INT
---R acsch : % -> % if Coef has ALGEBRA FRAC INT
---R asec : % -> % if Coef has ALGEBRA FRAC INT
---R asech : % -> % if Coef has ALGEBRA FRAC INT
---R asin : % -> % if Coef has ALGEBRA FRAC INT
---R asinh : % -> % if Coef has ALGEBRA FRAC INT
+--R acos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R associates? : (%,%) -> Boolean if Coef has INTDOM
---R atan : % -> % if Coef has ALGEBRA FRAC INT
---R atanh : % -> % if Coef has ALGEBRA FRAC INT
+--R atan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
---R coefficient : (%,List Var,List NonNegativeInteger) -> %
+--R coefficient : (%,List(Var),List(NonNegativeInteger)) -> %
--R coefficient : (%,Var,NonNegativeInteger) -> %
---R coefficient : (%,IndexedExponents Var) -> Coef
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
+--R coefficient : (%,IndexedExponents(Var)) -> Coef
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R coerce : % -> % if Coef has INTDOM
--R coerce : Coef -> % if Coef has COMRING
---R cos : % -> % if Coef has ALGEBRA FRAC INT
---R cosh : % -> % if Coef has ALGEBRA FRAC INT
---R cot : % -> % if Coef has ALGEBRA FRAC INT
---R coth : % -> % if Coef has ALGEBRA FRAC INT
---R csc : % -> % if Coef has ALGEBRA FRAC INT
---R csch : % -> % if Coef has ALGEBRA FRAC INT
---R degree : % -> IndexedExponents Var
---R differentiate : (%,List Var,List NonNegativeInteger) -> %
+--R cos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R coth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csch : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R degree : % -> IndexedExponents(Var)
+--R differentiate : (%,List(Var),List(NonNegativeInteger)) -> %
--R differentiate : (%,Var,NonNegativeInteger) -> %
---R differentiate : (%,List Var) -> %
---R exp : % -> % if Coef has ALGEBRA FRAC INT
+--R differentiate : (%,List(Var)) -> %
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
+--R eval : (%,List(Var),List(%)) -> %
+--R exp : % -> % if Coef has ALGEBRA(FRAC(INT))
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
--R extend : (%,NonNegativeInteger) -> %
---R integrate : (%,Var) -> % if Coef has ALGEBRA FRAC INT
---R log : % -> % if Coef has ALGEBRA FRAC INT
---R monomial : (%,List Var,List NonNegativeInteger) -> %
+--R integrate : (%,Var) -> % if Coef has ALGEBRA(FRAC(INT))
+--R log : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R monomial : (%,List(Var),List(NonNegativeInteger)) -> %
--R monomial : (%,Var,NonNegativeInteger) -> %
---R monomial : (Coef,IndexedExponents Var) -> %
---R monomial : (%,Var,IndexedExponents Var) -> %
---R monomial : (%,List Var,List IndexedExponents Var) -> %
---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT
+--R monomial : (Coef,IndexedExponents(Var)) -> %
+--R monomial : (%,Var,IndexedExponents(Var)) -> %
+--R monomial : (%,List(Var),List(IndexedExponents(Var))) -> %
+--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R order : (%,Var,NonNegativeInteger) -> NonNegativeInteger
--R order : (%,Var) -> NonNegativeInteger
---R pi : () -> % if Coef has ALGEBRA FRAC INT
---R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef
---R polynomial : (%,NonNegativeInteger) -> Polynomial Coef
---R sec : % -> % if Coef has ALGEBRA FRAC INT
---R sech : % -> % if Coef has ALGEBRA FRAC INT
---R sin : % -> % if Coef has ALGEBRA FRAC INT
---R sinh : % -> % if Coef has ALGEBRA FRAC INT
---R sqrt : % -> % if Coef has ALGEBRA FRAC INT
+--R pi : () -> % if Coef has ALGEBRA(FRAC(INT))
+--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial(Coef)
+--R polynomial : (%,NonNegativeInteger) -> Polynomial(Coef)
+--R sec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT))
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tan : % -> % if Coef has ALGEBRA FRAC INT
---R tanh : % -> % if Coef has ALGEBRA FRAC INT
+--R tan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
@@ -53031,6 +53165,7 @@ digraph pic {
--S 1 of 1
)show PolynomialFactorizationExplicit
+--R
--R PolynomialFactorizationExplicit is a category constructor
--R Abbreviation for PolynomialFactorizationExplicit is PFECAT
--R This constructor is exposed in this frame.
@@ -53044,13 +53179,13 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm factor : % -> Factored %
---R gcd : List % -> % gcd : (%,%) -> %
+--R coerce : % -> OutputForm factor : % -> Factored(%)
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R one? : % -> Boolean prime? : % -> Boolean
--R recip : % -> Union(%,"failed") sample : () -> %
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R unit? : % -> Boolean unitCanonical : % -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
@@ -53058,13 +53193,13 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ
---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ
--R exquo : (%,%) -> Union(%,"failed")
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed")
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed")
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -53367,6 +53502,7 @@ digraph pic {
--S 1 of 1
)show UnivariatePowerSeriesCategory
+--R
--R UnivariatePowerSeriesCategory(Coef: Ring,Expon: OrderedAbelianMonoid) is a category constructor
--R Abbreviation for UnivariatePowerSeriesCategory is UPSCAT
--R This constructor is exposed in this frame.
@@ -53393,17 +53529,17 @@ digraph pic {
--R sample : () -> % truncate : (%,Expon,Expon) -> %
--R truncate : (%,Expon) -> % variable : % -> Symbol
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,Coef) -> % if Coef has FIELD
--R D : % -> % if Coef has *: (Expon,Coef) -> Coef
--R D : (%,NonNegativeInteger) -> % if Coef has *: (Expon,Coef) -> Coef
---R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
---R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
+--R D : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
+--R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
+--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
--R ?^? : (%,NonNegativeInteger) -> %
--R approximate : (%,Expon) -> Coef if Coef has **: (Coef,Expon) -> Coef and Coef has coerce: Symbol -> Coef
--R associates? : (%,%) -> Boolean if Coef has INTDOM
@@ -53411,25 +53547,25 @@ digraph pic {
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
--R coerce : Coef -> % if Coef has COMRING
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R differentiate : % -> % if Coef has *: (Expon,Coef) -> Coef
--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Expon,Coef) -> Coef
---R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
---R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Expon,Coef) -> Coef
+--R differentiate : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
+--R differentiate : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef
--R ?.? : (%,%) -> % if Expon has SGROUP
---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Expon) -> Coef
+--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Expon) -> Coef
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
---R monomial : (%,List SingletonAsOrderedSet,List Expon) -> %
+--R monomial : (%,List(SingletonAsOrderedSet),List(Expon)) -> %
--R monomial : (%,SingletonAsOrderedSet,Expon) -> %
--R multiplyExponents : (%,PositiveInteger) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R terms : % -> Stream Record(k: Expon,c: Coef)
+--R terms : % -> Stream(Record(k: Expon,c: Coef))
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R
--E 1
@@ -53864,13 +54000,14 @@ digraph pic {
--S 1 of 1
)show Field
+--R
--R Field is a category constructor
--R Abbreviation for Field is FIELD
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FIELD
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -53878,17 +54015,17 @@ digraph pic {
--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> %
+--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> %
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm factor : % -> Factored %
---R gcd : List % -> % gcd : (%,%) -> %
+--R coerce : % -> OutputForm factor : % -> Factored(%)
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger inv : % -> %
---R latex : % -> String lcm : List % -> %
+--R latex : % -> String lcm : List(%) -> %
--R lcm : (%,%) -> % one? : % -> Boolean
--R prime? : % -> Boolean ?quo? : (%,%) -> %
--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
--R sample : () -> % sizeLess? : (%,%) -> Boolean
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R unit? : % -> Boolean unitCanonical : % -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
@@ -53897,13 +54034,13 @@ digraph pic {
--R characteristic : () -> NonNegativeInteger
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -54189,6 +54326,7 @@ digraph pic {
--S 1 of 1
)show IntegerNumberSystem
+--R
--R IntegerNumberSystem is a category constructor
--R Abbreviation for IntegerNumberSystem is INS
--R This constructor is exposed in this frame.
@@ -54209,16 +54347,16 @@ digraph pic {
--R bit? : (%,%) -> Boolean coerce : Integer -> %
--R coerce : % -> % coerce : Integer -> %
--R coerce : % -> OutputForm convert : % -> DoubleFloat
---R convert : % -> Float convert : % -> Pattern Integer
+--R convert : % -> Float convert : % -> Pattern(Integer)
--R convert : % -> InputForm convert : % -> Integer
--R copy : % -> % dec : % -> %
--R differentiate : % -> % even? : % -> Boolean
---R factor : % -> Factored % factorial : % -> %
---R gcd : List % -> % gcd : (%,%) -> %
+--R factor : % -> Factored(%) factorial : % -> %
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> % hash : % -> SingleInteger
--R inc : % -> % init : () -> %
--R invmod : (%,%) -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R length : % -> % mask : % -> %
--R max : (%,%) -> % min : (%,%) -> %
--R mulmod : (%,%,%) -> % negative? : % -> Boolean
@@ -54227,11 +54365,11 @@ digraph pic {
--R positiveRemainder : (%,%) -> % powmod : (%,%,%) -> %
--R prime? : % -> Boolean ?quo? : (%,%) -> %
--R random : % -> % random : () -> %
---R rational : % -> Fraction Integer rational? : % -> Boolean
+--R rational : % -> Fraction(Integer) rational? : % -> Boolean
--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
--R retract : % -> Integer sample : () -> %
--R shift : (%,%) -> % sign : % -> Integer
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % submod : (%,%,%) -> %
--R symmetricRemainder : (%,%) -> % unit? : % -> Boolean
--R unitCanonical : % -> % zero? : % -> Boolean
@@ -54243,18 +54381,18 @@ digraph pic {
--R differentiate : (%,NonNegativeInteger) -> %
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
--R nextItem : % -> Union(%,"failed")
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R rationalIfCan : % -> Union(Fraction Integer,"failed")
---R reducedSystem : Matrix % -> Matrix Integer
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer)
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R rationalIfCan : % -> Union(Fraction(Integer),"failed")
+--R reducedSystem : Matrix(%) -> Matrix(Integer)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer))
--R retractIfCan : % -> Union(Integer,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
@@ -54800,14 +54938,15 @@ digraph pic {
--S 1 of 1
)show LocalPowerSeriesCategory
---R LocalPowerSeriesCategory K: Field is a category constructor
+--R
+--R LocalPowerSeriesCategory(K: Field) is a category constructor
--R Abbreviation for LocalPowerSeriesCategory is LOCPOWC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LOCPOWC
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (%,K) -> % ?*? : (K,%) -> %
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -54817,15 +54956,15 @@ digraph pic {
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
--R associates? : (%,%) -> Boolean center : % -> K
--R coefOfFirstNonZeroTerm : % -> K coefficient : (%,Integer) -> K
---R coerce : Fraction Integer -> % coerce : % -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R complete : % -> % degree : % -> Integer
--R delay : (() -> %) -> % ?.? : (%,Integer) -> K
---R extend : (%,Integer) -> % factor : % -> Factored %
+--R extend : (%,Integer) -> % factor : % -> Factored(%)
--R filterUpTo : (%,Integer) -> % findCoef : (%,Integer) -> K
---R gcd : List % -> % gcd : (%,%) -> %
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger inv : % -> %
---R latex : % -> String lcm : List % -> %
+--R latex : % -> String lcm : List(%) -> %
--R lcm : (%,%) -> % leadingCoefficient : % -> K
--R leadingMonomial : % -> % map : ((K -> K),%) -> %
--R monomial : (K,Integer) -> % monomial? : % -> Boolean
@@ -54839,7 +54978,7 @@ digraph pic {
--R removeZeroes : % -> % removeZeroes : (Integer,%) -> %
--R sample : () -> % sbt : (%,%) -> %
--R series : (Integer,K,%) -> % shift : (%,Integer) -> %
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % truncate : (%,Integer) -> %
--R unit? : % -> Boolean unitCanonical : % -> %
--R variable : % -> Symbol zero? : % -> Boolean
@@ -54847,46 +54986,46 @@ digraph pic {
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,K) -> % if K has FIELD
---R D : (%,List Symbol,List NonNegativeInteger) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
---R D : (%,Symbol,NonNegativeInteger) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
---R D : (%,List Symbol) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
---R D : (%,Symbol) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
+--R D : (%,Symbol,NonNegativeInteger) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
+--R D : (%,List(Symbol)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
+--R D : (%,Symbol) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
--R D : (%,NonNegativeInteger) -> % if K has *: (Integer,K) -> K
--R D : % -> % if K has *: (Integer,K) -> K
--R ?^? : (%,NonNegativeInteger) -> %
--R approximate : (%,Integer) -> K if K has **: (K,Integer) -> K and K has coerce: Symbol -> K
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if K has CHARNZ
---R coerce : % -> Stream Record(k: Integer,c: K)
---R coerce : Stream Record(k: Integer,c: K) -> %
+--R coerce : % -> Stream(Record(k: Integer,c: K))
+--R coerce : Stream(Record(k: Integer,c: K)) -> %
--R coerce : K -> % if K has COMRING
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
---R differentiate : (%,List Symbol) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
---R differentiate : (%,Symbol) -> % if K has PDRING SYMBOL and K has *: (Integer,K) -> K
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
+--R differentiate : (%,List(Symbol)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
+--R differentiate : (%,Symbol) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K
--R differentiate : (%,NonNegativeInteger) -> % if K has *: (Integer,K) -> K
--R differentiate : % -> % if K has *: (Integer,K) -> K
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R ?.? : (%,%) -> % if Integer has SGROUP
--R euclideanSize : % -> NonNegativeInteger
---R eval : (%,K) -> Stream K if K has **: (K,Integer) -> K
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R eval : (%,K) -> Stream(K) if K has **: (K,Integer) -> K
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R monomial : (%,SingletonAsOrderedSet,Integer) -> %
---R monomial : (%,List SingletonAsOrderedSet,List Integer) -> %
---R monomial2series : (List %,List NonNegativeInteger,Integer) -> %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
+--R monomial : (%,List(SingletonAsOrderedSet),List(Integer)) -> %
+--R monomial2series : (List(%),List(NonNegativeInteger),Integer) -> %
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
--R multiplyExponents : (%,PositiveInteger) -> %
--R orderIfNegative : % -> Union(Integer,"failed")
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R terms : % -> Stream Record(k: Integer,c: K)
+--R terms : % -> Stream(Record(k: Integer,c: K))
--R truncate : (%,Integer,Integer) -> %
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R
--E 1
@@ -55268,7 +55407,8 @@ digraph pic {
--S 1 of 1
)show PAdicIntegerCategory
---R PAdicIntegerCategory p: Integer is a category constructor
+--R
+--R PAdicIntegerCategory(p: Integer) is a category constructor
--R Abbreviation for PAdicIntegerCategory is PADICCT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PADICCT
@@ -55282,10 +55422,10 @@ digraph pic {
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R coerce : % -> % coerce : Integer -> %
--R coerce : % -> OutputForm complete : % -> %
---R digits : % -> Stream Integer extend : (%,Integer) -> %
---R gcd : List % -> % gcd : (%,%) -> %
+--R digits : % -> Stream(Integer) extend : (%,Integer) -> %
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R moduloP : % -> Integer modulus : () -> Integer
--R one? : % -> Boolean order : % -> NonNegativeInteger
--R ?quo? : (%,%) -> % quotientByP : % -> %
@@ -55301,14 +55441,14 @@ digraph pic {
--R characteristic : () -> NonNegativeInteger
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R root : (SparseUnivariatePolynomial Integer,Integer) -> %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R root : (SparseUnivariatePolynomial(Integer),Integer) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -55592,6 +55732,7 @@ digraph pic {
--S 1 of 1
)show PolynomialCategory
+--R
--R PolynomialCategory(R: Ring,E: OrderedAbelianMonoidSup,VarSet: OrderedSet) is a category constructor
--R Abbreviation for PolynomialCategory is POLYCAT
--R This constructor is exposed in this frame.
@@ -55603,29 +55744,28 @@ digraph pic {
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
---R D : (%,List VarSet) -> % D : (%,VarSet) -> %
+--R D : (%,List(VarSet)) -> % D : (%,VarSet) -> %
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R
---R coefficients : % -> List R coerce : VarSet -> %
+--R coefficients : % -> List(R) coerce : VarSet -> %
--R coerce : R -> % coerce : Integer -> %
--R coerce : % -> OutputForm degree : % -> E
--R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> %
---R eval : (%,VarSet,R) -> % eval : (%,List %,List %) -> %
---R eval : (%,%,%) -> % eval : (%,Equation %) -> %
---R eval : (%,List Equation %) -> % ground : % -> R
+--R eval : (%,VarSet,R) -> % eval : (%,%,%) -> %
+--R eval : (%,Equation(%)) -> % ground : % -> R
--R ground? : % -> Boolean hash : % -> SingleInteger
--R latex : % -> String leadingCoefficient : % -> R
--R leadingMonomial : % -> % map : ((R -> R),%) -> %
--R mapExponents : ((E -> E),%) -> % minimumDegree : % -> E
--R monomial : (R,E) -> % monomial? : % -> Boolean
---R monomials : % -> List % one? : % -> Boolean
---R pomopo! : (%,R,E,%) -> % primitiveMonomials : % -> List %
---R recip : % -> Union(%,"failed") reductum : % -> %
---R retract : % -> VarSet retract : % -> R
---R sample : () -> % variables : % -> List VarSet
---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT
---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT
+--R monomials : % -> List(%) one? : % -> Boolean
+--R pomopo! : (%,R,E,%) -> % recip : % -> Union(%,"failed")
+--R reductum : % -> % retract : % -> VarSet
+--R retract : % -> R sample : () -> %
+--R variables : % -> List(VarSet) zero? : % -> Boolean
+--R ?~=? : (%,%) -> Boolean
+--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT))
+--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
@@ -55633,83 +55773,86 @@ digraph pic {
--R ?<=? : (%,%) -> Boolean if R has ORDSET
--R ?>? : (%,%) -> Boolean if R has ORDSET
--R ?>=? : (%,%) -> Boolean if R has ORDSET
---R D : (%,List VarSet,List NonNegativeInteger) -> %
+--R D : (%,List(VarSet),List(NonNegativeInteger)) -> %
--R D : (%,VarSet,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R associates? : (%,%) -> Boolean if R has INTDOM
--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ
---R coefficient : (%,List VarSet,List NonNegativeInteger) -> %
+--R coefficient : (%,List(VarSet),List(NonNegativeInteger)) -> %
--R coefficient : (%,VarSet,NonNegativeInteger) -> %
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT))
--R coerce : % -> % if R has INTDOM
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
--R content : (%,VarSet) -> % if R has GCDDOM
--R content : % -> R if R has GCDDOM
---R convert : % -> InputForm if VarSet has KONVERT INFORM and R has KONVERT INFORM
---R convert : % -> Pattern Integer if VarSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT
---R convert : % -> Pattern Float if VarSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT
---R degree : (%,List VarSet) -> List NonNegativeInteger
+--R convert : % -> InputForm if VarSet has KONVERT(INFORM) and R has KONVERT(INFORM)
+--R convert : % -> Pattern(Integer) if VarSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT))
+--R convert : % -> Pattern(Float) if VarSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT))
+--R degree : (%,List(VarSet)) -> List(NonNegativeInteger)
--R degree : (%,VarSet) -> NonNegativeInteger
---R differentiate : (%,List VarSet,List NonNegativeInteger) -> %
+--R differentiate : (%,List(VarSet),List(NonNegativeInteger)) -> %
--R differentiate : (%,VarSet,NonNegativeInteger) -> %
---R differentiate : (%,List VarSet) -> %
+--R differentiate : (%,List(VarSet)) -> %
--R discriminant : (%,VarSet) -> % if R has COMRING
---R eval : (%,List VarSet,List %) -> %
---R eval : (%,List VarSet,List R) -> %
+--R eval : (%,List(VarSet),List(%)) -> %
+--R eval : (%,List(VarSet),List(R)) -> %
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
---R factor : % -> Factored % if R has PFECAT
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R factor : % -> Factored(%) if R has PFECAT
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R gcd : (%,%) -> % if R has GCDDOM
---R gcd : List % -> % if R has GCDDOM
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM
+--R gcd : List(%) -> % if R has GCDDOM
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM
--R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed")
---R isPlus : % -> Union(List %,"failed")
---R isTimes : % -> Union(List %,"failed")
+--R isPlus : % -> Union(List(%),"failed")
+--R isTimes : % -> Union(List(%),"failed")
--R lcm : (%,%) -> % if R has GCDDOM
---R lcm : List % -> % if R has GCDDOM
+--R lcm : List(%) -> % if R has GCDDOM
--R mainVariable : % -> Union(VarSet,"failed")
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
---R minimumDegree : (%,List VarSet) -> List NonNegativeInteger
+--R minimumDegree : (%,List(VarSet)) -> List(NonNegativeInteger)
--R minimumDegree : (%,VarSet) -> NonNegativeInteger
--R monicDivide : (%,%,VarSet) -> Record(quotient: %,remainder: %)
---R monomial : (%,List VarSet,List NonNegativeInteger) -> %
+--R monomial : (%,List(VarSet),List(NonNegativeInteger)) -> %
--R monomial : (%,VarSet,NonNegativeInteger) -> %
---R multivariate : (SparseUnivariatePolynomial %,VarSet) -> %
---R multivariate : (SparseUnivariatePolynomial R,VarSet) -> %
+--R multivariate : (SparseUnivariatePolynomial(%),VarSet) -> %
+--R multivariate : (SparseUnivariatePolynomial(R),VarSet) -> %
--R numberOfMonomials : % -> NonNegativeInteger
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if VarSet has PATMAB INT and R has PATMAB INT
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if VarSet has PATMAB FLOAT and R has PATMAB FLOAT
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if VarSet has PATMAB(INT) and R has PATMAB(INT)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if VarSet has PATMAB(FLOAT) and R has PATMAB(FLOAT)
--R prime? : % -> Boolean if R has PFECAT
+--R primitiveMonomials : % -> List(%)
--R primitivePart : (%,VarSet) -> % if R has GCDDOM
--R primitivePart : % -> % if R has GCDDOM
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
--R resultant : (%,%,VarSet) -> % if R has COMRING
---R retract : % -> Integer if R has RETRACT INT
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
+--R retract : % -> Integer if R has RETRACT(INT)
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(VarSet,"failed")
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(R,"failed")
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT
---R squareFree : % -> Factored % if R has GCDDOM
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT
+--R squareFree : % -> Factored(%) if R has GCDDOM
--R squareFreePart : % -> % if R has GCDDOM
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R totalDegree : (%,List VarSet) -> NonNegativeInteger
+--R totalDegree : (%,List(VarSet)) -> NonNegativeInteger
--R totalDegree : % -> NonNegativeInteger
--R unit? : % -> Boolean if R has INTDOM
--R unitCanonical : % -> % if R has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM
---R univariate : % -> SparseUnivariatePolynomial R
---R univariate : (%,VarSet) -> SparseUnivariatePolynomial %
+--R univariate : % -> SparseUnivariatePolynomial(R)
+--R univariate : (%,VarSet) -> SparseUnivariatePolynomial(%)
--R
--E 1
@@ -56653,7 +56796,8 @@ digraph pic {
--S 1 of 1
)show UnivariateTaylorSeriesCategory
---R UnivariateTaylorSeriesCategory Coef: Ring is a category constructor
+--R
+--R UnivariateTaylorSeriesCategory(Coef: Ring) is a category constructor
--R Abbreviation for UnivariateTaylorSeriesCategory is UTSCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UTSCAT
@@ -56666,7 +56810,7 @@ digraph pic {
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % center : % -> Coef
---R coefficients : % -> Stream Coef coerce : Integer -> %
+--R coefficients : % -> Stream(Coef) coerce : Integer -> %
--R coerce : % -> OutputForm complete : % -> %
--R degree : % -> NonNegativeInteger hash : % -> SingleInteger
--R latex : % -> String leadingCoefficient : % -> Coef
@@ -56675,90 +56819,90 @@ digraph pic {
--R order : % -> NonNegativeInteger pole? : % -> Boolean
--R quoByVar : % -> % recip : % -> Union(%,"failed")
--R reductum : % -> % sample : () -> %
---R series : Stream Coef -> % variable : % -> Symbol
+--R series : Stream(Coef) -> % variable : % -> Symbol
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?**? : (%,Coef) -> % if Coef has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,Coef) -> % if Coef has FIELD
--R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef
--R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef
---R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
---R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R D : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
--R ?^? : (%,NonNegativeInteger) -> %
---R acos : % -> % if Coef has ALGEBRA FRAC INT
---R acosh : % -> % if Coef has ALGEBRA FRAC INT
---R acot : % -> % if Coef has ALGEBRA FRAC INT
---R acoth : % -> % if Coef has ALGEBRA FRAC INT
---R acsc : % -> % if Coef has ALGEBRA FRAC INT
---R acsch : % -> % if Coef has ALGEBRA FRAC INT
+--R acos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT))
--R approximate : (%,NonNegativeInteger) -> Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef and Coef has coerce: Symbol -> Coef
---R asec : % -> % if Coef has ALGEBRA FRAC INT
---R asech : % -> % if Coef has ALGEBRA FRAC INT
---R asin : % -> % if Coef has ALGEBRA FRAC INT
---R asinh : % -> % if Coef has ALGEBRA FRAC INT
+--R asec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R associates? : (%,%) -> Boolean if Coef has INTDOM
---R atan : % -> % if Coef has ALGEBRA FRAC INT
---R atanh : % -> % if Coef has ALGEBRA FRAC INT
+--R atan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
--R coefficient : (%,NonNegativeInteger) -> Coef
--R coerce : Coef -> % if Coef has COMRING
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
---R cos : % -> % if Coef has ALGEBRA FRAC INT
---R cosh : % -> % if Coef has ALGEBRA FRAC INT
---R cot : % -> % if Coef has ALGEBRA FRAC INT
---R coth : % -> % if Coef has ALGEBRA FRAC INT
---R csc : % -> % if Coef has ALGEBRA FRAC INT
---R csch : % -> % if Coef has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
+--R cos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R coth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csch : % -> % if Coef has ALGEBRA(FRAC(INT))
--R differentiate : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef
--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef
---R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
---R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R differentiate : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R differentiate : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef
--R ?.? : (%,%) -> % if NonNegativeInteger has SGROUP
--R ?.? : (%,NonNegativeInteger) -> Coef
---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef
---R exp : % -> % if Coef has ALGEBRA FRAC INT
+--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,NonNegativeInteger) -> Coef
+--R exp : % -> % if Coef has ALGEBRA(FRAC(INT))
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
--R extend : (%,NonNegativeInteger) -> %
---R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT
---R integrate : % -> % if Coef has ALGEBRA FRAC INT
---R log : % -> % if Coef has ALGEBRA FRAC INT
---R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> %
+--R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT))
+--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R log : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R monomial : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> %
--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> %
--R monomial : (Coef,NonNegativeInteger) -> %
--R multiplyCoefficients : ((Integer -> Coef),%) -> %
--R multiplyExponents : (%,PositiveInteger) -> %
---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT
+--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R order : (%,NonNegativeInteger) -> NonNegativeInteger
---R pi : () -> % if Coef has ALGEBRA FRAC INT
---R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef
---R polynomial : (%,NonNegativeInteger) -> Polynomial Coef
---R sec : % -> % if Coef has ALGEBRA FRAC INT
---R sech : % -> % if Coef has ALGEBRA FRAC INT
---R series : Stream Record(k: NonNegativeInteger,c: Coef) -> %
---R sin : % -> % if Coef has ALGEBRA FRAC INT
---R sinh : % -> % if Coef has ALGEBRA FRAC INT
---R sqrt : % -> % if Coef has ALGEBRA FRAC INT
+--R pi : () -> % if Coef has ALGEBRA(FRAC(INT))
+--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial(Coef)
+--R polynomial : (%,NonNegativeInteger) -> Polynomial(Coef)
+--R sec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R series : Stream(Record(k: NonNegativeInteger,c: Coef)) -> %
+--R sin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT))
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tan : % -> % if Coef has ALGEBRA FRAC INT
---R tanh : % -> % if Coef has ALGEBRA FRAC INT
---R terms : % -> Stream Record(k: NonNegativeInteger,c: Coef)
+--R tan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R terms : % -> Stream(Record(k: NonNegativeInteger,c: Coef))
--R truncate : (%,NonNegativeInteger,NonNegativeInteger) -> %
--R truncate : (%,NonNegativeInteger) -> %
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R
--E 1
@@ -57443,7 +57587,7 @@ pi:Polynomial(Integer):=-3*x^3+2*x+13
--R
--R 3
--R (1) - 3x + 2x + 13
---R Type: Polynomial Integer
+--R Type: Polynomial(Integer)
--E 1
--S 2 of 14
@@ -57459,7 +57603,7 @@ rootsOf(pi)
--R
--R
--R (3) [%x0,%x1,- %x1 - %x0]
---R Type: List AlgebraicNumber
+--R Type: List(AlgebraicNumber)
--E 3
--S 4 of 14
@@ -57479,7 +57623,7 @@ zerosOf(pi)
--R - \|- 27%x3 + 24 - 3%x3 \|- 27%x3 + 24 - 3%x3
--R (5) [%x3,-------------------------,-----------------------]
--R 6 6
---R Type: List AlgebraicNumber
+--R Type: List(AlgebraicNumber)
--E 5
--S 6 of 14
@@ -57488,7 +57632,7 @@ sup:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13
--R
--R 3
--R (6) - 3? + 2? + 13
---R Type: SparseUnivariatePolynomial Integer
+--R Type: SparseUnivariatePolynomial(Integer)
--E 6
--S 7 of 14
@@ -57512,7 +57656,7 @@ rootsOf(sup)
--R
--R
--R (9) [%%C0,%%C1,- %%C1 - %%C0]
---R Type: List AlgebraicNumber
+--R Type: List(AlgebraicNumber)
--E 9
--S 10 of 14
@@ -57520,7 +57664,7 @@ rootsOf(sup,x)
--R
--R
--R (10) [%x6,%x7,- %x7 - %x6]
---R Type: List AlgebraicNumber
+--R Type: List(AlgebraicNumber)
--E 10
--S 11 of 14
@@ -57548,7 +57692,7 @@ zerosOf(sup)
--R - \|- 27%%E0 + 24 - 3%%E0 \|- 27%%E0 + 24 - 3%%E0
--R (13) [%%E0,---------------------------,-------------------------]
--R 6 6
---R Type: List AlgebraicNumber
+--R Type: List(AlgebraicNumber)
--E 13
--S 14 of 14
@@ -57560,7 +57704,7 @@ zerosOf(sup,x)
--R - \|- 27%x9 + 24 - 3%x9 \|- 27%x9 + 24 - 3%x9
--R (14) [%x9,-------------------------,-----------------------]
--R 6 6
---R Type: List AlgebraicNumber
+--R Type: List(AlgebraicNumber)
--E 14
)spool
@@ -58075,7 +58219,8 @@ digraph pic {
--S 1 of 1
)show DifferentialPolynomialCategory
---R DifferentialPolynomialCategory(R: Ring,S: OrderedSet,V: DifferentialVariableCategory t#2,E: OrderedAbelianMonoidSup) is a category constructor
+--R
+--R DifferentialPolynomialCategory(R: Ring,S: OrderedSet,V: DifferentialVariableCategory(t#2),E: OrderedAbelianMonoidSup) is a category constructor
--R Abbreviation for DifferentialPolynomialCategory is DPOLCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for DPOLCAT
@@ -58087,35 +58232,33 @@ digraph pic {
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
--R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING
---R D : (%,List V) -> % D : (%,V) -> %
+--R D : (%,List(V)) -> % D : (%,V) -> %
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R
---R coefficients : % -> List R coerce : S -> %
+--R coefficients : % -> List(R) coerce : S -> %
--R coerce : V -> % coerce : R -> %
--R coerce : Integer -> % coerce : % -> OutputForm
---R degree : % -> E differentiate : (%,List V) -> %
---R differentiate : (%,V) -> % eval : (%,List V,List %) -> %
---R eval : (%,V,%) -> % eval : (%,List V,List R) -> %
---R eval : (%,V,R) -> % eval : (%,List %,List %) -> %
---R eval : (%,%,%) -> % eval : (%,Equation %) -> %
---R eval : (%,List Equation %) -> % ground : % -> R
+--R degree : % -> E differentiate : (%,List(V)) -> %
+--R differentiate : (%,V) -> % eval : (%,List(V),List(%)) -> %
+--R eval : (%,V,%) -> % eval : (%,List(V),List(R)) -> %
+--R eval : (%,V,R) -> % eval : (%,%,%) -> %
+--R eval : (%,Equation(%)) -> % ground : % -> R
--R ground? : % -> Boolean hash : % -> SingleInteger
--R initial : % -> % isobaric? : % -> Boolean
--R latex : % -> String leader : % -> V
--R leadingCoefficient : % -> R leadingMonomial : % -> %
--R map : ((R -> R),%) -> % mapExponents : ((E -> E),%) -> %
--R minimumDegree : % -> E monomial : (R,E) -> %
---R monomial? : % -> Boolean monomials : % -> List %
+--R monomial? : % -> Boolean monomials : % -> List(%)
--R one? : % -> Boolean order : % -> NonNegativeInteger
---R pomopo! : (%,R,E,%) -> % primitiveMonomials : % -> List %
---R recip : % -> Union(%,"failed") reductum : % -> %
---R retract : % -> S retract : % -> V
---R retract : % -> R sample : () -> %
---R separant : % -> % variables : % -> List V
---R weight : % -> NonNegativeInteger zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT
---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT
+--R pomopo! : (%,R,E,%) -> % recip : % -> Union(%,"failed")
+--R reductum : % -> % retract : % -> S
+--R retract : % -> V retract : % -> R
+--R sample : () -> % separant : % -> %
+--R variables : % -> List(V) weight : % -> NonNegativeInteger
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
+--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT))
+--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
@@ -58124,106 +58267,109 @@ digraph pic {
--R ?>? : (%,%) -> Boolean if R has ORDSET
--R ?>=? : (%,%) -> Boolean if R has ORDSET
--R D : (%,(R -> R),NonNegativeInteger) -> %
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol) -> % if R has PDRING SYMBOL
---R D : (%,Symbol) -> % if R has PDRING SYMBOL
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol) -> % if R has PDRING(SYMBOL)
--R D : (%,NonNegativeInteger) -> % if R has DIFRING
---R D : (%,List V,List NonNegativeInteger) -> %
+--R D : (%,List(V),List(NonNegativeInteger)) -> %
--R D : (%,V,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R associates? : (%,%) -> Boolean if R has INTDOM
--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ
---R coefficient : (%,List V,List NonNegativeInteger) -> %
+--R coefficient : (%,List(V),List(NonNegativeInteger)) -> %
--R coefficient : (%,V,NonNegativeInteger) -> %
--R coerce : % -> % if R has INTDOM
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT))
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
--R content : (%,V) -> % if R has GCDDOM
--R content : % -> R if R has GCDDOM
---R convert : % -> InputForm if V has KONVERT INFORM and R has KONVERT INFORM
---R convert : % -> Pattern Integer if V has KONVERT PATTERN INT and R has KONVERT PATTERN INT
---R convert : % -> Pattern Float if V has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT
+--R convert : % -> InputForm if V has KONVERT(INFORM) and R has KONVERT(INFORM)
+--R convert : % -> Pattern(Integer) if V has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT))
+--R convert : % -> Pattern(Float) if V has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT))
--R degree : (%,S) -> NonNegativeInteger
---R degree : (%,List V) -> List NonNegativeInteger
+--R degree : (%,List(V)) -> List(NonNegativeInteger)
--R degree : (%,V) -> NonNegativeInteger
---R differentialVariables : % -> List S
+--R differentialVariables : % -> List(S)
--R differentiate : (%,(R -> R)) -> %
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL)
--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING
--R differentiate : % -> % if R has DIFRING
---R differentiate : (%,List V,List NonNegativeInteger) -> %
+--R differentiate : (%,List(V),List(NonNegativeInteger)) -> %
--R differentiate : (%,V,NonNegativeInteger) -> %
--R discriminant : (%,V) -> % if R has COMRING
---R eval : (%,List S,List R) -> % if R has DIFRING
+--R eval : (%,List(S),List(R)) -> % if R has DIFRING
--R eval : (%,S,R) -> % if R has DIFRING
---R eval : (%,List S,List %) -> % if R has DIFRING
+--R eval : (%,List(S),List(%)) -> % if R has DIFRING
--R eval : (%,S,%) -> % if R has DIFRING
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
---R factor : % -> Factored % if R has PFECAT
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R factor : % -> Factored(%) if R has PFECAT
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R gcd : (%,%) -> % if R has GCDDOM
---R gcd : List % -> % if R has GCDDOM
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM
+--R gcd : List(%) -> % if R has GCDDOM
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM
--R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed")
---R isPlus : % -> Union(List %,"failed")
---R isTimes : % -> Union(List %,"failed")
+--R isPlus : % -> Union(List(%),"failed")
+--R isTimes : % -> Union(List(%),"failed")
--R lcm : (%,%) -> % if R has GCDDOM
---R lcm : List % -> % if R has GCDDOM
+--R lcm : List(%) -> % if R has GCDDOM
--R mainVariable : % -> Union(V,"failed")
--R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING
--R makeVariable : S -> (NonNegativeInteger -> %)
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
---R minimumDegree : (%,List V) -> List NonNegativeInteger
+--R minimumDegree : (%,List(V)) -> List(NonNegativeInteger)
--R minimumDegree : (%,V) -> NonNegativeInteger
--R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %)
---R monomial : (%,List V,List NonNegativeInteger) -> %
+--R monomial : (%,List(V),List(NonNegativeInteger)) -> %
--R monomial : (%,V,NonNegativeInteger) -> %
---R multivariate : (SparseUnivariatePolynomial %,V) -> %
---R multivariate : (SparseUnivariatePolynomial R,V) -> %
+--R multivariate : (SparseUnivariatePolynomial(%),V) -> %
+--R multivariate : (SparseUnivariatePolynomial(R),V) -> %
--R numberOfMonomials : % -> NonNegativeInteger
--R order : (%,S) -> NonNegativeInteger
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB INT and R has PATMAB INT
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB FLOAT and R has PATMAB FLOAT
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB(INT) and R has PATMAB(INT)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB(FLOAT) and R has PATMAB(FLOAT)
--R prime? : % -> Boolean if R has PFECAT
+--R primitiveMonomials : % -> List(%)
--R primitivePart : (%,V) -> % if R has GCDDOM
--R primitivePart : % -> % if R has GCDDOM
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
--R resultant : (%,%,V) -> % if R has COMRING
---R retract : % -> Integer if R has RETRACT INT
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
+--R retract : % -> Integer if R has RETRACT(INT)
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(S,"failed")
--R retractIfCan : % -> Union(V,"failed")
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(R,"failed")
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT
---R squareFree : % -> Factored % if R has GCDDOM
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT
+--R squareFree : % -> Factored(%) if R has GCDDOM
--R squareFreePart : % -> % if R has GCDDOM
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R totalDegree : (%,List V) -> NonNegativeInteger
+--R totalDegree : (%,List(V)) -> NonNegativeInteger
--R totalDegree : % -> NonNegativeInteger
--R unit? : % -> Boolean if R has INTDOM
--R unitCanonical : % -> % if R has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM
---R univariate : % -> SparseUnivariatePolynomial R
---R univariate : (%,V) -> SparseUnivariatePolynomial %
+--R univariate : % -> SparseUnivariatePolynomial(R)
+--R univariate : (%,V) -> SparseUnivariatePolynomial(%)
--R weight : (%,S) -> NonNegativeInteger
---R weights : (%,S) -> List NonNegativeInteger
---R weights : % -> List NonNegativeInteger
+--R weights : (%,S) -> List(NonNegativeInteger)
+--R weights : % -> List(NonNegativeInteger)
--R
--E 1
@@ -58961,13 +59107,14 @@ digraph pic {
--S 1 of 1
)show FieldOfPrimeCharacteristic
+--R
--R FieldOfPrimeCharacteristic is a category constructor
--R Abbreviation for FieldOfPrimeCharacteristic is FPC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FPC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -58975,17 +59122,17 @@ digraph pic {
--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> %
+--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> %
--R coerce : % -> % coerce : Integer -> %
---R coerce : % -> OutputForm factor : % -> Factored %
---R gcd : List % -> % gcd : (%,%) -> %
+--R coerce : % -> OutputForm factor : % -> Factored(%)
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger inv : % -> %
---R latex : % -> String lcm : List % -> %
+--R latex : % -> String lcm : List(%) -> %
--R lcm : (%,%) -> % one? : % -> Boolean
--R prime? : % -> Boolean primeFrobenius : % -> %
--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
--R ?rem? : (%,%) -> % sample : () -> %
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % unit? : % -> Boolean
--R unitCanonical : % -> % zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
@@ -58997,15 +59144,15 @@ digraph pic {
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed")
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R order : % -> OnePointCompletion PositiveInteger
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R order : % -> OnePointCompletion(PositiveInteger)
--R primeFrobenius : (%,NonNegativeInteger) -> %
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -59278,7 +59425,8 @@ digraph pic {
--S 1 of 1
)show FiniteRankAlgebra
---R FiniteRankAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory t#1) is a category constructor
+--R
+--R FiniteRankAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory(t#1)) is a category constructor
--R Abbreviation for FiniteRankAlgebra is FINRALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FINRALG
@@ -59292,7 +59440,7 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coerce : R -> %
--R coerce : Integer -> % coerce : % -> OutputForm
---R discriminant : Vector % -> R hash : % -> SingleInteger
+--R discriminant : Vector(%) -> R hash : % -> SingleInteger
--R latex : % -> String norm : % -> R
--R one? : % -> Boolean rank : () -> PositiveInteger
--R recip : % -> Union(%,"failed") sample : () -> %
@@ -59304,13 +59452,13 @@ digraph pic {
--R characteristic : () -> NonNegativeInteger
--R characteristicPolynomial : % -> UP
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coordinates : (Vector %,Vector %) -> Matrix R
---R coordinates : (%,Vector %) -> Vector R
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(R)
+--R coordinates : (%,Vector(%)) -> Vector(R)
--R minimalPolynomial : % -> UP if R has FIELD
---R regularRepresentation : (%,Vector %) -> Matrix R
---R represents : (Vector R,Vector %) -> %
+--R regularRepresentation : (%,Vector(%)) -> Matrix(R)
+--R represents : (Vector(R),Vector(%)) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R traceMatrix : Vector % -> Matrix R
+--R traceMatrix : Vector(%) -> Matrix(R)
--R
--E 1
@@ -59598,7 +59746,8 @@ digraph pic {
--S 1 of 1
)show FunctionSpace
---R FunctionSpace R: OrderedSet is a category constructor
+--R
+--R FunctionSpace(R: OrderedSet) is a category constructor
--R Abbreviation for FunctionSpace is FS
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FS
@@ -59609,161 +59758,163 @@ digraph pic {
--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean
--R 1 : () -> % if R has SGROUP 0 : () -> % if R has ABELSG
--R applyQuote : (Symbol,%,%) -> % applyQuote : (Symbol,%) -> %
---R belong? : BasicOperator -> Boolean box : List % -> %
+--R belong? : BasicOperator -> Boolean box : List(%) -> %
--R box : % -> % coerce : R -> %
---R coerce : Symbol -> % coerce : Kernel % -> %
+--R coerce : Symbol -> % coerce : Kernel(%) -> %
--R coerce : % -> OutputForm distribute : (%,%) -> %
--R distribute : % -> % elt : (BasicOperator,%,%) -> %
---R elt : (BasicOperator,%) -> % eval : (%,List %,List %) -> %
---R eval : (%,%,%) -> % eval : (%,Equation %) -> %
---R eval : (%,List Equation %) -> % eval : (%,Kernel %,%) -> %
+--R elt : (BasicOperator,%) -> % eval : (%,%,%) -> %
+--R eval : (%,Equation(%)) -> % eval : (%,Kernel(%),%) -> %
--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean
--R ground : % -> R ground? : % -> Boolean
--R hash : % -> SingleInteger height : % -> NonNegativeInteger
--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> %
---R kernels : % -> List Kernel % latex : % -> String
---R map : ((% -> %),Kernel %) -> % max : (%,%) -> %
---R min : (%,%) -> % paren : List % -> %
---R paren : % -> % retract : % -> R
---R retract : % -> Symbol retract : % -> Kernel %
---R subst : (%,Equation %) -> % tower : % -> List Kernel %
---R variables : % -> List Symbol ?~=? : (%,%) -> Boolean
+--R kernels : % -> List(Kernel(%)) latex : % -> String
+--R max : (%,%) -> % min : (%,%) -> %
+--R paren : List(%) -> % paren : % -> %
+--R retract : % -> R retract : % -> Symbol
+--R retract : % -> Kernel(%) subst : (%,Equation(%)) -> %
+--R tower : % -> List(Kernel(%)) variables : % -> List(Symbol)
+--R ?~=? : (%,%) -> Boolean
--R ?*? : (%,%) -> % if R has SGROUP
--R ?*? : (PositiveInteger,%) -> % if R has ABELSG
--R ?*? : (NonNegativeInteger,%) -> % if R has ABELSG
--R ?*? : (Integer,%) -> % if R has ABELGRP
--R ?*? : (%,R) -> % if R has COMRING
--R ?*? : (R,%) -> % if R has COMRING
---R ?*? : (%,Fraction Integer) -> % if R has INTDOM
---R ?*? : (Fraction Integer,%) -> % if R has INTDOM
+--R ?*? : (%,Fraction(Integer)) -> % if R has INTDOM
+--R ?*? : (Fraction(Integer),%) -> % if R has INTDOM
--R ?**? : (%,PositiveInteger) -> % if R has SGROUP
--R ?**? : (%,NonNegativeInteger) -> % if R has SGROUP
--R ?**? : (%,Integer) -> % if R has GROUP or R has INTDOM
--R ?+? : (%,%) -> % if R has ABELSG
--R ?-? : (%,%) -> % if R has ABELGRP
--R ?/? : (%,%) -> % if R has GROUP or R has INTDOM
---R ?/? : (SparseMultivariatePolynomial(R,Kernel %),SparseMultivariatePolynomial(R,Kernel %)) -> % if R has INTDOM
+--R ?/? : (SparseMultivariatePolynomial(R,Kernel(%)),SparseMultivariatePolynomial(R,Kernel(%))) -> % if R has INTDOM
--R D : (%,Symbol) -> % if R has RING
---R D : (%,List Symbol) -> % if R has RING
+--R D : (%,List(Symbol)) -> % if R has RING
--R D : (%,Symbol,NonNegativeInteger) -> % if R has RING
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has RING
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING
--R ?^? : (%,PositiveInteger) -> % if R has SGROUP
--R ?^? : (%,NonNegativeInteger) -> % if R has SGROUP
--R ?^? : (%,Integer) -> % if R has GROUP or R has INTDOM
---R applyQuote : (Symbol,List %) -> %
+--R applyQuote : (Symbol,List(%)) -> %
--R applyQuote : (Symbol,%,%,%,%) -> %
--R applyQuote : (Symbol,%,%,%) -> %
--R associates? : (%,%) -> Boolean if R has INTDOM
--R characteristic : () -> NonNegativeInteger if R has RING
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coerce : Integer -> % if R has RING or R has RETRACT INT
---R coerce : Fraction Integer -> % if R has INTDOM or R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT
---R coerce : Polynomial R -> % if R has RING
+--R coerce : Integer -> % if R has RING or R has RETRACT(INT)
+--R coerce : Fraction(Integer) -> % if R has INTDOM or R has RETRACT(INT) and R has INTDOM or R has RETRACT(FRAC(INT))
+--R coerce : Polynomial(R) -> % if R has RING
--R coerce : % -> % if R has INTDOM
---R coerce : Fraction Polynomial R -> % if R has INTDOM
---R coerce : Fraction Polynomial Fraction R -> % if R has INTDOM
---R coerce : Polynomial Fraction R -> % if R has INTDOM
---R coerce : Fraction R -> % if R has INTDOM
---R coerce : SparseMultivariatePolynomial(R,Kernel %) -> % if R has RING
+--R coerce : Fraction(Polynomial(R)) -> % if R has INTDOM
+--R coerce : Fraction(Polynomial(Fraction(R))) -> % if R has INTDOM
+--R coerce : Polynomial(Fraction(R)) -> % if R has INTDOM
+--R coerce : Fraction(R) -> % if R has INTDOM
+--R coerce : SparseMultivariatePolynomial(R,Kernel(%)) -> % if R has RING
--R commutator : (%,%) -> % if R has GROUP
--R conjugate : (%,%) -> % if R has GROUP
---R convert : % -> InputForm if R has KONVERT INFORM
---R convert : Factored % -> % if R has INTDOM
---R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT
---R convert : % -> Pattern Integer if R has KONVERT PATTERN INT
+--R convert : % -> InputForm if R has KONVERT(INFORM)
+--R convert : Factored(%) -> % if R has INTDOM
+--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT))
+--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT))
--R definingPolynomial : % -> % if $ has RING
---R denom : % -> SparseMultivariatePolynomial(R,Kernel %) if R has INTDOM
+--R denom : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has INTDOM
--R denominator : % -> % if R has INTDOM
--R differentiate : (%,Symbol) -> % if R has RING
---R differentiate : (%,List Symbol) -> % if R has RING
+--R differentiate : (%,List(Symbol)) -> % if R has RING
--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has RING
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has RING
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING
--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM
---R elt : (BasicOperator,List %) -> %
+--R elt : (BasicOperator,List(%)) -> %
--R elt : (BasicOperator,%,%,%,%) -> %
--R elt : (BasicOperator,%,%,%) -> %
--R euclideanSize : % -> NonNegativeInteger if R has INTDOM
--R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING
---R eval : (%,Symbol,NonNegativeInteger,(List % -> %)) -> % if R has RING
---R eval : (%,List Symbol,List NonNegativeInteger,List (List % -> %)) -> % if R has RING
---R eval : (%,List Symbol,List NonNegativeInteger,List (% -> %)) -> % if R has RING
---R eval : (%,List BasicOperator,List %,Symbol) -> % if R has KONVERT INFORM
---R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT INFORM
---R eval : % -> % if R has KONVERT INFORM
---R eval : (%,List Symbol) -> % if R has KONVERT INFORM
---R eval : (%,Symbol) -> % if R has KONVERT INFORM
+--R eval : (%,Symbol,NonNegativeInteger,(List(%) -> %)) -> % if R has RING
+--R eval : (%,List(Symbol),List(NonNegativeInteger),List((List(%) -> %))) -> % if R has RING
+--R eval : (%,List(Symbol),List(NonNegativeInteger),List((% -> %))) -> % if R has RING
+--R eval : (%,List(BasicOperator),List(%),Symbol) -> % if R has KONVERT(INFORM)
+--R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT(INFORM)
+--R eval : % -> % if R has KONVERT(INFORM)
+--R eval : (%,List(Symbol)) -> % if R has KONVERT(INFORM)
+--R eval : (%,Symbol) -> % if R has KONVERT(INFORM)
--R eval : (%,BasicOperator,(% -> %)) -> %
---R eval : (%,BasicOperator,(List % -> %)) -> %
---R eval : (%,List BasicOperator,List (List % -> %)) -> %
---R eval : (%,List BasicOperator,List (% -> %)) -> %
+--R eval : (%,BasicOperator,(List(%) -> %)) -> %
+--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> %
+--R eval : (%,List(BasicOperator),List((% -> %))) -> %
--R eval : (%,Symbol,(% -> %)) -> %
---R eval : (%,Symbol,(List % -> %)) -> %
---R eval : (%,List Symbol,List (List % -> %)) -> %
---R eval : (%,List Symbol,List (% -> %)) -> %
---R eval : (%,List Kernel %,List %) -> %
---R even? : % -> Boolean if $ has RETRACT INT
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has INTDOM
+--R eval : (%,Symbol,(List(%) -> %)) -> %
+--R eval : (%,List(Symbol),List((List(%) -> %))) -> %
+--R eval : (%,List(Symbol),List((% -> %))) -> %
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
+--R eval : (%,List(Kernel(%)),List(%)) -> %
+--R even? : % -> Boolean if $ has RETRACT(INT)
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has INTDOM
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has INTDOM
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has INTDOM
---R factor : % -> Factored % if R has INTDOM
+--R factor : % -> Factored(%) if R has INTDOM
--R gcd : (%,%) -> % if R has INTDOM
---R gcd : List % -> % if R has INTDOM
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has INTDOM
+--R gcd : List(%) -> % if R has INTDOM
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has INTDOM
--R inv : % -> % if R has GROUP or R has INTDOM
--R is? : (%,BasicOperator) -> Boolean
---R isExpt : (%,Symbol) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING
---R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING
---R isExpt : % -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has SGROUP
---R isMult : % -> Union(Record(coef: Integer,var: Kernel %),"failed") if R has ABELSG
---R isPlus : % -> Union(List %,"failed") if R has ABELSG
+--R isExpt : (%,Symbol) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING
+--R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING
+--R isExpt : % -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has SGROUP
+--R isMult : % -> Union(Record(coef: Integer,var: Kernel(%)),"failed") if R has ABELSG
+--R isPlus : % -> Union(List(%),"failed") if R has ABELSG
--R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING
---R isTimes : % -> Union(List %,"failed") if R has SGROUP
---R kernel : (BasicOperator,List %) -> %
+--R isTimes : % -> Union(List(%),"failed") if R has SGROUP
+--R kernel : (BasicOperator,List(%)) -> %
--R lcm : (%,%) -> % if R has INTDOM
---R lcm : List % -> % if R has INTDOM
---R mainKernel : % -> Union(Kernel %,"failed")
---R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has INTDOM
---R numer : % -> SparseMultivariatePolynomial(R,Kernel %) if R has RING
+--R lcm : List(%) -> % if R has INTDOM
+--R mainKernel : % -> Union(Kernel(%),"failed")
+--R map : ((% -> %),Kernel(%)) -> %
+--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has INTDOM
+--R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has RING
--R numerator : % -> % if R has RING
---R odd? : % -> Boolean if $ has RETRACT INT
+--R odd? : % -> Boolean if $ has RETRACT(INT)
--R one? : % -> Boolean if R has SGROUP
--R operator : BasicOperator -> BasicOperator
---R operators : % -> List BasicOperator
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT
+--R operators : % -> List(BasicOperator)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT)
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT)
--R prime? : % -> Boolean if R has INTDOM
---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has INTDOM
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has INTDOM
--R ?quo? : (%,%) -> % if R has INTDOM
--R recip : % -> Union(%,"failed") if R has SGROUP
---R reducedSystem : Matrix % -> Matrix R if R has RING
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring))
---R reducedSystem : Matrix % -> Matrix Integer if and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring))
+--R reducedSystem : Matrix(%) -> Matrix(R) if R has RING
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring))
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring))
--R ?rem? : (%,%) -> % if R has INTDOM
---R retract : % -> Fraction Integer if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT
---R retract : % -> Polynomial R if R has RING
---R retract : % -> Fraction Polynomial R if R has INTDOM
---R retract : % -> Integer if R has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Polynomial R,"failed") if R has RING
---R retractIfCan : % -> Union(Fraction Polynomial R,"failed") if R has INTDOM
+--R retract : % -> Fraction(Integer) if R has RETRACT(INT) and R has INTDOM or R has RETRACT(FRAC(INT))
+--R retract : % -> Polynomial(R) if R has RING
+--R retract : % -> Fraction(Polynomial(R)) if R has INTDOM
+--R retract : % -> Integer if R has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(INT) and R has INTDOM or R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Polynomial(R),"failed") if R has RING
+--R retractIfCan : % -> Union(Fraction(Polynomial(R)),"failed") if R has INTDOM
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R retractIfCan : % -> Union(Symbol,"failed")
---R retractIfCan : % -> Union(Kernel %,"failed")
+--R retractIfCan : % -> Union(Kernel(%),"failed")
--R sample : () -> % if R has SGROUP or R has ABELSG
--R sizeLess? : (%,%) -> Boolean if R has INTDOM
---R squareFree : % -> Factored % if R has INTDOM
+--R squareFree : % -> Factored(%) if R has INTDOM
--R squareFreePart : % -> % if R has INTDOM
---R subst : (%,List Kernel %,List %) -> %
---R subst : (%,List Equation %) -> %
+--R subst : (%,List(Kernel(%)),List(%)) -> %
+--R subst : (%,List(Equation(%))) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP
--R unit? : % -> Boolean if R has INTDOM
--R unitCanonical : % -> % if R has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM
---R univariate : (%,Kernel %) -> Fraction SparseUnivariatePolynomial % if R has INTDOM
+--R univariate : (%,Kernel(%)) -> Fraction(SparseUnivariatePolynomial(%)) if R has INTDOM
--R zero? : % -> Boolean if R has ABELSG
--R
--E 1
@@ -61315,7 +61466,7 @@ digraph pic {
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PACPERC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -61323,44 +61474,44 @@ digraph pic {
--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> %
+--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> %
--R coerce : % -> % coerce : Integer -> %
--R coerce : % -> OutputForm conjugate : % -> %
---R extDegree : % -> PositiveInteger factor : % -> Factored %
---R fullOutput : % -> OutputForm gcd : List % -> %
+--R extDegree : % -> PositiveInteger factor : % -> Factored(%)
+--R fullOutput : % -> OutputForm gcd : List(%) -> %
--R gcd : (%,%) -> % ground? : % -> Boolean
--R hash : % -> SingleInteger inv : % -> %
---R latex : % -> String lcm : List % -> %
---R lcm : (%,%) -> % maxTower : List % -> %
+--R latex : % -> String lcm : List(%) -> %
+--R lcm : (%,%) -> % maxTower : List(%) -> %
--R one? : % -> Boolean previousTower : % -> %
--R prime? : % -> Boolean ?quo? : (%,%) -> %
--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
--R sample : () -> % setTower! : % -> Void
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % unit? : % -> Boolean
---R unitCanonical : % -> % vectorise : (%,%) -> Vector %
+--R unitCanonical : % -> % vectorise : (%,%) -> Vector(%)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R definingPolynomial : % -> SparseUnivariatePolynomial %
---R definingPolynomial : () -> SparseUnivariatePolynomial %
---R distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List %
+--R definingPolynomial : % -> SparseUnivariatePolynomial(%)
+--R definingPolynomial : () -> SparseUnivariatePolynomial(%)
+--R distinguishedRootsOf : (SparseUnivariatePolynomial(%),%) -> List(%)
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R lift : (%,%) -> SparseUnivariatePolynomial %
---R lift : % -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R newElement : (SparseUnivariatePolynomial %,Symbol) -> %
---R newElement : (SparseUnivariatePolynomial %,%,Symbol) -> %
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R reduce : SparseUnivariatePolynomial % -> %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R lift : (%,%) -> SparseUnivariatePolynomial(%)
+--R lift : % -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R newElement : (SparseUnivariatePolynomial(%),Symbol) -> %
+--R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> %
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R reduce : SparseUnivariatePolynomial(%) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R
@@ -61663,14 +61814,15 @@ digraph pic {
--S 1 of 1
)show QuotientFieldCategory
---R QuotientFieldCategory S: IntegralDomain is a category constructor
+--R
+--R QuotientFieldCategory(S: IntegralDomain) is a category constructor
--R Abbreviation for QuotientFieldCategory is QFCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for QFCAT
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (%,S) -> % ?*? : (S,%) -> %
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -61681,21 +61833,21 @@ digraph pic {
--R 0 : () -> % ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean
--R ceiling : % -> S if S has INS coerce : S -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R denom : % -> S denominator : % -> %
---R factor : % -> Factored % floor : % -> S if S has INS
---R gcd : List % -> % gcd : (%,%) -> %
+--R factor : % -> Factored(%) floor : % -> S if S has INS
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger init : () -> % if S has STEP
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R map : ((S -> S),%) -> % numer : % -> S
--R numerator : % -> % one? : % -> Boolean
--R prime? : % -> Boolean ?quo? : (%,%) -> %
--R random : () -> % if S has INS recip : % -> Union(%,"failed")
--R ?rem? : (%,%) -> % retract : % -> S
--R sample : () -> % sizeLess? : (%,%) -> Boolean
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R unit? : % -> Boolean unitCanonical : % -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
@@ -61705,70 +61857,70 @@ digraph pic {
--R ?>? : (%,%) -> Boolean if S has ORDSET
--R ?>=? : (%,%) -> Boolean if S has ORDSET
--R D : (%,(S -> S),NonNegativeInteger) -> %
---R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL
---R D : (%,List Symbol) -> % if S has PDRING SYMBOL
---R D : (%,Symbol) -> % if S has PDRING SYMBOL
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL)
+--R D : (%,Symbol) -> % if S has PDRING(SYMBOL)
--R D : (%,NonNegativeInteger) -> % if S has DIFRING
--R ?^? : (%,NonNegativeInteger) -> %
--R abs : % -> % if S has OINTDOM
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if S has CHARNZ or and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit))
---R coerce : Symbol -> % if S has RETRACT SYMBOL
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit))
+--R coerce : Symbol -> % if S has RETRACT(SYMBOL)
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit))
--R convert : % -> DoubleFloat if S has REAL
--R convert : % -> Float if S has REAL
---R convert : % -> InputForm if S has KONVERT INFORM
---R convert : % -> Pattern Float if S has KONVERT PATTERN FLOAT
---R convert : % -> Pattern Integer if S has KONVERT PATTERN INT
+--R convert : % -> InputForm if S has KONVERT(INFORM)
+--R convert : % -> Pattern(Float) if S has KONVERT(PATTERN(FLOAT))
+--R convert : % -> Pattern(Integer) if S has KONVERT(PATTERN(INT))
--R differentiate : (%,(S -> S)) -> %
--R differentiate : (%,(S -> S),NonNegativeInteger) -> %
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL
---R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL)
+--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL)
--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING
--R differentiate : % -> % if S has DIFRING
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R ?.? : (%,S) -> % if S has ELTAB(S,S)
--R euclideanSize : % -> NonNegativeInteger
--R eval : (%,Symbol,S) -> % if S has IEVALAB(SYMBOL,S)
---R eval : (%,List Symbol,List S) -> % if S has IEVALAB(SYMBOL,S)
---R eval : (%,List Equation S) -> % if S has EVALAB S
---R eval : (%,Equation S) -> % if S has EVALAB S
---R eval : (%,S,S) -> % if S has EVALAB S
---R eval : (%,List S,List S) -> % if S has EVALAB S
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R eval : (%,List(Symbol),List(S)) -> % if S has IEVALAB(SYMBOL,S)
+--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S)
+--R eval : (%,Equation(S)) -> % if S has EVALAB(S)
+--R eval : (%,S,S) -> % if S has EVALAB(S)
+--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S)
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if S has PFECAT
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if S has PFECAT
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT
--R fractionPart : % -> % if S has EUCDOM
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R max : (%,%) -> % if S has ORDSET
--R min : (%,%) -> % if S has ORDSET
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
--R negative? : % -> Boolean if S has OINTDOM
--R nextItem : % -> Union(%,"failed") if S has STEP
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if S has PATMAB FLOAT
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if S has PATMAB INT
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if S has PATMAB(FLOAT)
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if S has PATMAB(INT)
--R positive? : % -> Boolean if S has OINTDOM
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R reducedSystem : Matrix % -> Matrix S
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT
---R retract : % -> Integer if S has RETRACT INT
---R retract : % -> Fraction Integer if S has RETRACT INT
---R retract : % -> Symbol if S has RETRACT SYMBOL
---R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT INT
---R retractIfCan : % -> Union(Symbol,"failed") if S has RETRACT SYMBOL
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R reducedSystem : Matrix(%) -> Matrix(S)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT)
+--R retract : % -> Integer if S has RETRACT(INT)
+--R retract : % -> Fraction(Integer) if S has RETRACT(INT)
+--R retract : % -> Symbol if S has RETRACT(SYMBOL)
+--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(INT)
+--R retractIfCan : % -> Union(Symbol,"failed") if S has RETRACT(SYMBOL)
--R retractIfCan : % -> Union(S,"failed")
--R sign : % -> Integer if S has OINTDOM
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if S has PFECAT
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if S has PFECAT
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if S has PFECAT
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
--R wholePart : % -> S if S has EUCDOM
@@ -62368,76 +62520,77 @@ digraph pic {
--S 1 of 1
)show RealClosedField
+--R
--R RealClosedField is a category constructor
--R Abbreviation for RealClosedField is RCFIELD
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RCFIELD
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> %
+--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> %
--R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> %
---R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> %
+--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> %
---R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> %
---R ?+? : (%,%) -> % ?-? : (%,%) -> %
---R -? : % -> % ?/? : (%,%) -> %
---R ? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
---R ?>=? : (%,%) -> Boolean 1 : () -> %
---R 0 : () -> % ?^? : (%,Integer) -> %
---R ?^? : (%,PositiveInteger) -> % abs : % -> %
---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> %
---R coerce : Integer -> % coerce : Fraction Integer -> %
---R coerce : % -> % coerce : Fraction Integer -> %
---R coerce : Integer -> % coerce : % -> OutputForm
---R factor : % -> Factored % gcd : (%,%) -> %
---R gcd : List % -> % hash : % -> SingleInteger
---R inv : % -> % latex : % -> String
---R lcm : (%,%) -> % lcm : List % -> %
---R max : (%,%) -> % min : (%,%) -> %
---R negative? : % -> Boolean nthRoot : (%,Integer) -> %
---R one? : % -> Boolean positive? : % -> Boolean
---R prime? : % -> Boolean ?quo? : (%,%) -> %
---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
---R rename : (%,OutputForm) -> % rename! : (%,OutputForm) -> %
---R retract : % -> Fraction Integer sample : () -> %
---R sign : % -> Integer sizeLess? : (%,%) -> Boolean
---R sqrt : Integer -> % sqrt : Fraction Integer -> %
---R sqrt : % -> % squareFree : % -> Factored %
---R squareFreePart : % -> % unit? : % -> Boolean
---R unitCanonical : % -> % zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
+--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
+--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
+--R ?-? : (%,%) -> % -? : % -> %
+--R ?/? : (%,%) -> % ? : (%,%) -> Boolean
+--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
+--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean
+--R 1 : () -> % 0 : () -> %
+--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
+--R abs : % -> % associates? : (%,%) -> Boolean
+--R coerce : Fraction(Integer) -> % coerce : Integer -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
+--R coerce : Fraction(Integer) -> % coerce : Integer -> %
+--R coerce : % -> OutputForm factor : % -> Factored(%)
+--R gcd : (%,%) -> % gcd : List(%) -> %
+--R hash : % -> SingleInteger inv : % -> %
+--R latex : % -> String lcm : (%,%) -> %
+--R lcm : List(%) -> % max : (%,%) -> %
+--R min : (%,%) -> % negative? : % -> Boolean
+--R nthRoot : (%,Integer) -> % one? : % -> Boolean
+--R positive? : % -> Boolean prime? : % -> Boolean
+--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
+--R ?rem? : (%,%) -> % rename : (%,OutputForm) -> %
+--R rename! : (%,OutputForm) -> % retract : % -> Fraction(Integer)
+--R sample : () -> % sign : % -> Integer
+--R sizeLess? : (%,%) -> Boolean sqrt : Integer -> %
+--R sqrt : Fraction(Integer) -> % sqrt : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
+--R unit? : % -> Boolean unitCanonical : % -> %
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
+--R ?**? : (%,Fraction(Integer)) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
---R allRootsOf : Polynomial Integer -> List %
---R allRootsOf : Polynomial Fraction Integer -> List %
---R allRootsOf : Polynomial % -> List %
---R allRootsOf : SparseUnivariatePolynomial Integer -> List %
---R allRootsOf : SparseUnivariatePolynomial Fraction Integer -> List %
---R allRootsOf : SparseUnivariatePolynomial % -> List %
---R approximate : (%,%) -> Fraction Integer
+--R allRootsOf : Polynomial(Integer) -> List(%)
+--R allRootsOf : Polynomial(Fraction(Integer)) -> List(%)
+--R allRootsOf : Polynomial(%) -> List(%)
+--R allRootsOf : SparseUnivariatePolynomial(Integer) -> List(%)
+--R allRootsOf : SparseUnivariatePolynomial(Fraction(Integer)) -> List(%)
+--R allRootsOf : SparseUnivariatePolynomial(%) -> List(%)
+--R approximate : (%,%) -> Fraction(Integer)
--R characteristic : () -> NonNegativeInteger
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R mainDefiningPolynomial : % -> Union(SparseUnivariatePolynomial %,"failed")
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R mainDefiningPolynomial : % -> Union(SparseUnivariatePolynomial(%),"failed")
--R mainForm : % -> Union(OutputForm,"failed")
---R mainValue : % -> Union(SparseUnivariatePolynomial %,"failed")
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R retract : % -> Fraction Integer if Fraction Integer has RETRACT FRAC INT
---R retract : % -> Integer if Fraction Integer has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction Integer has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if Fraction Integer has RETRACT INT
---R rootOf : (SparseUnivariatePolynomial %,PositiveInteger) -> Union(%,"failed")
---R rootOf : (SparseUnivariatePolynomial %,PositiveInteger,OutputForm) -> Union(%,"failed")
+--R mainValue : % -> Union(SparseUnivariatePolynomial(%),"failed")
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R retract : % -> Fraction(Integer) if Fraction(Integer) has RETRACT(FRAC(INT))
+--R retract : % -> Integer if Fraction(Integer) has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(Integer) has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if Fraction(Integer) has RETRACT(INT)
+--R rootOf : (SparseUnivariatePolynomial(%),PositiveInteger) -> Union(%,"failed")
+--R rootOf : (SparseUnivariatePolynomial(%),PositiveInteger,OutputForm) -> Union(%,"failed")
--R sqrt : (%,NonNegativeInteger) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
@@ -62920,62 +63073,63 @@ digraph pic {
--S 1 of 1
)show RealNumberSystem
+--R
--R RealNumberSystem is a category constructor
--R Abbreviation for RealNumberSystem is RNS
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for RNS
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> %
---R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> %
---R ?+? : (%,%) -> % ?-? : (%,%) -> %
---R -? : % -> % ?/? : (%,%) -> %
---R ? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
---R ?>=? : (%,%) -> Boolean 1 : () -> %
---R 0 : () -> % ?^? : (%,Integer) -> %
---R ?^? : (%,PositiveInteger) -> % abs : % -> %
---R associates? : (%,%) -> Boolean ceiling : % -> %
---R coerce : Fraction Integer -> % coerce : Integer -> %
---R coerce : Fraction Integer -> % coerce : % -> %
---R coerce : Integer -> % coerce : % -> OutputForm
---R convert : % -> Pattern Float convert : % -> DoubleFloat
---R convert : % -> Float factor : % -> Factored %
---R floor : % -> % fractionPart : % -> %
---R gcd : List % -> % gcd : (%,%) -> %
---R hash : % -> SingleInteger inv : % -> %
---R latex : % -> String lcm : List % -> %
---R lcm : (%,%) -> % max : (%,%) -> %
---R min : (%,%) -> % negative? : % -> Boolean
---R norm : % -> % nthRoot : (%,Integer) -> %
---R one? : % -> Boolean positive? : % -> Boolean
---R prime? : % -> Boolean ?quo? : (%,%) -> %
---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
---R retract : % -> Fraction Integer retract : % -> Integer
---R round : % -> % sample : () -> %
---R sign : % -> Integer sizeLess? : (%,%) -> Boolean
---R sqrt : % -> % squareFree : % -> Factored %
---R squareFreePart : % -> % truncate : % -> %
---R unit? : % -> Boolean unitCanonical : % -> %
---R wholePart : % -> Integer zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
+--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
+--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
+--R ?-? : (%,%) -> % -? : % -> %
+--R ?/? : (%,%) -> % ? : (%,%) -> Boolean
+--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
+--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean
+--R 1 : () -> % 0 : () -> %
+--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
+--R abs : % -> % associates? : (%,%) -> Boolean
+--R ceiling : % -> % coerce : Fraction(Integer) -> %
+--R coerce : Integer -> % coerce : Fraction(Integer) -> %
+--R coerce : % -> % coerce : Integer -> %
+--R coerce : % -> OutputForm convert : % -> Pattern(Float)
+--R convert : % -> DoubleFloat convert : % -> Float
+--R factor : % -> Factored(%) floor : % -> %
+--R fractionPart : % -> % gcd : List(%) -> %
+--R gcd : (%,%) -> % hash : % -> SingleInteger
+--R inv : % -> % latex : % -> String
+--R lcm : List(%) -> % lcm : (%,%) -> %
+--R max : (%,%) -> % min : (%,%) -> %
+--R negative? : % -> Boolean norm : % -> %
+--R nthRoot : (%,Integer) -> % one? : % -> Boolean
+--R positive? : % -> Boolean prime? : % -> Boolean
+--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
+--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer)
+--R retract : % -> Integer round : % -> %
+--R sample : () -> % sign : % -> Integer
+--R sizeLess? : (%,%) -> Boolean sqrt : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
+--R truncate : % -> % unit? : % -> Boolean
+--R unitCanonical : % -> % wholePart : % -> Integer
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
+--R ?**? : (%,Fraction(Integer)) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R retractIfCan : % -> Union(Fraction Integer,"failed")
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
--R retractIfCan : % -> Union(Integer,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
@@ -63352,6 +63506,7 @@ digraph pic {
--S 1 of 1
)show RecursivePolynomialCategory
+--R
--R RecursivePolynomialCategory(R: Ring,E: OrderedAbelianMonoidSup,V: OrderedSet) is a category constructor
--R Abbreviation for RecursivePolynomialCategory is RPOLCAT
--R This constructor is exposed in this frame.
@@ -63363,47 +63518,45 @@ digraph pic {
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
---R D : (%,List V) -> % D : (%,V) -> %
+--R D : (%,List(V)) -> % D : (%,V) -> %
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R
---R coefficients : % -> List R coerce : V -> %
+--R coefficients : % -> List(R) coerce : V -> %
--R coerce : R -> % coerce : Integer -> %
--R coerce : % -> OutputForm deepestInitial : % -> %
--R deepestTail : % -> % degree : % -> E
---R differentiate : (%,List V) -> % differentiate : (%,V) -> %
---R eval : (%,List V,List %) -> % eval : (%,V,%) -> %
---R eval : (%,List V,List R) -> % eval : (%,V,R) -> %
---R eval : (%,List %,List %) -> % eval : (%,%,%) -> %
---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> %
+--R differentiate : (%,List(V)) -> % differentiate : (%,V) -> %
+--R eval : (%,List(V),List(%)) -> % eval : (%,V,%) -> %
+--R eval : (%,List(V),List(R)) -> % eval : (%,V,R) -> %
+--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> %
--R ground : % -> R ground? : % -> Boolean
--R hash : % -> SingleInteger head : % -> %
--R headReduce : (%,%) -> % headReduced? : (%,%) -> Boolean
--R infRittWu? : (%,%) -> Boolean init : % -> %
---R initiallyReduce : (%,%) -> % iteratedInitials : % -> List %
+--R initiallyReduce : (%,%) -> % iteratedInitials : % -> List(%)
--R latex : % -> String lazyPquo : (%,%,V) -> %
--R lazyPquo : (%,%) -> % lazyPrem : (%,%,V) -> %
--R lazyPrem : (%,%) -> % leadingCoefficient : (%,V) -> %
--R leadingCoefficient : % -> R leadingMonomial : % -> %
---R leastMonomial : % -> % mainCoefficients : % -> List %
---R mainMonomial : % -> % mainMonomials : % -> List %
+--R leastMonomial : % -> % mainCoefficients : % -> List(%)
+--R mainMonomial : % -> % mainMonomials : % -> List(%)
--R map : ((R -> R),%) -> % mapExponents : ((E -> E),%) -> %
--R mdeg : % -> NonNegativeInteger minimumDegree : % -> E
--R monic? : % -> Boolean monicModulo : (%,%) -> %
--R monomial : (R,E) -> % monomial? : % -> Boolean
---R monomials : % -> List % mvar : % -> V
+--R monomials : % -> List(%) mvar : % -> V
--R normalized? : (%,%) -> Boolean one? : % -> Boolean
--R pomopo! : (%,R,E,%) -> % pquo : (%,%,V) -> %
--R pquo : (%,%) -> % prem : (%,%,V) -> %
---R prem : (%,%) -> % primitiveMonomials : % -> List %
---R quasiMonic? : % -> Boolean recip : % -> Union(%,"failed")
---R reduced? : (%,List %) -> Boolean reduced? : (%,%) -> Boolean
+--R prem : (%,%) -> % quasiMonic? : % -> Boolean
+--R recip : % -> Union(%,"failed") reduced? : (%,%) -> Boolean
--R reductum : (%,V) -> % reductum : % -> %
--R retract : % -> V retract : % -> R
--R sample : () -> % supRittWu? : (%,%) -> Boolean
---R tail : % -> % variables : % -> List V
+--R tail : % -> % variables : % -> List(V)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT
---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT
+--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT))
+--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
@@ -63411,7 +63564,7 @@ digraph pic {
--R ?<=? : (%,%) -> Boolean if R has ORDSET
--R ?>? : (%,%) -> Boolean if R has ORDSET
--R ?>=? : (%,%) -> Boolean if R has ORDSET
---R D : (%,List V,List NonNegativeInteger) -> %
+--R D : (%,List(V),List(NonNegativeInteger)) -> %
--R D : (%,V,NonNegativeInteger) -> %
--R LazardQuotient : (%,%,NonNegativeInteger) -> % if R has INTDOM
--R LazardQuotient2 : (%,%,%,NonNegativeInteger) -> % if R has INTDOM
@@ -63421,27 +63574,29 @@ digraph pic {
--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ
---R coefficient : (%,List V,List NonNegativeInteger) -> %
+--R coefficient : (%,List(V),List(NonNegativeInteger)) -> %
--R coefficient : (%,V,NonNegativeInteger) -> %
--R coerce : % -> % if R has INTDOM
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT
---R coerce : % -> Polynomial R if V has KONVERT SYMBOL
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT))
+--R coerce : % -> Polynomial(R) if V has KONVERT(SYMBOL)
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
--R content : (%,V) -> % if R has GCDDOM
--R content : % -> R if R has GCDDOM
---R convert : % -> Polynomial R if V has KONVERT SYMBOL
---R convert : % -> String if R has RETRACT INT and V has KONVERT SYMBOL
---R convert : Polynomial R -> % if V has KONVERT SYMBOL
---R convert : Polynomial Integer -> % if not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R convert : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R convert : % -> InputForm if V has KONVERT INFORM and R has KONVERT INFORM
---R convert : % -> Pattern Integer if V has KONVERT PATTERN INT and R has KONVERT PATTERN INT
---R convert : % -> Pattern Float if V has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT
---R degree : (%,List V) -> List NonNegativeInteger
+--R convert : % -> Polynomial(R) if V has KONVERT(SYMBOL)
+--R convert : % -> String if R has RETRACT(INT) and V has KONVERT(SYMBOL)
+--R convert : Polynomial(R) -> % if V has KONVERT(SYMBOL)
+--R convert : Polynomial(Integer) -> % if not(has(R,Algebra(Fraction(Integer)))) and R has ALGEBRA(INT) and V has KONVERT(SYMBOL) or R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R convert : Polynomial(Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R convert : % -> InputForm if V has KONVERT(INFORM) and R has KONVERT(INFORM)
+--R convert : % -> Pattern(Integer) if V has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT))
+--R convert : % -> Pattern(Float) if V has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT))
+--R degree : (%,List(V)) -> List(NonNegativeInteger)
--R degree : (%,V) -> NonNegativeInteger
---R differentiate : (%,List V,List NonNegativeInteger) -> %
+--R differentiate : (%,List(V),List(NonNegativeInteger)) -> %
--R differentiate : (%,V,NonNegativeInteger) -> %
--R discriminant : (%,V) -> % if R has COMRING
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
--R exactQuotient : (%,%) -> % if R has INTDOM
--R exactQuotient : (%,R) -> % if R has INTDOM
--R exactQuotient! : (%,%) -> % if R has INTDOM
@@ -63449,21 +63604,21 @@ digraph pic {
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R extendedSubResultantGcd : (%,%) -> Record(gcd: %,coef1: %,coef2: %) if R has INTDOM
---R factor : % -> Factored % if R has PFECAT
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R factor : % -> Factored(%) if R has PFECAT
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R gcd : (%,%) -> % if R has GCDDOM
---R gcd : List % -> % if R has GCDDOM
+--R gcd : List(%) -> % if R has GCDDOM
--R gcd : (R,%) -> R if R has GCDDOM
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM
--R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM
--R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM
---R headReduced? : (%,List %) -> Boolean
---R initiallyReduced? : (%,List %) -> Boolean
+--R headReduced? : (%,List(%)) -> Boolean
+--R initiallyReduced? : (%,List(%)) -> Boolean
--R initiallyReduced? : (%,%) -> Boolean
--R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed")
---R isPlus : % -> Union(List %,"failed")
---R isTimes : % -> Union(List %,"failed")
+--R isPlus : % -> Union(List(%),"failed")
+--R isTimes : % -> Union(List(%),"failed")
--R lastSubResultant : (%,%) -> % if R has INTDOM
--R lazyPremWithDefault : (%,%,V) -> Record(coef: %,gap: NonNegativeInteger,remainder: %)
--R lazyPremWithDefault : (%,%) -> Record(coef: %,gap: NonNegativeInteger,remainder: %)
@@ -63471,64 +63626,66 @@ digraph pic {
--R lazyPseudoDivide : (%,%) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %)
--R lazyResidueClass : (%,%) -> Record(polnum: %,polden: %,power: NonNegativeInteger)
--R lcm : (%,%) -> % if R has GCDDOM
---R lcm : List % -> % if R has GCDDOM
+--R lcm : List(%) -> % if R has GCDDOM
--R mainContent : % -> % if R has GCDDOM
--R mainPrimitivePart : % -> % if R has GCDDOM
--R mainSquareFreePart : % -> % if R has GCDDOM
--R mainVariable : % -> Union(V,"failed")
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
---R minimumDegree : (%,List V) -> List NonNegativeInteger
+--R minimumDegree : (%,List(V)) -> List(NonNegativeInteger)
--R minimumDegree : (%,V) -> NonNegativeInteger
--R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %)
---R monomial : (%,List V,List NonNegativeInteger) -> %
+--R monomial : (%,List(V),List(NonNegativeInteger)) -> %
--R monomial : (%,V,NonNegativeInteger) -> %
---R multivariate : (SparseUnivariatePolynomial %,V) -> %
---R multivariate : (SparseUnivariatePolynomial R,V) -> %
+--R multivariate : (SparseUnivariatePolynomial(%),V) -> %
+--R multivariate : (SparseUnivariatePolynomial(R),V) -> %
--R nextsubResultant2 : (%,%,%,%) -> % if R has INTDOM
---R normalized? : (%,List %) -> Boolean
+--R normalized? : (%,List(%)) -> Boolean
--R numberOfMonomials : % -> NonNegativeInteger
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB INT and R has PATMAB INT
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB FLOAT and R has PATMAB FLOAT
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB(INT) and R has PATMAB(INT)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB(FLOAT) and R has PATMAB(FLOAT)
--R primPartElseUnitCanonical : % -> % if R has INTDOM
--R primPartElseUnitCanonical! : % -> % if R has INTDOM
--R prime? : % -> Boolean if R has PFECAT
+--R primitiveMonomials : % -> List(%)
--R primitivePart : (%,V) -> % if R has GCDDOM
--R primitivePart : % -> % if R has GCDDOM
--R primitivePart! : % -> % if R has GCDDOM
--R pseudoDivide : (%,%) -> Record(quotient: %,remainder: %)
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
+--R reduced? : (%,List(%)) -> Boolean
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
--R resultant : (%,%) -> % if R has INTDOM
--R resultant : (%,%,V) -> % if R has COMRING
---R retract : Polynomial R -> % if not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) and V has KONVERT SYMBOL or not has(R,IntegerNumberSystem) and not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or not has(R,QuotientFieldCategory Integer) and R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R retract : Polynomial Integer -> % if not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R retract : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R retract : % -> Integer if R has RETRACT INT
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retractIfCan : Polynomial R -> Union(%,"failed") if not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) and V has KONVERT SYMBOL or not has(R,IntegerNumberSystem) and not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or not has(R,QuotientFieldCategory Integer) and R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R retractIfCan : Polynomial Integer -> Union(%,"failed") if not has(R,Algebra Fraction Integer) and R has ALGEBRA INT and V has KONVERT SYMBOL or R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
---R retractIfCan : Polynomial Fraction Integer -> Union(%,"failed") if R has ALGEBRA FRAC INT and V has KONVERT SYMBOL
+--R retract : Polynomial(R) -> % if not(has(R,Algebra(Fraction(Integer)))) and not(has(R,Algebra(Integer))) and V has KONVERT(SYMBOL) or not(has(R,IntegerNumberSystem)) and not(has(R,Algebra(Fraction(Integer)))) and R has ALGEBRA(INT) and V has KONVERT(SYMBOL) or not(has(R,QuotientFieldCategory(Integer))) and R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R retract : Polynomial(Integer) -> % if not(has(R,Algebra(Fraction(Integer)))) and R has ALGEBRA(INT) and V has KONVERT(SYMBOL) or R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R retract : Polynomial(Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R retract : % -> Integer if R has RETRACT(INT)
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retractIfCan : Polynomial(R) -> Union(%,"failed") if not(has(R,Algebra(Fraction(Integer)))) and not(has(R,Algebra(Integer))) and V has KONVERT(SYMBOL) or not(has(R,IntegerNumberSystem)) and not(has(R,Algebra(Fraction(Integer)))) and R has ALGEBRA(INT) and V has KONVERT(SYMBOL) or not(has(R,QuotientFieldCategory(Integer))) and R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") if not(has(R,Algebra(Fraction(Integer)))) and R has ALGEBRA(INT) and V has KONVERT(SYMBOL) or R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
+--R retractIfCan : Polynomial(Fraction(Integer)) -> Union(%,"failed") if R has ALGEBRA(FRAC(INT)) and V has KONVERT(SYMBOL)
--R retractIfCan : % -> Union(V,"failed")
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(R,"failed")
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT
---R squareFree : % -> Factored % if R has GCDDOM
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT
+--R squareFree : % -> Factored(%) if R has GCDDOM
--R squareFreePart : % -> % if R has GCDDOM
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
---R subResultantChain : (%,%) -> List % if R has INTDOM
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
+--R subResultantChain : (%,%) -> List(%) if R has INTDOM
--R subResultantGcd : (%,%) -> % if R has INTDOM
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R totalDegree : (%,List V) -> NonNegativeInteger
+--R totalDegree : (%,List(V)) -> NonNegativeInteger
--R totalDegree : % -> NonNegativeInteger
--R unit? : % -> Boolean if R has INTDOM
--R unitCanonical : % -> % if R has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM
---R univariate : % -> SparseUnivariatePolynomial R
---R univariate : (%,V) -> SparseUnivariatePolynomial %
+--R univariate : % -> SparseUnivariatePolynomial(R)
+--R univariate : (%,V) -> SparseUnivariatePolynomial(%)
--R
--E 1
@@ -65333,7 +65490,8 @@ digraph pic {
--S 1 of 1
)show UnivariateLaurentSeriesCategory
---R UnivariateLaurentSeriesCategory Coef: Ring is a category constructor
+--R
+--R UnivariateLaurentSeriesCategory(Coef: Ring) is a category constructor
--R Abbreviation for UnivariateLaurentSeriesCategory is ULSCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ULSCAT
@@ -65359,104 +65517,104 @@ digraph pic {
--R sample : () -> % truncate : (%,Integer) -> %
--R variable : % -> Symbol zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?**? : (%,Integer) -> % if Coef has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,%) -> % if Coef has FIELD
--R ?/? : (%,Coef) -> % if Coef has FIELD
--R D : % -> % if Coef has *: (Integer,Coef) -> Coef
--R D : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef
---R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
--R ?^? : (%,Integer) -> % if Coef has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
---R acos : % -> % if Coef has ALGEBRA FRAC INT
---R acosh : % -> % if Coef has ALGEBRA FRAC INT
---R acot : % -> % if Coef has ALGEBRA FRAC INT
---R acoth : % -> % if Coef has ALGEBRA FRAC INT
---R acsc : % -> % if Coef has ALGEBRA FRAC INT
---R acsch : % -> % if Coef has ALGEBRA FRAC INT
+--R acos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT))
--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef
---R asec : % -> % if Coef has ALGEBRA FRAC INT
---R asech : % -> % if Coef has ALGEBRA FRAC INT
---R asin : % -> % if Coef has ALGEBRA FRAC INT
---R asinh : % -> % if Coef has ALGEBRA FRAC INT
+--R asec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R associates? : (%,%) -> Boolean if Coef has INTDOM
---R atan : % -> % if Coef has ALGEBRA FRAC INT
---R atanh : % -> % if Coef has ALGEBRA FRAC INT
+--R atan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R coerce : Coef -> % if Coef has COMRING
---R cos : % -> % if Coef has ALGEBRA FRAC INT
---R cosh : % -> % if Coef has ALGEBRA FRAC INT
---R cot : % -> % if Coef has ALGEBRA FRAC INT
---R coth : % -> % if Coef has ALGEBRA FRAC INT
---R csc : % -> % if Coef has ALGEBRA FRAC INT
---R csch : % -> % if Coef has ALGEBRA FRAC INT
+--R cos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R coth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csch : % -> % if Coef has ALGEBRA(FRAC(INT))
--R differentiate : % -> % if Coef has *: (Integer,Coef) -> Coef
--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD
--R ?.? : (%,%) -> % if Integer has SGROUP
--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD
---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef
---R exp : % -> % if Coef has ALGEBRA FRAC INT
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD
+--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Integer) -> Coef
+--R exp : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD
---R factor : % -> Factored % if Coef has FIELD
+--R factor : % -> Factored(%) if Coef has FIELD
--R gcd : (%,%) -> % if Coef has FIELD
---R gcd : List % -> % if Coef has FIELD
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD
---R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT
---R integrate : % -> % if Coef has ALGEBRA FRAC INT
+--R gcd : List(%) -> % if Coef has FIELD
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD
+--R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT))
+--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT))
--R inv : % -> % if Coef has FIELD
--R lcm : (%,%) -> % if Coef has FIELD
---R lcm : List % -> % if Coef has FIELD
---R log : % -> % if Coef has ALGEBRA FRAC INT
---R monomial : (%,List SingletonAsOrderedSet,List Integer) -> %
+--R lcm : List(%) -> % if Coef has FIELD
+--R log : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R monomial : (%,List(SingletonAsOrderedSet),List(Integer)) -> %
--R monomial : (%,SingletonAsOrderedSet,Integer) -> %
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
--R multiplyCoefficients : ((Integer -> Coef),%) -> %
--R multiplyExponents : (%,PositiveInteger) -> %
---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT
---R pi : () -> % if Coef has ALGEBRA FRAC INT
+--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT))
+--R pi : () -> % if Coef has ALGEBRA(FRAC(INT))
--R prime? : % -> Boolean if Coef has FIELD
---R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Coef has FIELD
--R ?quo? : (%,%) -> % if Coef has FIELD
---R rationalFunction : (%,Integer,Integer) -> Fraction Polynomial Coef if Coef has INTDOM
---R rationalFunction : (%,Integer) -> Fraction Polynomial Coef if Coef has INTDOM
+--R rationalFunction : (%,Integer,Integer) -> Fraction(Polynomial(Coef)) if Coef has INTDOM
+--R rationalFunction : (%,Integer) -> Fraction(Polynomial(Coef)) if Coef has INTDOM
--R ?rem? : (%,%) -> % if Coef has FIELD
---R sec : % -> % if Coef has ALGEBRA FRAC INT
---R sech : % -> % if Coef has ALGEBRA FRAC INT
---R series : Stream Record(k: Integer,c: Coef) -> %
---R sin : % -> % if Coef has ALGEBRA FRAC INT
---R sinh : % -> % if Coef has ALGEBRA FRAC INT
+--R sec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R series : Stream(Record(k: Integer,c: Coef)) -> %
+--R sin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R sizeLess? : (%,%) -> Boolean if Coef has FIELD
---R sqrt : % -> % if Coef has ALGEBRA FRAC INT
---R squareFree : % -> Factored % if Coef has FIELD
+--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R squareFree : % -> Factored(%) if Coef has FIELD
--R squareFreePart : % -> % if Coef has FIELD
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tan : % -> % if Coef has ALGEBRA FRAC INT
---R tanh : % -> % if Coef has ALGEBRA FRAC INT
---R terms : % -> Stream Record(k: Integer,c: Coef)
+--R tan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R terms : % -> Stream(Record(k: Integer,c: Coef))
--R truncate : (%,Integer,Integer) -> %
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R
--E 1
@@ -65964,7 +66122,8 @@ digraph pic {
--S 1 of 1
)show UnivariatePuiseuxSeriesCategory
---R UnivariatePuiseuxSeriesCategory Coef: Ring is a category constructor
+--R
+--R UnivariatePuiseuxSeriesCategory(Coef: Ring) is a category constructor
--R Abbreviation for UnivariatePuiseuxSeriesCategory is UPXSCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPXSCAT
@@ -65978,117 +66137,117 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,PositiveInteger) -> % center : % -> Coef
--R coerce : Integer -> % coerce : % -> OutputForm
---R complete : % -> % degree : % -> Fraction Integer
+--R complete : % -> % degree : % -> Fraction(Integer)
--R hash : % -> SingleInteger latex : % -> String
--R leadingCoefficient : % -> Coef leadingMonomial : % -> %
--R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean
---R one? : % -> Boolean order : % -> Fraction Integer
+--R one? : % -> Boolean order : % -> Fraction(Integer)
--R pole? : % -> Boolean recip : % -> Union(%,"failed")
--R reductum : % -> % sample : () -> %
--R variable : % -> Symbol zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?**? : (%,Integer) -> % if Coef has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,%) -> % if Coef has FIELD
--R ?/? : (%,Coef) -> % if Coef has FIELD
---R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
+--R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
--R ?^? : (%,Integer) -> % if Coef has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
---R acos : % -> % if Coef has ALGEBRA FRAC INT
---R acosh : % -> % if Coef has ALGEBRA FRAC INT
---R acot : % -> % if Coef has ALGEBRA FRAC INT
---R acoth : % -> % if Coef has ALGEBRA FRAC INT
---R acsc : % -> % if Coef has ALGEBRA FRAC INT
---R acsch : % -> % if Coef has ALGEBRA FRAC INT
---R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef
---R asec : % -> % if Coef has ALGEBRA FRAC INT
---R asech : % -> % if Coef has ALGEBRA FRAC INT
---R asin : % -> % if Coef has ALGEBRA FRAC INT
---R asinh : % -> % if Coef has ALGEBRA FRAC INT
+--R acos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R approximate : (%,Fraction(Integer)) -> Coef if Coef has **: (Coef,Fraction(Integer)) -> Coef and Coef has coerce: Symbol -> Coef
+--R asec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R associates? : (%,%) -> Boolean if Coef has INTDOM
---R atan : % -> % if Coef has ALGEBRA FRAC INT
---R atanh : % -> % if Coef has ALGEBRA FRAC INT
+--R atan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
---R coefficient : (%,Fraction Integer) -> Coef
+--R coefficient : (%,Fraction(Integer)) -> Coef
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R coerce : Coef -> % if Coef has COMRING
---R cos : % -> % if Coef has ALGEBRA FRAC INT
---R cosh : % -> % if Coef has ALGEBRA FRAC INT
---R cot : % -> % if Coef has ALGEBRA FRAC INT
---R coth : % -> % if Coef has ALGEBRA FRAC INT
---R csc : % -> % if Coef has ALGEBRA FRAC INT
---R csch : % -> % if Coef has ALGEBRA FRAC INT
---R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
+--R cos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R coth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csch : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R differentiate : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD
---R ?.? : (%,%) -> % if Fraction Integer has SGROUP
---R ?.? : (%,Fraction Integer) -> Coef
+--R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP
+--R ?.? : (%,Fraction(Integer)) -> Coef
--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD
---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef
---R exp : % -> % if Coef has ALGEBRA FRAC INT
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD
+--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef
+--R exp : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
---R extend : (%,Fraction Integer) -> %
+--R extend : (%,Fraction(Integer)) -> %
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD
---R factor : % -> Factored % if Coef has FIELD
+--R factor : % -> Factored(%) if Coef has FIELD
--R gcd : (%,%) -> % if Coef has FIELD
---R gcd : List % -> % if Coef has FIELD
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD
---R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT
---R integrate : % -> % if Coef has ALGEBRA FRAC INT
+--R gcd : List(%) -> % if Coef has FIELD
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD
+--R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT))
+--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT))
--R inv : % -> % if Coef has FIELD
--R lcm : (%,%) -> % if Coef has FIELD
---R lcm : List % -> % if Coef has FIELD
---R log : % -> % if Coef has ALGEBRA FRAC INT
---R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> %
---R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> %
---R monomial : (Coef,Fraction Integer) -> %
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD
---R multiplyExponents : (%,Fraction Integer) -> %
+--R lcm : List(%) -> % if Coef has FIELD
+--R log : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R monomial : (%,List(SingletonAsOrderedSet),List(Fraction(Integer))) -> %
+--R monomial : (%,SingletonAsOrderedSet,Fraction(Integer)) -> %
+--R monomial : (Coef,Fraction(Integer)) -> %
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
+--R multiplyExponents : (%,Fraction(Integer)) -> %
--R multiplyExponents : (%,PositiveInteger) -> %
---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT
---R order : (%,Fraction Integer) -> Fraction Integer
---R pi : () -> % if Coef has ALGEBRA FRAC INT
+--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT))
+--R order : (%,Fraction(Integer)) -> Fraction(Integer)
+--R pi : () -> % if Coef has ALGEBRA(FRAC(INT))
--R prime? : % -> Boolean if Coef has FIELD
---R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Coef has FIELD
--R ?quo? : (%,%) -> % if Coef has FIELD
--R ?rem? : (%,%) -> % if Coef has FIELD
---R sec : % -> % if Coef has ALGEBRA FRAC INT
---R sech : % -> % if Coef has ALGEBRA FRAC INT
---R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> %
---R sin : % -> % if Coef has ALGEBRA FRAC INT
---R sinh : % -> % if Coef has ALGEBRA FRAC INT
+--R sec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R series : (NonNegativeInteger,Stream(Record(k: Fraction(Integer),c: Coef))) -> %
+--R sin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R sizeLess? : (%,%) -> Boolean if Coef has FIELD
---R sqrt : % -> % if Coef has ALGEBRA FRAC INT
---R squareFree : % -> Factored % if Coef has FIELD
+--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R squareFree : % -> Factored(%) if Coef has FIELD
--R squareFreePart : % -> % if Coef has FIELD
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tan : % -> % if Coef has ALGEBRA FRAC INT
---R tanh : % -> % if Coef has ALGEBRA FRAC INT
---R terms : % -> Stream Record(k: Fraction Integer,c: Coef)
---R truncate : (%,Fraction Integer,Fraction Integer) -> %
---R truncate : (%,Fraction Integer) -> %
+--R tan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R terms : % -> Stream(Record(k: Fraction(Integer),c: Coef))
+--R truncate : (%,Fraction(Integer),Fraction(Integer)) -> %
+--R truncate : (%,Fraction(Integer)) -> %
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R
--E 1
@@ -66580,7 +66739,8 @@ digraph pic {
--S 1 of 1
)show UnivariatePolynomialCategory
---R UnivariatePolynomialCategory R: Ring is a category constructor
+--R
+--R UnivariatePolynomialCategory(R: Ring) is a category constructor
--R Abbreviation for UnivariatePolynomialCategory is UPOLYC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPOLYC
@@ -66594,24 +66754,22 @@ digraph pic {
--R D : (%,(R -> R)) -> % D : % -> %
--R D : (%,NonNegativeInteger) -> % 1 : () -> %
--R 0 : () -> % ?^? : (%,PositiveInteger) -> %
---R coefficients : % -> List R coerce : R -> %
+--R coefficients : % -> List(R) coerce : R -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R degree : % -> NonNegativeInteger differentiate : % -> %
--R ?.? : (%,%) -> % ?.? : (%,R) -> R
---R eval : (%,List %,List %) -> % eval : (%,%,%) -> %
---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> %
+--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> %
--R ground : % -> R ground? : % -> Boolean
--R hash : % -> SingleInteger init : () -> % if R has STEP
--R latex : % -> String leadingCoefficient : % -> R
--R leadingMonomial : % -> % map : ((R -> R),%) -> %
---R monomial? : % -> Boolean monomials : % -> List %
---R one? : % -> Boolean primitiveMonomials : % -> List %
---R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed")
---R reductum : % -> % retract : % -> R
---R sample : () -> % zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT
---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT
+--R monomial? : % -> Boolean monomials : % -> List(%)
+--R one? : % -> Boolean pseudoRemainder : (%,%) -> %
+--R recip : % -> Union(%,"failed") reductum : % -> %
+--R retract : % -> R sample : () -> %
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
+--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT))
+--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,R) -> % if R has FIELD
@@ -66620,141 +66778,144 @@ digraph pic {
--R ?>? : (%,%) -> Boolean if R has ORDSET
--R ?>=? : (%,%) -> Boolean if R has ORDSET
--R D : (%,(R -> R),NonNegativeInteger) -> %
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol) -> % if R has PDRING SYMBOL
---R D : (%,Symbol) -> % if R has PDRING SYMBOL
---R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> %
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> %
--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> %
---R D : (%,List SingletonAsOrderedSet) -> %
+--R D : (%,List(SingletonAsOrderedSet)) -> %
--R D : (%,SingletonAsOrderedSet) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R associates? : (%,%) -> Boolean if R has INTDOM
--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ
---R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> %
+--R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> %
--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> %
--R coefficient : (%,NonNegativeInteger) -> R
--R coerce : % -> % if R has INTDOM
---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT or R has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT))
--R coerce : SingletonAsOrderedSet -> %
---R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM
+--R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM
--R composite : (%,%) -> Union(%,"failed") if R has INTDOM
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit))
--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM
--R content : % -> R if R has GCDDOM
---R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM
---R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT
---R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT
---R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger
+--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM)
+--R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT))
+--R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT))
+--R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger)
--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger
--R differentiate : (%,(R -> R),%) -> %
--R differentiate : (%,(R -> R)) -> %
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL)
--R differentiate : (%,NonNegativeInteger) -> %
---R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> %
+--R differentiate : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> %
--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> %
---R differentiate : (%,List SingletonAsOrderedSet) -> %
+--R differentiate : (%,List(SingletonAsOrderedSet)) -> %
--R differentiate : (%,SingletonAsOrderedSet) -> %
--R discriminant : % -> R if R has COMRING
--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING
--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed")
---R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM
---R elt : (Fraction %,R) -> R if R has FIELD
---R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM
+--R ?.? : (%,Fraction(%)) -> Fraction(%) if R has INTDOM
+--R elt : (Fraction(%),R) -> R if R has FIELD
+--R elt : (Fraction(%),Fraction(%)) -> Fraction(%) if R has INTDOM
--R euclideanSize : % -> NonNegativeInteger if R has FIELD
---R eval : (%,List SingletonAsOrderedSet,List %) -> %
+--R eval : (%,List(SingletonAsOrderedSet),List(%)) -> %
--R eval : (%,SingletonAsOrderedSet,%) -> %
---R eval : (%,List SingletonAsOrderedSet,List R) -> %
+--R eval : (%,List(SingletonAsOrderedSet),List(R)) -> %
--R eval : (%,SingletonAsOrderedSet,R) -> %
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD
---R factor : % -> Factored % if R has PFECAT
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R factor : % -> Factored(%) if R has PFECAT
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R gcd : (%,%) -> % if R has GCDDOM
---R gcd : List % -> % if R has GCDDOM
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM
---R integrate : % -> % if R has ALGEBRA FRAC INT
+--R gcd : List(%) -> % if R has GCDDOM
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM
+--R integrate : % -> % if R has ALGEBRA(FRAC(INT))
--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed")
---R isPlus : % -> Union(List %,"failed")
---R isTimes : % -> Union(List %,"failed")
+--R isPlus : % -> Union(List(%),"failed")
+--R isTimes : % -> Union(List(%),"failed")
--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %)
--R lcm : (%,%) -> % if R has GCDDOM
---R lcm : List % -> % if R has GCDDOM
+--R lcm : List(%) -> % if R has GCDDOM
--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed")
---R makeSUP : % -> SparseUnivariatePolynomial R
+--R makeSUP : % -> SparseUnivariatePolynomial(R)
--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> %
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
---R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger
+--R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger)
--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger
--R minimumDegree : % -> NonNegativeInteger
--R monicDivide : (%,%) -> Record(quotient: %,remainder: %)
--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %)
---R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> %
+--R monomial : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> %
--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> %
--R monomial : (R,NonNegativeInteger) -> %
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD
--R multiplyExponents : (%,NonNegativeInteger) -> %
---R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> %
---R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> %
+--R multivariate : (SparseUnivariatePolynomial(%),SingletonAsOrderedSet) -> %
+--R multivariate : (SparseUnivariatePolynomial(R),SingletonAsOrderedSet) -> %
--R nextItem : % -> Union(%,"failed") if R has STEP
--R numberOfMonomials : % -> NonNegativeInteger
--R order : (%,%) -> NonNegativeInteger if R has INTDOM
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB(INT) and R has PATMAB(INT)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT)
--R pomopo! : (%,R,NonNegativeInteger,%) -> %
--R prime? : % -> Boolean if R has PFECAT
+--R primitiveMonomials : % -> List(%)
--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM
--R primitivePart : % -> % if R has GCDDOM
---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD
--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM
--R pseudoQuotient : (%,%) -> % if R has INTDOM
--R ?quo? : (%,%) -> % if R has FIELD
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
--R ?rem? : (%,%) -> % if R has FIELD
--R resultant : (%,%) -> R if R has COMRING
--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING
--R retract : % -> SingletonAsOrderedSet
---R retract : % -> Integer if R has RETRACT INT
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
+--R retract : % -> Integer if R has RETRACT(INT)
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed")
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
--R retractIfCan : % -> Union(R,"failed")
--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM
--R shiftLeft : (%,NonNegativeInteger) -> %
--R shiftRight : (%,NonNegativeInteger) -> %
--R sizeLess? : (%,%) -> Boolean if R has FIELD
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT
---R squareFree : % -> Factored % if R has GCDDOM
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT
+--R squareFree : % -> Factored(%) if R has GCDDOM
--R squareFreePart : % -> % if R has GCDDOM
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT
--R subResultantGcd : (%,%) -> % if R has INTDOM
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger
+--R totalDegree : (%,List(SingletonAsOrderedSet)) -> NonNegativeInteger
--R totalDegree : % -> NonNegativeInteger
--R unit? : % -> Boolean if R has INTDOM
--R unitCanonical : % -> % if R has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM
---R univariate : % -> SparseUnivariatePolynomial R
---R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial %
---R unmakeSUP : SparseUnivariatePolynomial R -> %
---R variables : % -> List SingletonAsOrderedSet
---R vectorise : (%,NonNegativeInteger) -> Vector R
+--R univariate : % -> SparseUnivariatePolynomial(R)
+--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial(%)
+--R unmakeSUP : SparseUnivariatePolynomial(R) -> %
+--R variables : % -> List(SingletonAsOrderedSet)
+--R vectorise : (%,NonNegativeInteger) -> Vector(R)
--R
--E 1
@@ -67767,172 +67928,176 @@ digraph pic {
--S 1 of 1
)show AlgebraicallyClosedFunctionSpace
---R AlgebraicallyClosedFunctionSpace R: Join(OrderedSet,IntegralDomain) is a category constructor
+--R
+--R AlgebraicallyClosedFunctionSpace(R: Join(OrderedSet,IntegralDomain)) is a category constructor
--R Abbreviation for AlgebraicallyClosedFunctionSpace is ACFS
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ACFS
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> %
---R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> %
---R ?+? : (%,%) -> % ?-? : (%,%) -> %
---R -? : % -> % ?/? : (%,%) -> %
---R ? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
---R ?>=? : (%,%) -> Boolean 1 : () -> %
---R 0 : () -> % ?^? : (%,Integer) -> %
---R ?^? : (%,PositiveInteger) -> % applyQuote : (Symbol,%) -> %
---R applyQuote : (Symbol,%,%) -> % associates? : (%,%) -> Boolean
---R belong? : BasicOperator -> Boolean box : % -> %
---R box : List % -> % coerce : Kernel % -> %
---R coerce : Symbol -> % coerce : R -> %
---R coerce : Fraction Integer -> % coerce : % -> %
---R coerce : Integer -> % coerce : % -> OutputForm
---R distribute : % -> % distribute : (%,%) -> %
---R elt : (BasicOperator,%) -> % elt : (BasicOperator,%,%) -> %
---R eval : (%,Kernel %,%) -> % eval : (%,List Equation %) -> %
---R eval : (%,Equation %) -> % eval : (%,%,%) -> %
---R eval : (%,List %,List %) -> % factor : % -> Factored %
---R freeOf? : (%,%) -> Boolean freeOf? : (%,Symbol) -> Boolean
---R gcd : List % -> % gcd : (%,%) -> %
---R ground : % -> R ground? : % -> Boolean
---R hash : % -> SingleInteger height : % -> NonNegativeInteger
---R inv : % -> % is? : (%,Symbol) -> Boolean
---R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel %
---R latex : % -> String lcm : List % -> %
---R lcm : (%,%) -> % map : ((% -> %),Kernel %) -> %
+--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
+--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
+--R ?-? : (%,%) -> % -? : % -> %
+--R ?/? : (%,%) -> % ? : (%,%) -> Boolean
+--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
+--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean
+--R 1 : () -> % 0 : () -> %
+--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
+--R applyQuote : (Symbol,%) -> % applyQuote : (Symbol,%,%) -> %
+--R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean
+--R box : % -> % box : List(%) -> %
+--R coerce : Kernel(%) -> % coerce : Symbol -> %
+--R coerce : R -> % coerce : Fraction(Integer) -> %
+--R coerce : % -> % coerce : Integer -> %
+--R coerce : % -> OutputForm distribute : % -> %
+--R distribute : (%,%) -> % elt : (BasicOperator,%) -> %
+--R elt : (BasicOperator,%,%) -> % eval : (%,Kernel(%),%) -> %
+--R eval : (%,Equation(%)) -> % eval : (%,%,%) -> %
+--R factor : % -> Factored(%) freeOf? : (%,%) -> Boolean
+--R freeOf? : (%,Symbol) -> Boolean gcd : List(%) -> %
+--R gcd : (%,%) -> % ground : % -> R
+--R ground? : % -> Boolean hash : % -> SingleInteger
+--R height : % -> NonNegativeInteger inv : % -> %
+--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> %
+--R kernels : % -> List(Kernel(%)) latex : % -> String
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R max : (%,%) -> % min : (%,%) -> %
--R nthRoot : (%,Integer) -> % one? : % -> Boolean
---R paren : % -> % paren : List % -> %
+--R paren : % -> % paren : List(%) -> %
--R prime? : % -> Boolean ?quo? : (%,%) -> %
--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
---R retract : % -> Kernel % retract : % -> Symbol
+--R retract : % -> Kernel(%) retract : % -> Symbol
--R retract : % -> R rootOf : (%,Symbol) -> %
---R rootOf : % -> % rootOf : Polynomial % -> %
---R rootsOf : (%,Symbol) -> List % rootsOf : % -> List %
---R rootsOf : Polynomial % -> List % sample : () -> %
---R sizeLess? : (%,%) -> Boolean sqrt : % -> %
---R squareFree : % -> Factored % squareFreePart : % -> %
---R subst : (%,Equation %) -> % tower : % -> List Kernel %
---R unit? : % -> Boolean unitCanonical : % -> %
---R variables : % -> List Symbol zero? : % -> Boolean
---R zeroOf : (%,Symbol) -> % zeroOf : % -> %
---R zeroOf : Polynomial % -> % zerosOf : (%,Symbol) -> List %
---R zerosOf : % -> List % zerosOf : Polynomial % -> List %
+--R rootOf : % -> % rootOf : Polynomial(%) -> %
+--R rootsOf : (%,Symbol) -> List(%) rootsOf : % -> List(%)
+--R sample : () -> % sizeLess? : (%,%) -> Boolean
+--R sqrt : % -> % squareFree : % -> Factored(%)
+--R squareFreePart : % -> % subst : (%,Equation(%)) -> %
+--R tower : % -> List(Kernel(%)) unit? : % -> Boolean
+--R unitCanonical : % -> % variables : % -> List(Symbol)
+--R zero? : % -> Boolean zeroOf : (%,Symbol) -> %
+--R zeroOf : % -> % zeroOf : Polynomial(%) -> %
+--R zerosOf : (%,Symbol) -> List(%) zerosOf : % -> List(%)
--R ?~=? : (%,%) -> Boolean
--R ?*? : (R,%) -> % if R has COMRING
--R ?*? : (%,R) -> % if R has COMRING
--R ?*? : (NonNegativeInteger,%) -> %
+--R ?**? : (%,Fraction(Integer)) -> %
--R ?**? : (%,NonNegativeInteger) -> %
---R ?/? : (SparseMultivariatePolynomial(R,Kernel %),SparseMultivariatePolynomial(R,Kernel %)) -> % if R has INTDOM
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has RING
+--R ?/? : (SparseMultivariatePolynomial(R,Kernel(%)),SparseMultivariatePolynomial(R,Kernel(%))) -> % if R has INTDOM
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING
--R D : (%,Symbol,NonNegativeInteger) -> % if R has RING
---R D : (%,List Symbol) -> % if R has RING
+--R D : (%,List(Symbol)) -> % if R has RING
--R D : (%,Symbol) -> % if R has RING
--R ?^? : (%,NonNegativeInteger) -> %
--R applyQuote : (Symbol,%,%,%) -> %
--R applyQuote : (Symbol,%,%,%,%) -> %
---R applyQuote : (Symbol,List %) -> %
+--R applyQuote : (Symbol,List(%)) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coerce : SparseMultivariatePolynomial(R,Kernel %) -> % if R has RING
---R coerce : Fraction R -> % if R has INTDOM
---R coerce : Polynomial Fraction R -> % if R has INTDOM
---R coerce : Fraction Polynomial Fraction R -> % if R has INTDOM
---R coerce : Fraction Polynomial R -> % if R has INTDOM
---R coerce : Polynomial R -> % if R has RING
+--R coerce : SparseMultivariatePolynomial(R,Kernel(%)) -> % if R has RING
+--R coerce : Fraction(R) -> % if R has INTDOM
+--R coerce : Polynomial(Fraction(R)) -> % if R has INTDOM
+--R coerce : Fraction(Polynomial(Fraction(R))) -> % if R has INTDOM
+--R coerce : Fraction(Polynomial(R)) -> % if R has INTDOM
+--R coerce : Polynomial(R) -> % if R has RING
--R commutator : (%,%) -> % if R has GROUP
--R conjugate : (%,%) -> % if R has GROUP
---R convert : % -> Pattern Integer if R has KONVERT PATTERN INT
---R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT
---R convert : Factored % -> % if R has INTDOM
---R convert : % -> InputForm if R has KONVERT INFORM
+--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT))
+--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT))
+--R convert : Factored(%) -> % if R has INTDOM
+--R convert : % -> InputForm if R has KONVERT(INFORM)
--R definingPolynomial : % -> % if $ has RING
---R denom : % -> SparseMultivariatePolynomial(R,Kernel %) if R has INTDOM
+--R denom : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has INTDOM
--R denominator : % -> % if R has INTDOM
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has RING
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING
--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has RING
---R differentiate : (%,List Symbol) -> % if R has RING
+--R differentiate : (%,List(Symbol)) -> % if R has RING
--R differentiate : (%,Symbol) -> % if R has RING
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R elt : (BasicOperator,%,%,%) -> %
--R elt : (BasicOperator,%,%,%,%) -> %
---R elt : (BasicOperator,List %) -> %
+--R elt : (BasicOperator,List(%)) -> %
--R euclideanSize : % -> NonNegativeInteger
---R eval : (%,List Kernel %,List %) -> %
---R eval : (%,List Symbol,List (% -> %)) -> %
---R eval : (%,List Symbol,List (List % -> %)) -> %
---R eval : (%,Symbol,(List % -> %)) -> %
+--R eval : (%,List(Kernel(%)),List(%)) -> %
+--R eval : (%,List(Equation(%))) -> %
+--R eval : (%,List(%),List(%)) -> %
+--R eval : (%,List(Symbol),List((% -> %))) -> %
+--R eval : (%,List(Symbol),List((List(%) -> %))) -> %
+--R eval : (%,Symbol,(List(%) -> %)) -> %
--R eval : (%,Symbol,(% -> %)) -> %
---R eval : (%,List BasicOperator,List (% -> %)) -> %
---R eval : (%,List BasicOperator,List (List % -> %)) -> %
---R eval : (%,BasicOperator,(List % -> %)) -> %
+--R eval : (%,List(BasicOperator),List((% -> %))) -> %
+--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> %
+--R eval : (%,BasicOperator,(List(%) -> %)) -> %
--R eval : (%,BasicOperator,(% -> %)) -> %
---R eval : (%,Symbol) -> % if R has KONVERT INFORM
---R eval : (%,List Symbol) -> % if R has KONVERT INFORM
---R eval : % -> % if R has KONVERT INFORM
---R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT INFORM
---R eval : (%,List BasicOperator,List %,Symbol) -> % if R has KONVERT INFORM
---R eval : (%,List Symbol,List NonNegativeInteger,List (% -> %)) -> % if R has RING
---R eval : (%,List Symbol,List NonNegativeInteger,List (List % -> %)) -> % if R has RING
---R eval : (%,Symbol,NonNegativeInteger,(List % -> %)) -> % if R has RING
+--R eval : (%,Symbol) -> % if R has KONVERT(INFORM)
+--R eval : (%,List(Symbol)) -> % if R has KONVERT(INFORM)
+--R eval : % -> % if R has KONVERT(INFORM)
+--R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT(INFORM)
+--R eval : (%,List(BasicOperator),List(%),Symbol) -> % if R has KONVERT(INFORM)
+--R eval : (%,List(Symbol),List(NonNegativeInteger),List((% -> %))) -> % if R has RING
+--R eval : (%,List(Symbol),List(NonNegativeInteger),List((List(%) -> %))) -> % if R has RING
+--R eval : (%,Symbol,NonNegativeInteger,(List(%) -> %)) -> % if R has RING
--R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING
---R even? : % -> Boolean if $ has RETRACT INT
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R even? : % -> Boolean if $ has RETRACT(INT)
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R is? : (%,BasicOperator) -> Boolean
---R isExpt : % -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has SGROUP
---R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING
---R isExpt : (%,Symbol) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING
---R isMult : % -> Union(Record(coef: Integer,var: Kernel %),"failed") if R has ABELSG
---R isPlus : % -> Union(List %,"failed") if R has ABELSG
+--R isExpt : % -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has SGROUP
+--R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING
+--R isExpt : (%,Symbol) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING
+--R isMult : % -> Union(Record(coef: Integer,var: Kernel(%)),"failed") if R has ABELSG
+--R isPlus : % -> Union(List(%),"failed") if R has ABELSG
--R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING
---R isTimes : % -> Union(List %,"failed") if R has SGROUP
---R kernel : (BasicOperator,List %) -> %
---R mainKernel : % -> Union(Kernel %,"failed")
---R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R numer : % -> SparseMultivariatePolynomial(R,Kernel %) if R has RING
+--R isTimes : % -> Union(List(%),"failed") if R has SGROUP
+--R kernel : (BasicOperator,List(%)) -> %
+--R mainKernel : % -> Union(Kernel(%),"failed")
+--R map : ((% -> %),Kernel(%)) -> %
+--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has RING
--R numerator : % -> % if R has RING
---R odd? : % -> Boolean if $ has RETRACT INT
+--R odd? : % -> Boolean if $ has RETRACT(INT)
--R operator : BasicOperator -> BasicOperator
---R operators : % -> List BasicOperator
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R reducedSystem : Matrix % -> Matrix Integer if and(has(R,Ring),has(R,LinearlyExplicitRingOver Integer)) or and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring))
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(R,Ring),has(R,LinearlyExplicitRingOver Integer)) or and(has(R,LinearlyExplicitRingOver Integer),has(R,Ring))
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING
---R reducedSystem : Matrix % -> Matrix R if R has RING
---R retract : % -> Fraction Integer if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
---R retract : % -> Fraction Polynomial R if R has INTDOM
---R retract : % -> Polynomial R if R has RING
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT INT and R has INTDOM or R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Kernel %,"failed")
+--R operators : % -> List(BasicOperator)
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT)
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if and(has(R,Ring),has(R,LinearlyExplicitRingOver(Integer))) or and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if and(has(R,Ring),has(R,LinearlyExplicitRingOver(Integer))) or and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING
+--R reducedSystem : Matrix(%) -> Matrix(R) if R has RING
+--R retract : % -> Fraction(Integer) if R has RETRACT(INT) and R has INTDOM or R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
+--R retract : % -> Fraction(Polynomial(R)) if R has INTDOM
+--R retract : % -> Polynomial(R) if R has RING
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(INT) and R has INTDOM or R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Kernel(%),"failed")
--R retractIfCan : % -> Union(Symbol,"failed")
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Polynomial R,"failed") if R has INTDOM
---R retractIfCan : % -> Union(Polynomial R,"failed") if R has RING
---R rootOf : (SparseUnivariatePolynomial %,Symbol) -> %
---R rootOf : SparseUnivariatePolynomial % -> %
---R rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List %
---R rootsOf : SparseUnivariatePolynomial % -> List %
---R subst : (%,List Equation %) -> %
---R subst : (%,List Kernel %,List %) -> %
+--R retractIfCan : % -> Union(Fraction(Polynomial(R)),"failed") if R has INTDOM
+--R retractIfCan : % -> Union(Polynomial(R),"failed") if R has RING
+--R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> %
+--R rootOf : SparseUnivariatePolynomial(%) -> %
+--R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%)
+--R rootsOf : SparseUnivariatePolynomial(%) -> List(%)
+--R rootsOf : Polynomial(%) -> List(%)
+--R subst : (%,List(Equation(%))) -> %
+--R subst : (%,List(Kernel(%)),List(%)) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
---R univariate : (%,Kernel %) -> Fraction SparseUnivariatePolynomial % if R has INTDOM
---R zeroOf : (SparseUnivariatePolynomial %,Symbol) -> %
---R zeroOf : SparseUnivariatePolynomial % -> %
---R zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List %
---R zerosOf : SparseUnivariatePolynomial % -> List %
+--R univariate : (%,Kernel(%)) -> Fraction(SparseUnivariatePolynomial(%)) if R has INTDOM
+--R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> %
+--R zeroOf : SparseUnivariatePolynomial(%) -> %
+--R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%)
+--R zerosOf : SparseUnivariatePolynomial(%) -> List(%)
+--R zerosOf : Polynomial(%) -> List(%)
--R
--E 1
@@ -68536,14 +68701,15 @@ digraph pic {
--S 1 of 1
)show ExtensionField
---R ExtensionField F: Field is a category constructor
+--R
+--R ExtensionField(F: Field) is a category constructor
--R Abbreviation for ExtensionField is XF
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for XF
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (F,%) -> % ?*? : (%,F) -> %
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -68553,18 +68719,18 @@ digraph pic {
--R 0 : () -> % ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean
--R associates? : (%,%) -> Boolean coerce : F -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
---R dimension : () -> CardinalNumber factor : % -> Factored %
---R gcd : List % -> % gcd : (%,%) -> %
+--R dimension : () -> CardinalNumber factor : % -> Factored(%)
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger inGroundField? : % -> Boolean
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R one? : % -> Boolean prime? : % -> Boolean
--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
--R ?rem? : (%,%) -> % retract : % -> F
--R sample : () -> % sizeLess? : (%,%) -> Boolean
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R transcendent? : % -> Boolean unit? : % -> Boolean
--R unitCanonical : % -> % zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
@@ -68575,21 +68741,21 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if F has CHARNZ or F has FINITE
---R degree : % -> OnePointCompletion PositiveInteger
+--R degree : % -> OnePointCompletion(PositiveInteger)
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if F has CHARNZ or F has FINITE
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R extensionDegree : () -> OnePointCompletion PositiveInteger
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R order : % -> OnePointCompletion PositiveInteger if F has CHARNZ or F has FINITE
+--R extensionDegree : () -> OnePointCompletion(PositiveInteger)
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R order : % -> OnePointCompletion(PositiveInteger) if F has CHARNZ or F has FINITE
--R primeFrobenius : % -> % if F has CHARNZ or F has FINITE
--R primeFrobenius : (%,NonNegativeInteger) -> % if F has CHARNZ or F has FINITE
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R retractIfCan : % -> Union(F,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R transcendenceDegree : () -> NonNegativeInteger
@@ -68946,13 +69112,14 @@ digraph pic {
--S 1 of 1
)show FiniteFieldCategory
+--R
--R FiniteFieldCategory is a category constructor
--R Abbreviation for FiniteFieldCategory is FFIELDC
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FFIELDC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -68962,14 +69129,14 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
--R associates? : (%,%) -> Boolean charthRoot : % -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R createPrimitiveElement : () -> % differentiate : % -> %
---R factor : % -> Factored % gcd : List % -> %
+--R factor : % -> Factored(%) gcd : List(%) -> %
--R gcd : (%,%) -> % hash : % -> SingleInteger
--R index : PositiveInteger -> % init : () -> %
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R lookup : % -> PositiveInteger one? : % -> Boolean
--R order : % -> PositiveInteger prime? : % -> Boolean
--R primeFrobenius : % -> % primitive? : % -> Boolean
@@ -68977,7 +69144,7 @@ digraph pic {
--R random : () -> % recip : % -> Union(%,"failed")
--R ?rem? : (%,%) -> % sample : () -> %
--R size : () -> NonNegativeInteger sizeLess? : (%,%) -> Boolean
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R unit? : % -> Boolean unitCanonical : % -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
@@ -68985,23 +69152,23 @@ digraph pic {
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed")
---R conditionP : Matrix % -> Union(Vector %,"failed")
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed")
--R differentiate : (%,NonNegativeInteger) -> %
--R discreteLog : % -> NonNegativeInteger
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed")
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
+--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer))
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
--R nextItem : % -> Union(%,"failed")
---R order : % -> OnePointCompletion PositiveInteger
+--R order : % -> OnePointCompletion(PositiveInteger)
--R primeFrobenius : (%,NonNegativeInteger) -> %
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R representationType : () -> Union("prime",polynomial,normal,cyclic)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger)
@@ -69533,52 +69700,53 @@ digraph pic {
--S 1 of 1
)show FloatingPointSystem
+--R
--R FloatingPointSystem is a category constructor
--R Abbreviation for FloatingPointSystem is FPS
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FPS
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> %
---R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> %
---R ?+? : (%,%) -> % ?-? : (%,%) -> %
---R -? : % -> % ?/? : (%,%) -> %
---R ? : (%,%) -> Boolean ?<=? : (%,%) -> Boolean
---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean
---R ?>=? : (%,%) -> Boolean 1 : () -> %
---R 0 : () -> % ?^? : (%,Integer) -> %
---R ?^? : (%,PositiveInteger) -> % abs : % -> %
---R associates? : (%,%) -> Boolean base : () -> PositiveInteger
---R bits : () -> PositiveInteger ceiling : % -> %
---R coerce : Fraction Integer -> % coerce : Integer -> %
---R coerce : Fraction Integer -> % coerce : % -> %
---R coerce : Integer -> % coerce : % -> OutputForm
---R convert : % -> Pattern Float convert : % -> DoubleFloat
---R convert : % -> Float digits : () -> PositiveInteger
---R exponent : % -> Integer factor : % -> Factored %
---R float : (Integer,Integer) -> % floor : % -> %
---R fractionPart : % -> % gcd : List % -> %
---R gcd : (%,%) -> % hash : % -> SingleInteger
---R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
---R mantissa : % -> Integer max : (%,%) -> %
---R min : (%,%) -> % negative? : % -> Boolean
---R norm : % -> % nthRoot : (%,Integer) -> %
---R one? : % -> Boolean order : % -> Integer
---R positive? : % -> Boolean precision : () -> PositiveInteger
---R prime? : % -> Boolean ?quo? : (%,%) -> %
---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
---R retract : % -> Fraction Integer retract : % -> Integer
---R round : % -> % sample : () -> %
---R sign : % -> Integer sizeLess? : (%,%) -> Boolean
---R sqrt : % -> % squareFree : % -> Factored %
---R squareFreePart : % -> % truncate : % -> %
---R unit? : % -> Boolean unitCanonical : % -> %
---R wholePart : % -> Integer zero? : % -> Boolean
---R ?~=? : (%,%) -> Boolean
+--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
+--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
+--R ?-? : (%,%) -> % -? : % -> %
+--R ?/? : (%,%) -> % ? : (%,%) -> Boolean
+--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean
+--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean
+--R 1 : () -> % 0 : () -> %
+--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
+--R abs : % -> % associates? : (%,%) -> Boolean
+--R base : () -> PositiveInteger bits : () -> PositiveInteger
+--R ceiling : % -> % coerce : Fraction(Integer) -> %
+--R coerce : Integer -> % coerce : Fraction(Integer) -> %
+--R coerce : % -> % coerce : Integer -> %
+--R coerce : % -> OutputForm convert : % -> Pattern(Float)
+--R convert : % -> DoubleFloat convert : % -> Float
+--R digits : () -> PositiveInteger exponent : % -> Integer
+--R factor : % -> Factored(%) float : (Integer,Integer) -> %
+--R floor : % -> % fractionPart : % -> %
+--R gcd : List(%) -> % gcd : (%,%) -> %
+--R hash : % -> SingleInteger inv : % -> %
+--R latex : % -> String lcm : List(%) -> %
+--R lcm : (%,%) -> % mantissa : % -> Integer
+--R max : (%,%) -> % min : (%,%) -> %
+--R negative? : % -> Boolean norm : % -> %
+--R nthRoot : (%,Integer) -> % one? : % -> Boolean
+--R order : % -> Integer positive? : % -> Boolean
+--R precision : () -> PositiveInteger prime? : % -> Boolean
+--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
+--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer)
+--R retract : % -> Integer round : % -> %
+--R sample : () -> % sign : % -> Integer
+--R sizeLess? : (%,%) -> Boolean sqrt : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
+--R truncate : % -> % unit? : % -> Boolean
+--R unitCanonical : % -> % wholePart : % -> Integer
+--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
+--R ?**? : (%,Fraction(Integer)) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision
@@ -69587,20 +69755,20 @@ digraph pic {
--R digits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
--R float : (Integer,Integer,PositiveInteger) -> %
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision
---R max : () -> % if not has($,arbitraryPrecision) and not has($,arbitraryExponent)
---R min : () -> % if not has($,arbitraryPrecision) and not has($,arbitraryExponent)
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
+--R max : () -> % if not(has($,arbitraryPrecision)) and not(has($,arbitraryExponent))
+--R min : () -> % if not(has($,arbitraryPrecision)) and not(has($,arbitraryExponent))
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%)
--R precision : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R retractIfCan : % -> Union(Fraction Integer,"failed")
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
--R retractIfCan : % -> Union(Integer,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %)
@@ -70010,7 +70178,8 @@ digraph pic {
--S 1 of 1
)show FramedAlgebra
---R FramedAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory t#1) is a category constructor
+--R
+--R FramedAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory(t#1)) is a category constructor
--R Abbreviation for FramedAlgebra is FRAMALG
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FRAMALG
@@ -70022,16 +70191,16 @@ digraph pic {
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector %
+--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%)
--R coerce : R -> % coerce : Integer -> %
---R coerce : % -> OutputForm convert : Vector R -> %
---R convert : % -> Vector R coordinates : % -> Vector R
---R discriminant : () -> R discriminant : Vector % -> R
+--R coerce : % -> OutputForm convert : Vector(R) -> %
+--R convert : % -> Vector(R) coordinates : % -> Vector(R)
+--R discriminant : () -> R discriminant : Vector(%) -> R
--R hash : % -> SingleInteger latex : % -> String
--R norm : % -> R one? : % -> Boolean
--R rank : () -> PositiveInteger recip : % -> Union(%,"failed")
---R represents : Vector R -> % sample : () -> %
---R trace : % -> R traceMatrix : () -> Matrix R
+--R represents : Vector(R) -> % sample : () -> %
+--R trace : % -> R traceMatrix : () -> Matrix(R)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
@@ -70039,15 +70208,15 @@ digraph pic {
--R characteristic : () -> NonNegativeInteger
--R characteristicPolynomial : % -> UP
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
---R coordinates : Vector % -> Matrix R
---R coordinates : (Vector %,Vector %) -> Matrix R
---R coordinates : (%,Vector %) -> Vector R
+--R coordinates : Vector(%) -> Matrix(R)
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(R)
+--R coordinates : (%,Vector(%)) -> Vector(R)
--R minimalPolynomial : % -> UP if R has FIELD
---R regularRepresentation : % -> Matrix R
---R regularRepresentation : (%,Vector %) -> Matrix R
---R represents : (Vector R,Vector %) -> %
+--R regularRepresentation : % -> Matrix(R)
+--R regularRepresentation : (%,Vector(%)) -> Matrix(R)
+--R represents : (Vector(R),Vector(%)) -> %
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R traceMatrix : Vector % -> Matrix R
+--R traceMatrix : Vector(%) -> Matrix(R)
--R
--E 1
@@ -70347,7 +70516,7 @@ digraph pic {
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PACFFC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -70357,17 +70526,17 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
--R associates? : (%,%) -> Boolean charthRoot : % -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R conjugate : % -> % createPrimitiveElement : () -> %
--R differentiate : % -> % extDegree : % -> PositiveInteger
---R factor : % -> Factored % fullOutput : % -> OutputForm
---R gcd : List % -> % gcd : (%,%) -> %
+--R factor : % -> Factored(%) fullOutput : % -> OutputForm
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R ground? : % -> Boolean hash : % -> SingleInteger
--R index : PositiveInteger -> % init : () -> %
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
---R lookup : % -> PositiveInteger maxTower : List % -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
+--R lookup : % -> PositiveInteger maxTower : List(%) -> %
--R one? : % -> Boolean order : % -> PositiveInteger
--R previousTower : % -> % prime? : % -> Boolean
--R primeFrobenius : % -> % primitive? : % -> Boolean
@@ -70375,40 +70544,40 @@ digraph pic {
--R random : () -> % recip : % -> Union(%,"failed")
--R ?rem? : (%,%) -> % sample : () -> %
--R setTower! : % -> Void size : () -> NonNegativeInteger
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % unit? : % -> Boolean
---R unitCanonical : % -> % vectorise : (%,%) -> Vector %
+--R unitCanonical : % -> % vectorise : (%,%) -> Vector(%)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed")
---R conditionP : Matrix % -> Union(Vector %,"failed")
---R definingPolynomial : () -> SparseUnivariatePolynomial %
---R definingPolynomial : % -> SparseUnivariatePolynomial %
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed")
+--R definingPolynomial : () -> SparseUnivariatePolynomial(%)
+--R definingPolynomial : % -> SparseUnivariatePolynomial(%)
--R differentiate : (%,NonNegativeInteger) -> %
--R discreteLog : % -> NonNegativeInteger
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed")
---R distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List %
+--R distinguishedRootsOf : (SparseUnivariatePolynomial(%),%) -> List(%)
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer)
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R lift : % -> SparseUnivariatePolynomial %
---R lift : (%,%) -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R newElement : (SparseUnivariatePolynomial %,%,Symbol) -> %
---R newElement : (SparseUnivariatePolynomial %,Symbol) -> %
+--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer))
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R lift : % -> SparseUnivariatePolynomial(%)
+--R lift : (%,%) -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> %
+--R newElement : (SparseUnivariatePolynomial(%),Symbol) -> %
--R nextItem : % -> Union(%,"failed")
---R order : % -> OnePointCompletion PositiveInteger
+--R order : % -> OnePointCompletion(PositiveInteger)
--R primeFrobenius : (%,NonNegativeInteger) -> %
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R reduce : SparseUnivariatePolynomial % -> %
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R reduce : SparseUnivariatePolynomial(%) -> %
--R representationType : () -> Union("prime",polynomial,normal,cyclic)
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger)
@@ -70712,7 +70881,8 @@ digraph pic {
--S 1 of 1
)show UnivariateLaurentSeriesConstructorCategory
---R UnivariateLaurentSeriesConstructorCategory(Coef: Ring,UTS: UnivariateTaylorSeriesCategory t#1) is a category constructor
+--R
+--R UnivariateLaurentSeriesConstructorCategory(Coef: Ring,UTS: UnivariateTaylorSeriesCategory(t#1)) is a category constructor
--R Abbreviation for UnivariateLaurentSeriesConstructorCategory is ULSCCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ULSCCAT
@@ -70741,13 +70911,13 @@ digraph pic {
--R taylor : % -> UTS taylorRep : % -> UTS
--R truncate : (%,Integer) -> % variable : % -> Symbol
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (UTS,%) -> % if Coef has FIELD
--R ?*? : (%,UTS) -> % if Coef has FIELD
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?**? : (%,Integer) -> % if Coef has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (UTS,UTS) -> % if Coef has FIELD
@@ -70757,10 +70927,10 @@ digraph pic {
--R ?<=? : (%,%) -> Boolean if and(has(UTS,OrderedSet),has(Coef,Field))
--R ?>? : (%,%) -> Boolean if and(has(UTS,OrderedSet),has(Coef,Field))
--R ?>=? : (%,%) -> Boolean if and(has(UTS,OrderedSet),has(Coef,Field))
---R D : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R D : (%,List Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R D : (%,Symbol,NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,List(Symbol)) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
--R D : % -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef
--R D : (%,NonNegativeInteger) -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef
--R D : (%,(UTS -> UTS),NonNegativeInteger) -> % if Coef has FIELD
@@ -70768,45 +70938,45 @@ digraph pic {
--R ?^? : (%,Integer) -> % if Coef has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
--R abs : % -> % if and(has(UTS,OrderedIntegralDomain),has(Coef,Field))
---R acos : % -> % if Coef has ALGEBRA FRAC INT
---R acosh : % -> % if Coef has ALGEBRA FRAC INT
---R acot : % -> % if Coef has ALGEBRA FRAC INT
---R acoth : % -> % if Coef has ALGEBRA FRAC INT
---R acsc : % -> % if Coef has ALGEBRA FRAC INT
---R acsch : % -> % if Coef has ALGEBRA FRAC INT
+--R acos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT))
--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef
---R asec : % -> % if Coef has ALGEBRA FRAC INT
---R asech : % -> % if Coef has ALGEBRA FRAC INT
---R asin : % -> % if Coef has ALGEBRA FRAC INT
---R asinh : % -> % if Coef has ALGEBRA FRAC INT
+--R asec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R associates? : (%,%) -> Boolean if Coef has INTDOM
---R atan : % -> % if Coef has ALGEBRA FRAC INT
---R atanh : % -> % if Coef has ALGEBRA FRAC INT
+--R atan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R ceiling : % -> UTS if and(has(UTS,IntegerNumberSystem),has(Coef,Field))
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if and(OR(has(UTS,CharacteristicNonZero),and(has($,CharacteristicNonZero),has(UTS,PolynomialFactorizationExplicit))),has(Coef,Field)) or Coef has CHARNZ
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
---R coerce : Symbol -> % if and(has(UTS,RetractableTo Symbol),has(Coef,Field))
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
+--R coerce : Symbol -> % if and(has(UTS,RetractableTo(Symbol)),has(Coef,Field))
--R coerce : Coef -> % if Coef has COMRING
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(and(has($,CharacteristicNonZero),has(UTS,PolynomialFactorizationExplicit)),has(Coef,Field))
---R convert : % -> Pattern Integer if and(has(UTS,ConvertibleTo Pattern Integer),has(Coef,Field))
---R convert : % -> Pattern Float if and(has(UTS,ConvertibleTo Pattern Float),has(Coef,Field))
---R convert : % -> InputForm if and(has(UTS,ConvertibleTo InputForm),has(Coef,Field))
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(and(has($,CharacteristicNonZero),has(UTS,PolynomialFactorizationExplicit)),has(Coef,Field))
+--R convert : % -> Pattern(Integer) if and(has(UTS,ConvertibleTo(Pattern(Integer))),has(Coef,Field))
+--R convert : % -> Pattern(Float) if and(has(UTS,ConvertibleTo(Pattern(Float))),has(Coef,Field))
+--R convert : % -> InputForm if and(has(UTS,ConvertibleTo(InputForm)),has(Coef,Field))
--R convert : % -> Float if and(has(UTS,RealConstant),has(Coef,Field))
--R convert : % -> DoubleFloat if and(has(UTS,RealConstant),has(Coef,Field))
---R cos : % -> % if Coef has ALGEBRA FRAC INT
---R cosh : % -> % if Coef has ALGEBRA FRAC INT
---R cot : % -> % if Coef has ALGEBRA FRAC INT
---R coth : % -> % if Coef has ALGEBRA FRAC INT
---R csc : % -> % if Coef has ALGEBRA FRAC INT
---R csch : % -> % if Coef has ALGEBRA FRAC INT
+--R cos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R coth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csch : % -> % if Coef has ALGEBRA(FRAC(INT))
--R denom : % -> UTS if Coef has FIELD
--R denominator : % -> % if Coef has FIELD
---R differentiate : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,List Symbol) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing Symbol),has(Coef,Field)) or Coef has PDRING SYMBOL and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,List(Symbol)) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef
--R differentiate : % -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef
--R differentiate : (%,NonNegativeInteger) -> % if and(has(UTS,DifferentialRing),has(Coef,Field)) or Coef has *: (Integer,Coef) -> Coef
--R differentiate : (%,(UTS -> UTS),NonNegativeInteger) -> % if Coef has FIELD
@@ -70815,90 +70985,90 @@ digraph pic {
--R ?.? : (%,UTS) -> % if and(has(UTS,Eltable(UTS,UTS)),has(Coef,Field))
--R ?.? : (%,%) -> % if Integer has SGROUP
--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD
---R eval : (%,List UTS,List UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field))
---R eval : (%,UTS,UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field))
---R eval : (%,Equation UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field))
---R eval : (%,List Equation UTS) -> % if and(has(UTS,Evalable UTS),has(Coef,Field))
---R eval : (%,List Symbol,List UTS) -> % if and(has(UTS,InnerEvalable(Symbol,UTS)),has(Coef,Field))
+--R eval : (%,List(UTS),List(UTS)) -> % if and(has(UTS,Evalable(UTS)),has(Coef,Field))
+--R eval : (%,UTS,UTS) -> % if and(has(UTS,Evalable(UTS)),has(Coef,Field))
+--R eval : (%,Equation(UTS)) -> % if and(has(UTS,Evalable(UTS)),has(Coef,Field))
+--R eval : (%,List(Equation(UTS))) -> % if and(has(UTS,Evalable(UTS)),has(Coef,Field))
+--R eval : (%,List(Symbol),List(UTS)) -> % if and(has(UTS,InnerEvalable(Symbol,UTS)),has(Coef,Field))
--R eval : (%,Symbol,UTS) -> % if and(has(UTS,InnerEvalable(Symbol,UTS)),has(Coef,Field))
---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef
---R exp : % -> % if Coef has ALGEBRA FRAC INT
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD
+--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Integer) -> Coef
+--R exp : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD
---R factor : % -> Factored % if Coef has FIELD
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
+--R factor : % -> Factored(%) if Coef has FIELD
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
--R floor : % -> UTS if and(has(UTS,IntegerNumberSystem),has(Coef,Field))
--R fractionPart : % -> % if and(has(UTS,EuclideanDomain),has(Coef,Field))
--R gcd : (%,%) -> % if Coef has FIELD
---R gcd : List % -> % if Coef has FIELD
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD
+--R gcd : List(%) -> % if Coef has FIELD
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD
--R init : () -> % if and(has(UTS,StepThrough),has(Coef,Field))
---R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT
---R integrate : % -> % if Coef has ALGEBRA FRAC INT
+--R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT))
+--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT))
--R inv : % -> % if Coef has FIELD
--R lcm : (%,%) -> % if Coef has FIELD
---R lcm : List % -> % if Coef has FIELD
---R log : % -> % if Coef has ALGEBRA FRAC INT
+--R lcm : List(%) -> % if Coef has FIELD
+--R log : % -> % if Coef has ALGEBRA(FRAC(INT))
--R map : ((UTS -> UTS),%) -> % if Coef has FIELD
--R max : (%,%) -> % if and(has(UTS,OrderedSet),has(Coef,Field))
--R min : (%,%) -> % if and(has(UTS,OrderedSet),has(Coef,Field))
---R monomial : (%,List SingletonAsOrderedSet,List Integer) -> %
+--R monomial : (%,List(SingletonAsOrderedSet),List(Integer)) -> %
--R monomial : (%,SingletonAsOrderedSet,Integer) -> %
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
--R multiplyCoefficients : ((Integer -> Coef),%) -> %
--R multiplyExponents : (%,PositiveInteger) -> %
--R negative? : % -> Boolean if and(has(UTS,OrderedIntegralDomain),has(Coef,Field))
--R nextItem : % -> Union(%,"failed") if and(has(UTS,StepThrough),has(Coef,Field))
---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT
+--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R numer : % -> UTS if Coef has FIELD
--R numerator : % -> % if Coef has FIELD
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if and(has(UTS,PatternMatchable Integer),has(Coef,Field))
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if and(has(UTS,PatternMatchable Float),has(Coef,Field))
---R pi : () -> % if Coef has ALGEBRA FRAC INT
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if and(has(UTS,PatternMatchable(Integer)),has(Coef,Field))
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if and(has(UTS,PatternMatchable(Float)),has(Coef,Field))
+--R pi : () -> % if Coef has ALGEBRA(FRAC(INT))
--R positive? : % -> Boolean if and(has(UTS,OrderedIntegralDomain),has(Coef,Field))
--R prime? : % -> Boolean if Coef has FIELD
---R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Coef has FIELD
--R ?quo? : (%,%) -> % if Coef has FIELD
--R random : () -> % if and(has(UTS,IntegerNumberSystem),has(Coef,Field))
---R rationalFunction : (%,Integer,Integer) -> Fraction Polynomial Coef if Coef has INTDOM
---R rationalFunction : (%,Integer) -> Fraction Polynomial Coef if Coef has INTDOM
---R reducedSystem : Matrix % -> Matrix Integer if and(has(UTS,LinearlyExplicitRingOver Integer),has(Coef,Field))
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if and(has(UTS,LinearlyExplicitRingOver Integer),has(Coef,Field))
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix UTS,vec: Vector UTS) if Coef has FIELD
---R reducedSystem : Matrix % -> Matrix UTS if Coef has FIELD
+--R rationalFunction : (%,Integer,Integer) -> Fraction(Polynomial(Coef)) if Coef has INTDOM
+--R rationalFunction : (%,Integer) -> Fraction(Polynomial(Coef)) if Coef has INTDOM
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if and(has(UTS,LinearlyExplicitRingOver(Integer)),has(Coef,Field))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if and(has(UTS,LinearlyExplicitRingOver(Integer)),has(Coef,Field))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(UTS),vec: Vector(UTS)) if Coef has FIELD
+--R reducedSystem : Matrix(%) -> Matrix(UTS) if Coef has FIELD
--R ?rem? : (%,%) -> % if Coef has FIELD
---R retract : % -> Symbol if and(has(UTS,RetractableTo Symbol),has(Coef,Field))
---R retract : % -> Fraction Integer if and(has(UTS,RetractableTo Integer),has(Coef,Field))
---R retract : % -> Integer if and(has(UTS,RetractableTo Integer),has(Coef,Field))
---R retractIfCan : % -> Union(Symbol,"failed") if and(has(UTS,RetractableTo Symbol),has(Coef,Field))
---R retractIfCan : % -> Union(Fraction Integer,"failed") if and(has(UTS,RetractableTo Integer),has(Coef,Field))
---R retractIfCan : % -> Union(Integer,"failed") if and(has(UTS,RetractableTo Integer),has(Coef,Field))
+--R retract : % -> Symbol if and(has(UTS,RetractableTo(Symbol)),has(Coef,Field))
+--R retract : % -> Fraction(Integer) if and(has(UTS,RetractableTo(Integer)),has(Coef,Field))
+--R retract : % -> Integer if and(has(UTS,RetractableTo(Integer)),has(Coef,Field))
+--R retractIfCan : % -> Union(Symbol,"failed") if and(has(UTS,RetractableTo(Symbol)),has(Coef,Field))
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if and(has(UTS,RetractableTo(Integer)),has(Coef,Field))
+--R retractIfCan : % -> Union(Integer,"failed") if and(has(UTS,RetractableTo(Integer)),has(Coef,Field))
--R retractIfCan : % -> Union(UTS,"failed")
---R sec : % -> % if Coef has ALGEBRA FRAC INT
---R sech : % -> % if Coef has ALGEBRA FRAC INT
---R series : Stream Record(k: Integer,c: Coef) -> %
+--R sec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R series : Stream(Record(k: Integer,c: Coef)) -> %
--R sign : % -> Integer if and(has(UTS,OrderedIntegralDomain),has(Coef,Field))
---R sin : % -> % if Coef has ALGEBRA FRAC INT
---R sinh : % -> % if Coef has ALGEBRA FRAC INT
+--R sin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R sizeLess? : (%,%) -> Boolean if Coef has FIELD
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
---R sqrt : % -> % if Coef has ALGEBRA FRAC INT
---R squareFree : % -> Factored % if Coef has FIELD
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
+--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R squareFree : % -> Factored(%) if Coef has FIELD
--R squareFreePart : % -> % if Coef has FIELD
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if and(has(UTS,PolynomialFactorizationExplicit),has(Coef,Field))
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tan : % -> % if Coef has ALGEBRA FRAC INT
---R tanh : % -> % if Coef has ALGEBRA FRAC INT
+--R tan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R taylorIfCan : % -> Union(UTS,"failed")
---R terms : % -> Stream Record(k: Integer,c: Coef)
+--R terms : % -> Stream(Record(k: Integer,c: Coef))
--R truncate : (%,Integer,Integer) -> %
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R wholePart : % -> UTS if and(has(UTS,EuclideanDomain),has(Coef,Field))
--R
--E 1
@@ -71579,7 +71749,8 @@ digraph pic {
--S 1 of 1
)show UnivariatePuiseuxSeriesConstructorCategory
---R UnivariatePuiseuxSeriesConstructorCategory(Coef: Ring,ULS: UnivariateLaurentSeriesCategory t#1) is a category constructor
+--R
+--R UnivariatePuiseuxSeriesConstructorCategory(Coef: Ring,ULS: UnivariateLaurentSeriesCategory(t#1)) is a category constructor
--R Abbreviation for UnivariatePuiseuxSeriesConstructorCategory is UPXSCCA
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for UPXSCCA
@@ -71594,122 +71765,122 @@ digraph pic {
--R ?^? : (%,PositiveInteger) -> % center : % -> Coef
--R coerce : ULS -> % coerce : Integer -> %
--R coerce : % -> OutputForm complete : % -> %
---R degree : % -> Fraction Integer hash : % -> SingleInteger
+--R degree : % -> Fraction(Integer) hash : % -> SingleInteger
--R latex : % -> String laurent : % -> ULS
--R laurentRep : % -> ULS leadingCoefficient : % -> Coef
--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> %
--R monomial? : % -> Boolean one? : % -> Boolean
---R order : % -> Fraction Integer pole? : % -> Boolean
+--R order : % -> Fraction(Integer) pole? : % -> Boolean
--R recip : % -> Union(%,"failed") reductum : % -> %
--R retract : % -> ULS sample : () -> %
--R variable : % -> Symbol zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT
---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT
+--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT))
+--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT))
--R ?**? : (%,Integer) -> % if Coef has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,%) -> % if Coef has FIELD
--R ?/? : (%,Coef) -> % if Coef has FIELD
---R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
+--R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
--R ?^? : (%,Integer) -> % if Coef has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
---R acos : % -> % if Coef has ALGEBRA FRAC INT
---R acosh : % -> % if Coef has ALGEBRA FRAC INT
---R acot : % -> % if Coef has ALGEBRA FRAC INT
---R acoth : % -> % if Coef has ALGEBRA FRAC INT
---R acsc : % -> % if Coef has ALGEBRA FRAC INT
---R acsch : % -> % if Coef has ALGEBRA FRAC INT
---R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef
---R asec : % -> % if Coef has ALGEBRA FRAC INT
---R asech : % -> % if Coef has ALGEBRA FRAC INT
---R asin : % -> % if Coef has ALGEBRA FRAC INT
---R asinh : % -> % if Coef has ALGEBRA FRAC INT
+--R acos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R approximate : (%,Fraction(Integer)) -> Coef if Coef has **: (Coef,Fraction(Integer)) -> Coef and Coef has coerce: Symbol -> Coef
+--R asec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R associates? : (%,%) -> Boolean if Coef has INTDOM
---R atan : % -> % if Coef has ALGEBRA FRAC INT
---R atanh : % -> % if Coef has ALGEBRA FRAC INT
+--R atan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ
---R coefficient : (%,Fraction Integer) -> Coef
+--R coefficient : (%,Fraction(Integer)) -> Coef
--R coerce : % -> % if Coef has INTDOM
---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT
+--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT))
--R coerce : Coef -> % if Coef has COMRING
---R cos : % -> % if Coef has ALGEBRA FRAC INT
---R cosh : % -> % if Coef has ALGEBRA FRAC INT
---R cot : % -> % if Coef has ALGEBRA FRAC INT
---R coth : % -> % if Coef has ALGEBRA FRAC INT
---R csc : % -> % if Coef has ALGEBRA FRAC INT
---R csch : % -> % if Coef has ALGEBRA FRAC INT
---R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,List Symbol) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has PDRING SYMBOL and Coef has *: (Fraction Integer,Coef) -> Coef
+--R cos : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R cot : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R coth : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csc : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R csch : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R differentiate : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,Symbol) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef
--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD
---R ?.? : (%,%) -> % if Fraction Integer has SGROUP
---R ?.? : (%,Fraction Integer) -> Coef
+--R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP
+--R ?.? : (%,Fraction(Integer)) -> Coef
--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD
---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef
---R exp : % -> % if Coef has ALGEBRA FRAC INT
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD
+--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef
+--R exp : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM
---R extend : (%,Fraction Integer) -> %
+--R extend : (%,Fraction(Integer)) -> %
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD
---R factor : % -> Factored % if Coef has FIELD
+--R factor : % -> Factored(%) if Coef has FIELD
--R gcd : (%,%) -> % if Coef has FIELD
---R gcd : List % -> % if Coef has FIELD
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD
---R integrate : (%,Symbol) -> % if Coef has ACFS INT and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA FRAC INT or Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA FRAC INT
---R integrate : % -> % if Coef has ALGEBRA FRAC INT
+--R gcd : List(%) -> % if Coef has FIELD
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD
+--R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT))
+--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT))
--R inv : % -> % if Coef has FIELD
--R laurentIfCan : % -> Union(ULS,"failed")
--R lcm : (%,%) -> % if Coef has FIELD
---R lcm : List % -> % if Coef has FIELD
---R log : % -> % if Coef has ALGEBRA FRAC INT
---R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> %
---R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> %
---R monomial : (Coef,Fraction Integer) -> %
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD
---R multiplyExponents : (%,Fraction Integer) -> %
+--R lcm : List(%) -> % if Coef has FIELD
+--R log : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R monomial : (%,List(SingletonAsOrderedSet),List(Fraction(Integer))) -> %
+--R monomial : (%,SingletonAsOrderedSet,Fraction(Integer)) -> %
+--R monomial : (Coef,Fraction(Integer)) -> %
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD
+--R multiplyExponents : (%,Fraction(Integer)) -> %
--R multiplyExponents : (%,PositiveInteger) -> %
---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT
---R order : (%,Fraction Integer) -> Fraction Integer
---R pi : () -> % if Coef has ALGEBRA FRAC INT
+--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT))
+--R order : (%,Fraction(Integer)) -> Fraction(Integer)
+--R pi : () -> % if Coef has ALGEBRA(FRAC(INT))
--R prime? : % -> Boolean if Coef has FIELD
---R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD
---R puiseux : (Fraction Integer,ULS) -> %
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Coef has FIELD
+--R puiseux : (Fraction(Integer),ULS) -> %
--R ?quo? : (%,%) -> % if Coef has FIELD
---R rationalPower : % -> Fraction Integer
+--R rationalPower : % -> Fraction(Integer)
--R ?rem? : (%,%) -> % if Coef has FIELD
--R retractIfCan : % -> Union(ULS,"failed")
---R sec : % -> % if Coef has ALGEBRA FRAC INT
---R sech : % -> % if Coef has ALGEBRA FRAC INT
---R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> %
---R sin : % -> % if Coef has ALGEBRA FRAC INT
---R sinh : % -> % if Coef has ALGEBRA FRAC INT
+--R sec : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sech : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R series : (NonNegativeInteger,Stream(Record(k: Fraction(Integer),c: Coef))) -> %
+--R sin : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT))
--R sizeLess? : (%,%) -> Boolean if Coef has FIELD
---R sqrt : % -> % if Coef has ALGEBRA FRAC INT
---R squareFree : % -> Factored % if Coef has FIELD
+--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R squareFree : % -> Factored(%) if Coef has FIELD
--R squareFreePart : % -> % if Coef has FIELD
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tan : % -> % if Coef has ALGEBRA FRAC INT
---R tanh : % -> % if Coef has ALGEBRA FRAC INT
---R terms : % -> Stream Record(k: Fraction Integer,c: Coef)
---R truncate : (%,Fraction Integer,Fraction Integer) -> %
---R truncate : (%,Fraction Integer) -> %
+--R tan : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT))
+--R terms : % -> Stream(Record(k: Fraction(Integer),c: Coef))
+--R truncate : (%,Fraction(Integer),Fraction(Integer)) -> %
+--R truncate : (%,Fraction(Integer)) -> %
--R unit? : % -> Boolean if Coef has INTDOM
--R unitCanonical : % -> % if Coef has INTDOM
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM
---R variables : % -> List SingletonAsOrderedSet
+--R variables : % -> List(SingletonAsOrderedSet)
--R
--E 1
@@ -72200,14 +72371,15 @@ digraph pic {
--S 1 of 1
)show FiniteAlgebraicExtensionField
---R FiniteAlgebraicExtensionField F: Field is a category constructor
+--R
+--R FiniteAlgebraicExtensionField(F: Field) is a category constructor
--R Abbreviation for FiniteAlgebraicExtensionField is FAXF
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FAXF
--R
--R------------------------------- Operations --------------------------------
--R ?*? : (F,%) -> % ?*? : (%,F) -> %
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
@@ -72217,21 +72389,21 @@ digraph pic {
--R 1 : () -> % 0 : () -> %
--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> %
--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean
---R basis : () -> Vector % coerce : F -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R basis : () -> Vector(%) coerce : F -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
---R coordinates : % -> Vector F degree : % -> PositiveInteger
---R dimension : () -> CardinalNumber factor : % -> Factored %
---R gcd : List % -> % gcd : (%,%) -> %
+--R coordinates : % -> Vector(F) degree : % -> PositiveInteger
+--R dimension : () -> CardinalNumber factor : % -> Factored(%)
+--R gcd : List(%) -> % gcd : (%,%) -> %
--R hash : % -> SingleInteger inGroundField? : % -> Boolean
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
+--R lcm : List(%) -> % lcm : (%,%) -> %
--R norm : % -> F one? : % -> Boolean
--R prime? : % -> Boolean ?quo? : (%,%) -> %
--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> %
---R represents : Vector F -> % retract : % -> F
+--R represents : Vector(F) -> % retract : % -> F
--R sample : () -> % sizeLess? : (%,%) -> Boolean
---R squareFree : % -> Factored % squareFreePart : % -> %
+--R squareFree : % -> Factored(%) squareFreePart : % -> %
--R trace : % -> F transcendent? : % -> Boolean
--R unit? : % -> Boolean unitCanonical : % -> %
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
@@ -72241,52 +72413,52 @@ digraph pic {
--R Frobenius : (%,NonNegativeInteger) -> % if F has FINITE
--R Frobenius : % -> % if F has FINITE
--R ?^? : (%,NonNegativeInteger) -> %
---R basis : PositiveInteger -> Vector %
+--R basis : PositiveInteger -> Vector(%)
--R characteristic : () -> NonNegativeInteger
--R charthRoot : % -> Union(%,"failed") if F has CHARNZ or F has FINITE
--R charthRoot : % -> % if F has FINITE
---R conditionP : Matrix % -> Union(Vector %,"failed") if F has FINITE
---R coordinates : Vector % -> Matrix F
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if F has FINITE
+--R coordinates : Vector(%) -> Matrix(F)
--R createNormalElement : () -> % if F has FINITE
--R createPrimitiveElement : () -> % if F has FINITE
---R definingPolynomial : () -> SparseUnivariatePolynomial F
---R degree : % -> OnePointCompletion PositiveInteger
+--R definingPolynomial : () -> SparseUnivariatePolynomial(F)
+--R degree : % -> OnePointCompletion(PositiveInteger)
--R differentiate : (%,NonNegativeInteger) -> % if F has FINITE
--R differentiate : % -> % if F has FINITE
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if F has CHARNZ or F has FINITE
--R discreteLog : % -> NonNegativeInteger if F has FINITE
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
--R extensionDegree : () -> PositiveInteger
---R extensionDegree : () -> OnePointCompletion PositiveInteger
---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if F has FINITE
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
+--R extensionDegree : () -> OnePointCompletion(PositiveInteger)
+--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if F has FINITE
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
--R generator : () -> % if F has FINITE
--R index : PositiveInteger -> % if F has FINITE
--R init : () -> % if F has FINITE
---R linearAssociatedExp : (%,SparseUnivariatePolynomial F) -> % if F has FINITE
---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial F,"failed") if F has FINITE
---R linearAssociatedLog : % -> SparseUnivariatePolynomial F if F has FINITE
---R linearAssociatedOrder : % -> SparseUnivariatePolynomial F if F has FINITE
+--R linearAssociatedExp : (%,SparseUnivariatePolynomial(F)) -> % if F has FINITE
+--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(F),"failed") if F has FINITE
+--R linearAssociatedLog : % -> SparseUnivariatePolynomial(F) if F has FINITE
+--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(F) if F has FINITE
--R lookup : % -> PositiveInteger if F has FINITE
---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if F has FINITE
---R minimalPolynomial : % -> SparseUnivariatePolynomial F
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
+--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if F has FINITE
+--R minimalPolynomial : % -> SparseUnivariatePolynomial(F)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
--R nextItem : % -> Union(%,"failed") if F has FINITE
--R norm : (%,PositiveInteger) -> % if F has FINITE
--R normal? : % -> Boolean if F has FINITE
--R normalElement : () -> % if F has FINITE
---R order : % -> OnePointCompletion PositiveInteger if F has CHARNZ or F has FINITE
+--R order : % -> OnePointCompletion(PositiveInteger) if F has CHARNZ or F has FINITE
--R order : % -> PositiveInteger if F has FINITE
--R primeFrobenius : % -> % if F has CHARNZ or F has FINITE
--R primeFrobenius : (%,NonNegativeInteger) -> % if F has CHARNZ or F has FINITE
--R primitive? : % -> Boolean if F has FINITE
--R primitiveElement : () -> % if F has FINITE
---R principalIdeal : List % -> Record(coef: List %,generator: %)
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
--R random : () -> % if F has FINITE
--R representationType : () -> Union("prime",polynomial,normal,cyclic) if F has FINITE
--R retractIfCan : % -> Union(F,"failed")
@@ -72969,7 +73141,8 @@ digraph pic {
--S 1 of 1
)show MonogenicAlgebra
---R MonogenicAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory t#1) is a category constructor
+--R
+--R MonogenicAlgebra(R: CommutativeRing,UP: UnivariatePolynomialCategory(t#1)) is a category constructor
--R Abbreviation for MonogenicAlgebra is MONOGEN
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONOGEN
@@ -72981,33 +73154,33 @@ digraph pic {
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector %
+--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%)
--R coerce : R -> % coerce : Integer -> %
--R coerce : % -> OutputForm convert : UP -> %
---R convert : % -> UP convert : Vector R -> %
---R convert : % -> Vector R coordinates : % -> Vector R
+--R convert : % -> UP convert : Vector(R) -> %
+--R convert : % -> Vector(R) coordinates : % -> Vector(R)
--R definingPolynomial : () -> UP discriminant : () -> R
---R discriminant : Vector % -> R generator : () -> %
+--R discriminant : Vector(%) -> R generator : () -> %
--R hash : % -> SingleInteger inv : % -> % if R has FIELD
--R latex : % -> String lift : % -> UP
--R norm : % -> R one? : % -> Boolean
--R rank : () -> PositiveInteger recip : % -> Union(%,"failed")
---R reduce : UP -> % represents : Vector R -> %
+--R reduce : UP -> % represents : Vector(R) -> %
--R retract : % -> R sample : () -> %
---R trace : % -> R traceMatrix : () -> Matrix R
+--R trace : % -> R traceMatrix : () -> Matrix(R)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if R has FIELD
---R ?*? : (Fraction Integer,%) -> % if R has FIELD
+--R ?*? : (%,Fraction(Integer)) -> % if R has FIELD
+--R ?*? : (Fraction(Integer),%) -> % if R has FIELD
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,%) -> % if R has FIELD
--R D : (%,(R -> R)) -> % if R has FIELD
--R D : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD
---R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
---R D : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
---R D : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
---R D : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
+--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
+--R D : (%,List(Symbol)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
+--R D : (%,Symbol) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
--R D : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC
--R D : % -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC
--R ?^? : (%,Integer) -> % if R has FIELD
@@ -73017,75 +73190,75 @@ digraph pic {
--R characteristicPolynomial : % -> UP
--R charthRoot : % -> Union(%,"failed") if R has CHARNZ
--R charthRoot : % -> % if R has FFIELDC
---R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT
+--R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT))
--R coerce : % -> % if R has FIELD
---R conditionP : Matrix % -> Union(Vector %,"failed") if R has FFIELDC
---R coordinates : Vector % -> Matrix R
---R coordinates : (Vector %,Vector %) -> Matrix R
---R coordinates : (%,Vector %) -> Vector R
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if R has FFIELDC
+--R coordinates : Vector(%) -> Matrix(R)
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(R)
+--R coordinates : (%,Vector(%)) -> Vector(R)
--R createPrimitiveElement : () -> % if R has FFIELDC
---R derivationCoordinates : (Vector %,(R -> R)) -> Matrix R if R has FIELD
+--R derivationCoordinates : (Vector(%),(R -> R)) -> Matrix(R) if R has FIELD
--R differentiate : (%,(R -> R)) -> % if R has FIELD
--R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
---R differentiate : (%,List Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
---R differentiate : (%,Symbol) -> % if and(has(R,PartialDifferentialRing Symbol),has(R,Field))
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
+--R differentiate : (%,List(Symbol)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
+--R differentiate : (%,Symbol) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field))
--R differentiate : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC
--R differentiate : % -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC
--R discreteLog : % -> NonNegativeInteger if R has FFIELDC
--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD
--R euclideanSize : % -> NonNegativeInteger if R has FIELD
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD
--R exquo : (%,%) -> Union(%,"failed") if R has FIELD
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD
---R factor : % -> Factored % if R has FIELD
---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if R has FFIELDC
+--R factor : % -> Factored(%) if R has FIELD
+--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if R has FFIELDC
--R gcd : (%,%) -> % if R has FIELD
---R gcd : List % -> % if R has FIELD
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD
+--R gcd : List(%) -> % if R has FIELD
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD
--R index : PositiveInteger -> % if R has FINITE
--R init : () -> % if R has FFIELDC
--R lcm : (%,%) -> % if R has FIELD
---R lcm : List % -> % if R has FIELD
+--R lcm : List(%) -> % if R has FIELD
--R lookup : % -> PositiveInteger if R has FINITE
--R minimalPolynomial : % -> UP if R has FIELD
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD
--R nextItem : % -> Union(%,"failed") if R has FFIELDC
---R order : % -> OnePointCompletion PositiveInteger if R has FFIELDC
+--R order : % -> OnePointCompletion(PositiveInteger) if R has FFIELDC
--R order : % -> PositiveInteger if R has FFIELDC
--R prime? : % -> Boolean if R has FIELD
--R primeFrobenius : % -> % if R has FFIELDC
--R primeFrobenius : (%,NonNegativeInteger) -> % if R has FFIELDC
--R primitive? : % -> Boolean if R has FFIELDC
--R primitiveElement : () -> % if R has FFIELDC
---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD
--R ?quo? : (%,%) -> % if R has FIELD
--R random : () -> % if R has FINITE
---R reduce : Fraction UP -> Union(%,"failed") if R has FIELD
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
---R regularRepresentation : % -> Matrix R
---R regularRepresentation : (%,Vector %) -> Matrix R
+--R reduce : Fraction(UP) -> Union(%,"failed") if R has FIELD
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
+--R regularRepresentation : % -> Matrix(R)
+--R regularRepresentation : (%,Vector(%)) -> Matrix(R)
--R ?rem? : (%,%) -> % if R has FIELD
--R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC
---R represents : (Vector R,Vector %) -> %
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R represents : (Vector(R),Vector(%)) -> %
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R size : () -> NonNegativeInteger if R has FINITE
--R sizeLess? : (%,%) -> Boolean if R has FIELD
---R squareFree : % -> Factored % if R has FIELD
+--R squareFree : % -> Factored(%) if R has FIELD
--R squareFreePart : % -> % if R has FIELD
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC
---R traceMatrix : Vector % -> Matrix R
+--R traceMatrix : Vector(%) -> Matrix(R)
--R unit? : % -> Boolean if R has FIELD
--R unitCanonical : % -> % if R has FIELD
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD
@@ -73617,70 +73790,70 @@ digraph pic {
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PACRATC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> %
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
--R ?-? : (%,%) -> % -? : % -> %
---R ?/? : (%,Fraction Integer) -> % ?/? : (%,%) -> %
+--R ?/? : (%,Fraction(Integer)) -> % ?/? : (%,%) -> %
--R ?=? : (%,%) -> Boolean 1 : () -> %
--R 0 : () -> % ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean
---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> %
---R coerce : Fraction Integer -> % coerce : Integer -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> %
+--R coerce : Fraction(Integer) -> % coerce : Integer -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R conjugate : % -> % dimension : () -> CardinalNumber
---R extDegree : % -> PositiveInteger factor : % -> Factored %
---R fullOutput : % -> OutputForm gcd : List % -> %
+--R extDegree : % -> PositiveInteger factor : % -> Factored(%)
+--R fullOutput : % -> OutputForm gcd : List(%) -> %
--R gcd : (%,%) -> % ground? : % -> Boolean
--R hash : % -> SingleInteger inGroundField? : % -> Boolean
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
---R maxTower : List % -> % one? : % -> Boolean
+--R lcm : List(%) -> % lcm : (%,%) -> %
+--R maxTower : List(%) -> % one? : % -> Boolean
--R previousTower : % -> % prime? : % -> Boolean
--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
---R ?rem? : (%,%) -> % retract : % -> Fraction Integer
---R retract : % -> Fraction Integer retract : % -> Integer
+--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer)
+--R retract : % -> Fraction(Integer) retract : % -> Integer
--R sample : () -> % setTower! : % -> Void
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % transcendent? : % -> Boolean
--R unit? : % -> Boolean unitCanonical : % -> %
---R vectorise : (%,%) -> Vector % zero? : % -> Boolean
+--R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
---R Frobenius : % -> % if Fraction Integer has FINITE
---R Frobenius : (%,NonNegativeInteger) -> % if Fraction Integer has FINITE
+--R Frobenius : % -> % if Fraction(Integer) has FINITE
+--R Frobenius : (%,NonNegativeInteger) -> % if Fraction(Integer) has FINITE
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R charthRoot : % -> Union(%,"failed") if Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R definingPolynomial : % -> SparseUnivariatePolynomial %
---R definingPolynomial : () -> SparseUnivariatePolynomial %
---R degree : % -> OnePointCompletion PositiveInteger
---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List %
+--R charthRoot : % -> Union(%,"failed") if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R definingPolynomial : % -> SparseUnivariatePolynomial(%)
+--R definingPolynomial : () -> SparseUnivariatePolynomial(%)
+--R degree : % -> OnePointCompletion(PositiveInteger)
+--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R distinguishedRootsOf : (SparseUnivariatePolynomial(%),%) -> List(%)
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R extensionDegree : () -> OnePointCompletion PositiveInteger
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R lift : (%,%) -> SparseUnivariatePolynomial %
---R lift : % -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R newElement : (SparseUnivariatePolynomial %,Symbol) -> %
---R newElement : (SparseUnivariatePolynomial %,%,Symbol) -> %
---R order : % -> OnePointCompletion PositiveInteger if Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R primeFrobenius : % -> % if Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R reduce : SparseUnivariatePolynomial % -> %
---R retractIfCan : % -> Union(Fraction Integer,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed")
+--R extensionDegree : () -> OnePointCompletion(PositiveInteger)
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R lift : (%,%) -> SparseUnivariatePolynomial(%)
+--R lift : % -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R newElement : (SparseUnivariatePolynomial(%),Symbol) -> %
+--R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> %
+--R order : % -> OnePointCompletion(PositiveInteger) if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R primeFrobenius : % -> % if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R reduce : SparseUnivariatePolynomial(%) -> %
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
--R retractIfCan : % -> Union(Integer,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R transcendenceDegree : () -> NonNegativeInteger
@@ -73989,7 +74162,8 @@ digraph pic {
--S 1 of 1
)show ComplexCategory
---R ComplexCategory R: CommutativeRing is a category constructor
+--R
+--R ComplexCategory(R: CommutativeRing) is a category constructor
--R Abbreviation for ComplexCategory is COMPCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for COMPCAT
@@ -74002,28 +74176,28 @@ digraph pic {
--R -? : % -> % ?=? : (%,%) -> Boolean
--R D : (%,(R -> R)) -> % 1 : () -> %
--R 0 : () -> % ?^? : (%,PositiveInteger) -> %
---R abs : % -> % if R has RNS basis : () -> Vector %
+--R abs : % -> % if R has RNS basis : () -> Vector(%)
--R coerce : R -> % coerce : Integer -> %
--R coerce : % -> OutputForm complex : (R,R) -> %
---R conjugate : % -> % convert : Vector R -> %
---R convert : % -> Vector R coordinates : % -> Vector R
---R discriminant : () -> R discriminant : Vector % -> R
+--R conjugate : % -> % convert : Vector(R) -> %
+--R convert : % -> Vector(R) coordinates : % -> Vector(R)
+--R discriminant : () -> R discriminant : Vector(%) -> R
--R generator : () -> % hash : % -> SingleInteger
--R imag : % -> R imaginary : () -> %
--R inv : % -> % if R has FIELD latex : % -> String
--R map : ((R -> R),%) -> % norm : % -> R
--R one? : % -> Boolean pi : () -> % if R has TRANFUN
--R rank : () -> PositiveInteger real : % -> R
---R recip : % -> Union(%,"failed") represents : Vector R -> %
+--R recip : % -> Union(%,"failed") represents : Vector(R) -> %
--R retract : % -> R sample : () -> %
---R trace : % -> R traceMatrix : () -> Matrix R
+--R trace : % -> R traceMatrix : () -> Matrix(R)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if R has FIELD
---R ?*? : (Fraction Integer,%) -> % if R has FIELD
+--R ?*? : (%,Fraction(Integer)) -> % if R has FIELD
+--R ?*? : (Fraction(Integer),%) -> % if R has FIELD
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,Integer) -> % if R has FIELD
--R ?**? : (%,%) -> % if R has TRANFUN
---R ?**? : (%,Fraction Integer) -> % if R has RADCAT and R has TRANFUN
+--R ?**? : (%,Fraction(Integer)) -> % if R has RADCAT and R has TRANFUN
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,%) -> % if R has FIELD
--R ? : (%,%) -> Boolean if R has ORDSET
@@ -74032,10 +74206,10 @@ digraph pic {
--R ?>=? : (%,%) -> Boolean if R has ORDSET
--R D : % -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field))
--R D : (%,NonNegativeInteger) -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field))
---R D : (%,Symbol) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol) -> % if R has PDRING SYMBOL
---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
+--R D : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
--R D : (%,(R -> R),NonNegativeInteger) -> %
--R ?^? : (%,Integer) -> % if R has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
@@ -74054,22 +74228,22 @@ digraph pic {
--R atan : % -> % if R has TRANFUN
--R atanh : % -> % if R has TRANFUN
--R characteristic : () -> NonNegativeInteger
---R characteristicPolynomial : % -> SparseUnivariatePolynomial R
+--R characteristicPolynomial : % -> SparseUnivariatePolynomial(R)
--R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),AND(has(R,EuclideanDomain),has(R,PolynomialFactorizationExplicit))) or R has CHARNZ
--R charthRoot : % -> % if R has FFIELDC
--R coerce : % -> % if R has INTDOM or R has EUCDOM and R has PFECAT
---R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT
---R conditionP : Matrix % -> Union(Vector %,"failed") if and(has($,CharacteristicNonZero),AND(has(R,EuclideanDomain),has(R,PolynomialFactorizationExplicit))) or R has FFIELDC
---R convert : % -> InputForm if R has KONVERT INFORM
---R convert : % -> Complex DoubleFloat if R has REAL
---R convert : % -> Complex Float if R has REAL
---R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT
---R convert : % -> Pattern Integer if R has KONVERT PATTERN INT
---R convert : SparseUnivariatePolynomial R -> %
---R convert : % -> SparseUnivariatePolynomial R
---R coordinates : Vector % -> Matrix R
---R coordinates : (Vector %,Vector %) -> Matrix R
---R coordinates : (%,Vector %) -> Vector R
+--R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT))
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),AND(has(R,EuclideanDomain),has(R,PolynomialFactorizationExplicit))) or R has FFIELDC
+--R convert : % -> InputForm if R has KONVERT(INFORM)
+--R convert : % -> Complex(DoubleFloat) if R has REAL
+--R convert : % -> Complex(Float) if R has REAL
+--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT))
+--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT))
+--R convert : SparseUnivariatePolynomial(R) -> %
+--R convert : % -> SparseUnivariatePolynomial(R)
+--R coordinates : Vector(%) -> Matrix(R)
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(R)
+--R coordinates : (%,Vector(%)) -> Vector(R)
--R cos : % -> % if R has TRANFUN
--R cosh : % -> % if R has TRANFUN
--R cot : % -> % if R has TRANFUN
@@ -74077,14 +74251,14 @@ digraph pic {
--R createPrimitiveElement : () -> % if R has FFIELDC
--R csc : % -> % if R has TRANFUN
--R csch : % -> % if R has TRANFUN
---R definingPolynomial : () -> SparseUnivariatePolynomial R
---R derivationCoordinates : (Vector %,(R -> R)) -> Matrix R if R has FIELD
+--R definingPolynomial : () -> SparseUnivariatePolynomial(R)
+--R derivationCoordinates : (Vector(%),(R -> R)) -> Matrix(R) if R has FIELD
--R differentiate : % -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field))
--R differentiate : (%,NonNegativeInteger) -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field))
---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL
+--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL)
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL)
--R differentiate : (%,(R -> R)) -> %
--R differentiate : (%,(R -> R),NonNegativeInteger) -> %
--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC
@@ -74093,85 +74267,85 @@ digraph pic {
--R ?.? : (%,R) -> % if R has ELTAB(R,R)
--R euclideanSize : % -> NonNegativeInteger if R has EUCDOM
--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R)
---R eval : (%,List Symbol,List R) -> % if R has IEVALAB(SYMBOL,R)
---R eval : (%,List Equation R) -> % if R has EVALAB R
---R eval : (%,Equation R) -> % if R has EVALAB R
---R eval : (%,R,R) -> % if R has EVALAB R
---R eval : (%,List R,List R) -> % if R has EVALAB R
+--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R)
+--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R)
+--R eval : (%,Equation(R)) -> % if R has EVALAB(R)
+--R eval : (%,R,R) -> % if R has EVALAB(R)
+--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R)
--R exp : % -> % if R has TRANFUN
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has EUCDOM
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has EUCDOM
--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM or R has EUCDOM and R has PFECAT
--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has EUCDOM
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has EUCDOM
---R factor : % -> Factored % if R has EUCDOM and R has PFECAT or R has FIELD
---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has EUCDOM and R has PFECAT
---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has EUCDOM and R has PFECAT
---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if R has FFIELDC
+--R factor : % -> Factored(%) if R has EUCDOM and R has PFECAT or R has FIELD
+--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT
+--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT
+--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if R has FFIELDC
--R gcd : (%,%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT
---R gcd : List % -> % if R has EUCDOM or R has EUCDOM and R has PFECAT
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has EUCDOM or R has EUCDOM and R has PFECAT
+--R gcd : List(%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has EUCDOM or R has EUCDOM and R has PFECAT
--R index : PositiveInteger -> % if R has FINITE
--R init : () -> % if R has FFIELDC
--R lcm : (%,%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT
---R lcm : List % -> % if R has EUCDOM or R has EUCDOM and R has PFECAT
---R lift : % -> SparseUnivariatePolynomial R
+--R lcm : List(%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT
+--R lift : % -> SparseUnivariatePolynomial(R)
--R log : % -> % if R has TRANFUN
--R lookup : % -> PositiveInteger if R has FINITE
--R max : (%,%) -> % if R has ORDSET
--R min : (%,%) -> % if R has ORDSET
---R minimalPolynomial : % -> SparseUnivariatePolynomial R if R has FIELD
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has EUCDOM
+--R minimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has FIELD
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has EUCDOM
--R nextItem : % -> Union(%,"failed") if R has FFIELDC
--R nthRoot : (%,Integer) -> % if R has RADCAT and R has TRANFUN
---R order : % -> OnePointCompletion PositiveInteger if R has FFIELDC
+--R order : % -> OnePointCompletion(PositiveInteger) if R has FFIELDC
--R order : % -> PositiveInteger if R has FFIELDC
---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT
---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT
+--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT)
+--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT)
--R polarCoordinates : % -> Record(r: R,phi: R) if R has RNS and R has TRANFUN
--R prime? : % -> Boolean if R has EUCDOM and R has PFECAT or R has FIELD
--R primeFrobenius : % -> % if R has FFIELDC
--R primeFrobenius : (%,NonNegativeInteger) -> % if R has FFIELDC
--R primitive? : % -> Boolean if R has FFIELDC
--R primitiveElement : () -> % if R has FFIELDC
---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has EUCDOM
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has EUCDOM
--R ?quo? : (%,%) -> % if R has EUCDOM
--R random : () -> % if R has FINITE
---R rational : % -> Fraction Integer if R has INS
+--R rational : % -> Fraction(Integer) if R has INS
--R rational? : % -> Boolean if R has INS
---R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS
---R reduce : Fraction SparseUnivariatePolynomial R -> Union(%,"failed") if R has FIELD
---R reduce : SparseUnivariatePolynomial R -> %
---R reducedSystem : Matrix % -> Matrix R
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT
---R regularRepresentation : % -> Matrix R
---R regularRepresentation : (%,Vector %) -> Matrix R
+--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS
+--R reduce : Fraction(SparseUnivariatePolynomial(R)) -> Union(%,"failed") if R has FIELD
+--R reduce : SparseUnivariatePolynomial(R) -> %
+--R reducedSystem : Matrix(%) -> Matrix(R)
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT)
+--R regularRepresentation : % -> Matrix(R)
+--R regularRepresentation : (%,Vector(%)) -> Matrix(R)
--R ?rem? : (%,%) -> % if R has EUCDOM
--R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC
---R represents : (Vector R,Vector %) -> %
---R retract : % -> Fraction Integer if R has RETRACT FRAC INT
---R retract : % -> Integer if R has RETRACT INT
+--R represents : (Vector(R),Vector(%)) -> %
+--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT))
+--R retract : % -> Integer if R has RETRACT(INT)
--R retractIfCan : % -> Union(R,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT)
--R sec : % -> % if R has TRANFUN
--R sech : % -> % if R has TRANFUN
--R sin : % -> % if R has TRANFUN
--R sinh : % -> % if R has TRANFUN
--R size : () -> NonNegativeInteger if R has FINITE
--R sizeLess? : (%,%) -> Boolean if R has EUCDOM
---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has EUCDOM and R has PFECAT
+--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has EUCDOM and R has PFECAT
--R sqrt : % -> % if R has RADCAT and R has TRANFUN
---R squareFree : % -> Factored % if R has EUCDOM and R has PFECAT or R has FIELD
+--R squareFree : % -> Factored(%) if R has EUCDOM and R has PFECAT or R has FIELD
--R squareFreePart : % -> % if R has EUCDOM and R has PFECAT or R has FIELD
---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has EUCDOM and R has PFECAT
+--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC
--R tan : % -> % if R has TRANFUN
--R tanh : % -> % if R has TRANFUN
---R traceMatrix : Vector % -> Matrix R
+--R traceMatrix : Vector(%) -> Matrix(R)
--R unit? : % -> Boolean if R has INTDOM or R has EUCDOM and R has PFECAT
--R unitCanonical : % -> % if R has INTDOM or R has EUCDOM and R has PFECAT
--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM or R has EUCDOM and R has PFECAT
@@ -75137,160 +75311,162 @@ digraph pic {
--S 1 of 1
)show FunctionFieldCategory
---R FunctionFieldCategory(F: UniqueFactorizationDomain,UP: UnivariatePolynomialCategory t#1,UPUP: UnivariatePolynomialCategory Fraction t#2) is a category constructor
+--R
+--R FunctionFieldCategory(F: UniqueFactorizationDomain,UP: UnivariatePolynomialCategory(t#1),UPUP: UnivariatePolynomialCategory(Fraction(t#2))) is a category constructor
--R Abbreviation for FunctionFieldCategory is FFCAT
--R This constructor is exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for FFCAT
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (Fraction UP,%) -> % ?*? : (%,Fraction UP) -> %
+--R ?*? : (Fraction(UP),%) -> % ?*? : (%,Fraction(UP)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> %
--R ?+? : (%,%) -> % ?-? : (%,%) -> %
--R -? : % -> % ?=? : (%,%) -> Boolean
--R 1 : () -> % 0 : () -> %
---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector %
+--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%)
--R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean
---R coerce : Fraction UP -> % coerce : Integer -> %
+--R coerce : Fraction(UP) -> % coerce : Integer -> %
--R coerce : % -> OutputForm convert : UPUP -> %
---R convert : % -> UPUP convert : Vector Fraction UP -> %
---R convert : % -> Vector Fraction UP definingPolynomial : () -> UPUP
---R discriminant : () -> Fraction UP elt : (%,F,F) -> F
+--R convert : % -> UPUP definingPolynomial : () -> UPUP
+--R discriminant : () -> Fraction(UP) elt : (%,F,F) -> F
--R generator : () -> % genus : () -> NonNegativeInteger
--R hash : % -> SingleInteger integral? : (%,UP) -> Boolean
--R integral? : (%,F) -> Boolean integral? : % -> Boolean
---R integralBasis : () -> Vector % latex : % -> String
---R lift : % -> UPUP norm : % -> Fraction UP
+--R integralBasis : () -> Vector(%) latex : % -> String
+--R lift : % -> UPUP norm : % -> Fraction(UP)
--R one? : % -> Boolean primitivePart : % -> %
--R ramified? : UP -> Boolean ramified? : F -> Boolean
--R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean
--R recip : % -> Union(%,"failed") reduce : UPUP -> %
---R represents : (Vector UP,UP) -> % retract : % -> Fraction UP
+--R represents : (Vector(UP),UP) -> % retract : % -> Fraction(UP)
--R sample : () -> % singular? : UP -> Boolean
---R singular? : F -> Boolean trace : % -> Fraction UP
+--R singular? : F -> Boolean trace : % -> Fraction(UP)
--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean
---R ?*? : (%,Fraction Integer) -> % if Fraction UP has FIELD
---R ?*? : (Fraction Integer,%) -> % if Fraction UP has FIELD
+--R ?*? : (%,Fraction(Integer)) -> % if Fraction(UP) has FIELD
+--R ?*? : (Fraction(Integer),%) -> % if Fraction(UP) has FIELD
--R ?*? : (NonNegativeInteger,%) -> %
---R ?**? : (%,Integer) -> % if Fraction UP has FIELD
+--R ?**? : (%,Integer) -> % if Fraction(UP) has FIELD
--R ?**? : (%,NonNegativeInteger) -> %
---R ?/? : (%,%) -> % if Fraction UP has FIELD
---R D : % -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC
---R D : (%,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC
---R D : (%,Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R D : (%,List Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R D : (%,Symbol,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R D : (%,List Symbol,List NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R D : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD
---R D : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD
---R ?^? : (%,Integer) -> % if Fraction UP has FIELD
+--R ?/? : (%,%) -> % if Fraction(UP) has FIELD
+--R D : % -> % if and(has(Fraction(UP),Field),has(Fraction(UP),DifferentialRing)) or and(has(Fraction(UP),DifferentialRing),has(Fraction(UP),Field)) or Fraction(UP) has FFIELDC
+--R D : (%,NonNegativeInteger) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),DifferentialRing)) or and(has(Fraction(UP),DifferentialRing),has(Fraction(UP),Field)) or Fraction(UP) has FFIELDC
+--R D : (%,Symbol) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R D : (%,List(Symbol)) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R D : (%,Symbol,NonNegativeInteger) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R D : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD
+--R D : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD
+--R ?^? : (%,Integer) -> % if Fraction(UP) has FIELD
--R ?^? : (%,NonNegativeInteger) -> %
--R absolutelyIrreducible? : () -> Boolean
--R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP)
---R associates? : (%,%) -> Boolean if Fraction UP has FIELD
+--R associates? : (%,%) -> Boolean if Fraction(UP) has FIELD
--R branchPointAtInfinity? : () -> Boolean
--R characteristic : () -> NonNegativeInteger
--R characteristicPolynomial : % -> UPUP
---R charthRoot : % -> Union(%,"failed") if Fraction UP has CHARNZ
---R charthRoot : % -> % if Fraction UP has FFIELDC
---R coerce : % -> % if Fraction UP has FIELD
---R coerce : Fraction Integer -> % if Fraction UP has FIELD or Fraction UP has RETRACT FRAC INT
---R complementaryBasis : Vector % -> Vector %
---R conditionP : Matrix % -> Union(Vector %,"failed") if Fraction UP has FFIELDC
---R coordinates : Vector % -> Matrix Fraction UP
---R coordinates : % -> Vector Fraction UP
---R coordinates : (Vector %,Vector %) -> Matrix Fraction UP
---R coordinates : (%,Vector %) -> Vector Fraction UP
---R createPrimitiveElement : () -> % if Fraction UP has FFIELDC
---R derivationCoordinates : (Vector %,(Fraction UP -> Fraction UP)) -> Matrix Fraction UP if Fraction UP has FIELD
---R differentiate : % -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC
---R differentiate : (%,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,DifferentialRing)) or and(has(Fraction UP,DifferentialRing),has(Fraction UP,Field)) or Fraction UP has FFIELDC
---R differentiate : (%,Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R differentiate : (%,List Symbol) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if and(has(Fraction UP,Field),has(Fraction UP,PartialDifferentialRing Symbol)) or and(has(Fraction UP,PartialDifferentialRing Symbol),has(Fraction UP,Field))
+--R charthRoot : % -> Union(%,"failed") if Fraction(UP) has CHARNZ
+--R charthRoot : % -> % if Fraction(UP) has FFIELDC
+--R coerce : % -> % if Fraction(UP) has FIELD
+--R coerce : Fraction(Integer) -> % if Fraction(UP) has FIELD or Fraction(UP) has RETRACT(FRAC(INT))
+--R complementaryBasis : Vector(%) -> Vector(%)
+--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if Fraction(UP) has FFIELDC
+--R convert : Vector(Fraction(UP)) -> %
+--R convert : % -> Vector(Fraction(UP))
+--R coordinates : Vector(%) -> Matrix(Fraction(UP))
+--R coordinates : % -> Vector(Fraction(UP))
+--R coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(UP))
+--R coordinates : (%,Vector(%)) -> Vector(Fraction(UP))
+--R createPrimitiveElement : () -> % if Fraction(UP) has FFIELDC
+--R derivationCoordinates : (Vector(%),(Fraction(UP) -> Fraction(UP))) -> Matrix(Fraction(UP)) if Fraction(UP) has FIELD
+--R differentiate : % -> % if and(has(Fraction(UP),Field),has(Fraction(UP),DifferentialRing)) or and(has(Fraction(UP),DifferentialRing),has(Fraction(UP),Field)) or Fraction(UP) has FFIELDC
+--R differentiate : (%,NonNegativeInteger) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),DifferentialRing)) or and(has(Fraction(UP),DifferentialRing),has(Fraction(UP),Field)) or Fraction(UP) has FFIELDC
+--R differentiate : (%,Symbol) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R differentiate : (%,List(Symbol)) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R differentiate : (%,Symbol,NonNegativeInteger) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
+--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),PartialDifferentialRing(Symbol))) or and(has(Fraction(UP),PartialDifferentialRing(Symbol)),has(Fraction(UP),Field))
--R differentiate : (%,(UP -> UP)) -> %
---R differentiate : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD
---R differentiate : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD
---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction UP has FFIELDC
---R discreteLog : % -> NonNegativeInteger if Fraction UP has FFIELDC
---R discriminant : Vector % -> Fraction UP
---R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction UP has FIELD
+--R differentiate : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD
+--R differentiate : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD
+--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction(UP) has FFIELDC
+--R discreteLog : % -> NonNegativeInteger if Fraction(UP) has FFIELDC
+--R discriminant : Vector(%) -> Fraction(UP)
+--R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction(UP) has FIELD
--R elliptic : () -> Union(UP,"failed")
---R euclideanSize : % -> NonNegativeInteger if Fraction UP has FIELD
---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD
---R exquo : (%,%) -> Union(%,"failed") if Fraction UP has FIELD
---R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction UP has FIELD
---R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction UP has FIELD
---R factor : % -> Factored % if Fraction UP has FIELD
---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if Fraction UP has FFIELDC
---R gcd : (%,%) -> % if Fraction UP has FIELD
---R gcd : List % -> % if Fraction UP has FIELD
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Fraction UP has FIELD
+--R euclideanSize : % -> NonNegativeInteger if Fraction(UP) has FIELD
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD
+--R exquo : (%,%) -> Union(%,"failed") if Fraction(UP) has FIELD
+--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction(UP) has FIELD
+--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction(UP) has FIELD
+--R factor : % -> Factored(%) if Fraction(UP) has FIELD
+--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if Fraction(UP) has FFIELDC
+--R gcd : (%,%) -> % if Fraction(UP) has FIELD
+--R gcd : List(%) -> % if Fraction(UP) has FIELD
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Fraction(UP) has FIELD
--R hyperelliptic : () -> Union(UP,"failed")
---R index : PositiveInteger -> % if Fraction UP has FINITE
---R init : () -> % if Fraction UP has FFIELDC
+--R index : PositiveInteger -> % if Fraction(UP) has FINITE
+--R init : () -> % if Fraction(UP) has FFIELDC
--R integralAtInfinity? : % -> Boolean
---R integralBasisAtInfinity : () -> Vector %
---R integralCoordinates : % -> Record(num: Vector UP,den: UP)
---R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix UP,den: UP)
---R integralMatrix : () -> Matrix Fraction UP
---R integralMatrixAtInfinity : () -> Matrix Fraction UP
---R integralRepresents : (Vector UP,UP) -> %
---R inv : % -> % if Fraction UP has FIELD
---R inverseIntegralMatrix : () -> Matrix Fraction UP
---R inverseIntegralMatrixAtInfinity : () -> Matrix Fraction UP
---R lcm : (%,%) -> % if Fraction UP has FIELD
---R lcm : List % -> % if Fraction UP has FIELD
---R lookup : % -> PositiveInteger if Fraction UP has FINITE
---R minimalPolynomial : % -> UPUP if Fraction UP has FIELD
---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD
---R nextItem : % -> Union(%,"failed") if Fraction UP has FFIELDC
---R nonSingularModel : Symbol -> List Polynomial F if F has FIELD
---R normalizeAtInfinity : Vector % -> Vector %
+--R integralBasisAtInfinity : () -> Vector(%)
+--R integralCoordinates : % -> Record(num: Vector(UP),den: UP)
+--R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix(UP),den: UP)
+--R integralMatrix : () -> Matrix(Fraction(UP))
+--R integralMatrixAtInfinity : () -> Matrix(Fraction(UP))
+--R integralRepresents : (Vector(UP),UP) -> %
+--R inv : % -> % if Fraction(UP) has FIELD
+--R inverseIntegralMatrix : () -> Matrix(Fraction(UP))
+--R inverseIntegralMatrixAtInfinity : () -> Matrix(Fraction(UP))
+--R lcm : (%,%) -> % if Fraction(UP) has FIELD
+--R lcm : List(%) -> % if Fraction(UP) has FIELD
+--R lookup : % -> PositiveInteger if Fraction(UP) has FINITE
+--R minimalPolynomial : % -> UPUP if Fraction(UP) has FIELD
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD
+--R nextItem : % -> Union(%,"failed") if Fraction(UP) has FFIELDC
+--R nonSingularModel : Symbol -> List(Polynomial(F)) if F has FIELD
+--R normalizeAtInfinity : Vector(%) -> Vector(%)
--R numberOfComponents : () -> NonNegativeInteger
---R order : % -> OnePointCompletion PositiveInteger if Fraction UP has FFIELDC
---R order : % -> PositiveInteger if Fraction UP has FFIELDC
---R prime? : % -> Boolean if Fraction UP has FIELD
---R primeFrobenius : % -> % if Fraction UP has FFIELDC
---R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction UP has FFIELDC
---R primitive? : % -> Boolean if Fraction UP has FFIELDC
---R primitiveElement : () -> % if Fraction UP has FFIELDC
---R principalIdeal : List % -> Record(coef: List %,generator: %) if Fraction UP has FIELD
---R ?quo? : (%,%) -> % if Fraction UP has FIELD
+--R order : % -> OnePointCompletion(PositiveInteger) if Fraction(UP) has FFIELDC
+--R order : % -> PositiveInteger if Fraction(UP) has FFIELDC
+--R prime? : % -> Boolean if Fraction(UP) has FIELD
+--R primeFrobenius : % -> % if Fraction(UP) has FFIELDC
+--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction(UP) has FFIELDC
+--R primitive? : % -> Boolean if Fraction(UP) has FFIELDC
+--R primitiveElement : () -> % if Fraction(UP) has FFIELDC
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Fraction(UP) has FIELD
+--R ?quo? : (%,%) -> % if Fraction(UP) has FIELD
--R ramifiedAtInfinity? : () -> Boolean
---R random : () -> % if Fraction UP has FINITE
---R rationalPoints : () -> List List F if F has FINITE
---R reduce : Fraction UPUP -> Union(%,"failed") if Fraction UP has FIELD
---R reduceBasisAtInfinity : Vector % -> Vector %
---R reducedSystem : Matrix % -> Matrix Fraction UP
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction UP,vec: Vector Fraction UP)
---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if Fraction UP has LINEXP INT
---R reducedSystem : Matrix % -> Matrix Integer if Fraction UP has LINEXP INT
---R regularRepresentation : % -> Matrix Fraction UP
---R regularRepresentation : (%,Vector %) -> Matrix Fraction UP
---R ?rem? : (%,%) -> % if Fraction UP has FIELD
---R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction UP has FFIELDC
---R represents : Vector Fraction UP -> %
---R represents : (Vector Fraction UP,Vector %) -> %
---R retract : % -> Fraction Integer if Fraction UP has RETRACT FRAC INT
---R retract : % -> Integer if Fraction UP has RETRACT INT
---R retractIfCan : % -> Union(Fraction UP,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction UP has RETRACT FRAC INT
---R retractIfCan : % -> Union(Integer,"failed") if Fraction UP has RETRACT INT
+--R random : () -> % if Fraction(UP) has FINITE
+--R rationalPoints : () -> List(List(F)) if F has FINITE
+--R reduce : Fraction(UPUP) -> Union(%,"failed") if Fraction(UP) has FIELD
+--R reduceBasisAtInfinity : Vector(%) -> Vector(%)
+--R reducedSystem : Matrix(%) -> Matrix(Fraction(UP))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Fraction(UP)),vec: Vector(Fraction(UP)))
+--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if Fraction(UP) has LINEXP(INT)
+--R reducedSystem : Matrix(%) -> Matrix(Integer) if Fraction(UP) has LINEXP(INT)
+--R regularRepresentation : % -> Matrix(Fraction(UP))
+--R regularRepresentation : (%,Vector(%)) -> Matrix(Fraction(UP))
+--R ?rem? : (%,%) -> % if Fraction(UP) has FIELD
+--R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction(UP) has FFIELDC
+--R represents : Vector(Fraction(UP)) -> %
+--R represents : (Vector(Fraction(UP)),Vector(%)) -> %
+--R retract : % -> Fraction(Integer) if Fraction(UP) has RETRACT(FRAC(INT))
+--R retract : % -> Integer if Fraction(UP) has RETRACT(INT)
+--R retractIfCan : % -> Union(Fraction(UP),"failed")
+--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(UP) has RETRACT(FRAC(INT))
+--R retractIfCan : % -> Union(Integer,"failed") if Fraction(UP) has RETRACT(INT)
--R singularAtInfinity? : () -> Boolean
---R size : () -> NonNegativeInteger if Fraction UP has FINITE
---R sizeLess? : (%,%) -> Boolean if Fraction UP has FIELD
---R squareFree : % -> Factored % if Fraction UP has FIELD
---R squareFreePart : % -> % if Fraction UP has FIELD
+--R size : () -> NonNegativeInteger if Fraction(UP) has FINITE
+--R sizeLess? : (%,%) -> Boolean if Fraction(UP) has FIELD
+--R squareFree : % -> Factored(%) if Fraction(UP) has FIELD
+--R squareFreePart : % -> % if Fraction(UP) has FIELD
--R subtractIfCan : (%,%) -> Union(%,"failed")
---R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction UP has FFIELDC
---R traceMatrix : () -> Matrix Fraction UP
---R traceMatrix : Vector % -> Matrix Fraction UP
---R unit? : % -> Boolean if Fraction UP has FIELD
---R unitCanonical : % -> % if Fraction UP has FIELD
---R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction UP has FIELD
---R yCoordinates : % -> Record(num: Vector UP,den: UP)
+--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction(UP) has FFIELDC
+--R traceMatrix : () -> Matrix(Fraction(UP))
+--R traceMatrix : Vector(%) -> Matrix(Fraction(UP))
+--R unit? : % -> Boolean if Fraction(UP) has FIELD
+--R unitCanonical : % -> % if Fraction(UP) has FIELD
+--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction(UP) has FIELD
+--R yCoordinates : % -> Record(num: Vector(UP),den: UP)
--R
--E 1
@@ -76301,85 +76477,86 @@ digraph pic {
--S 1 of 1
)show PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory
+--R
--R PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory is a category constructor
--R Abbreviation for PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory is PACEXTC
--R This constructor is not exposed in this frame.
--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PACEXTC
--R
--R------------------------------- Operations --------------------------------
---R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> %
---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> %
+--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> %
+--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> %
--R ?*? : (%,%) -> % ?*? : (Integer,%) -> %
--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> %
--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> %
--R ?-? : (%,%) -> % -? : % -> %
---R ?/? : (%,Fraction Integer) -> % ?/? : (%,%) -> %
+--R ?/? : (%,Fraction(Integer)) -> % ?/? : (%,%) -> %
--R ?=? : (%,%) -> Boolean 1 : () -> %
--R 0 : () -> % ?^? : (%,Integer) -> %
--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean
---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> %
---R coerce : Fraction Integer -> % coerce : Integer -> %
---R coerce : Fraction Integer -> % coerce : % -> %
+--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> %
+--R coerce : Fraction(Integer) -> % coerce : Integer -> %
+--R coerce : Fraction(Integer) -> % coerce : % -> %
--R coerce : Integer -> % coerce : % -> OutputForm
--R conjugate : % -> % dimension : () -> CardinalNumber
---R extDegree : % -> PositiveInteger factor : % -> Factored %
---R fullOutput : % -> OutputForm gcd : List % -> %
+--R extDegree : % -> PositiveInteger factor : % -> Factored(%)
+--R fullOutput : % -> OutputForm gcd : List(%) -> %
--R gcd : (%,%) -> % ground? : % -> Boolean
--R hash : % -> SingleInteger inGroundField? : % -> Boolean
--R inv : % -> % latex : % -> String
---R lcm : List % -> % lcm : (%,%) -> %
---R maxTower : List % -> % one? : % -> Boolean
+--R lcm : List(%) -> % lcm : (%,%) -> %
+--R maxTower : List(%) -> % one? : % -> Boolean
--R previousTower : % -> % prime? : % -> Boolean
--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed")
---R ?rem? : (%,%) -> % retract : % -> Fraction Integer
---R retract : % -> Fraction Integer retract : % -> Integer
+--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer)
+--R retract : % -> Fraction(Integer) retract : % -> Integer
--R sample : () -> % setTower! : % -> Void
---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored %
+--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%)
--R squareFreePart : % -> % transcendent? : % -> Boolean
--R unit? : % -> Boolean unitCanonical : % -> %
---R vectorise : (%,%) -> Vector % zero? : % -> Boolean
+--R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean
--R ?~=? : (%,%) -> Boolean
--R ?*? : (%,PseudoAlgebraicClosureOfRationalNumber) -> %
--R ?*? : (PseudoAlgebraicClosureOfRationalNumber,%) -> %
--R ?*? : (NonNegativeInteger,%) -> %
--R ?**? : (%,NonNegativeInteger) -> %
--R ?/? : (%,PseudoAlgebraicClosureOfRationalNumber) -> %
---R Frobenius : % -> % if PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has FINITE
---R Frobenius : (%,NonNegativeInteger) -> % if PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has FINITE
+--R Frobenius : % -> % if PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has FINITE
+--R Frobenius : (%,NonNegativeInteger) -> % if PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has FINITE
--R ?^? : (%,NonNegativeInteger) -> %
--R characteristic : () -> NonNegativeInteger
---R charthRoot : % -> Union(%,"failed") if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has CHARNZ or Fraction Integer has FINITE
+--R charthRoot : % -> Union(%,"failed") if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
--R coerce : PseudoAlgebraicClosureOfRationalNumber -> %
--R coerce : PseudoAlgebraicClosureOfRationalNumber -> %
---R definingPolynomial : % -> SparseUnivariatePolynomial %
---R definingPolynomial : () -> SparseUnivariatePolynomial %
---R degree : % -> OnePointCompletion PositiveInteger
---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List %
+--R definingPolynomial : % -> SparseUnivariatePolynomial(%)
+--R definingPolynomial : () -> SparseUnivariatePolynomial(%)
+--R degree : % -> OnePointCompletion(PositiveInteger)
+--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R distinguishedRootsOf : (SparseUnivariatePolynomial(%),%) -> List(%)
--R divide : (%,%) -> Record(quotient: %,remainder: %)
--R euclideanSize : % -> NonNegativeInteger
---R expressIdealMember : (List %,%) -> Union(List %,"failed")
+--R expressIdealMember : (List(%),%) -> Union(List(%),"failed")
--R exquo : (%,%) -> Union(%,"failed")
--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed")
--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %)
---R extensionDegree : () -> OnePointCompletion PositiveInteger
---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
---R lift : (%,%) -> SparseUnivariatePolynomial %
---R lift : % -> SparseUnivariatePolynomial %
---R multiEuclidean : (List %,%) -> Union(List %,"failed")
---R newElement : (SparseUnivariatePolynomial %,Symbol) -> %
---R newElement : (SparseUnivariatePolynomial %,%,Symbol) -> %
---R order : % -> OnePointCompletion PositiveInteger if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R primeFrobenius : % -> % if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R primeFrobenius : (%,NonNegativeInteger) -> % if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction Integer has CHARNZ or Fraction Integer has FINITE
---R principalIdeal : List % -> Record(coef: List %,generator: %)
---R reduce : SparseUnivariatePolynomial % -> %
+--R extensionDegree : () -> OnePointCompletion(PositiveInteger)
+--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)
+--R lift : (%,%) -> SparseUnivariatePolynomial(%)
+--R lift : % -> SparseUnivariatePolynomial(%)
+--R multiEuclidean : (List(%),%) -> Union(List(%),"failed")
+--R newElement : (SparseUnivariatePolynomial(%),Symbol) -> %
+--R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> %
+--R order : % -> OnePointCompletion(PositiveInteger) if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R primeFrobenius : % -> % if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R primeFrobenius : (%,NonNegativeInteger) -> % if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE
+--R principalIdeal : List(%) -> Record(coef: List(%),generator: %)
+--R reduce : SparseUnivariatePolynomial(%) -> %
--R retract : % -> PseudoAlgebraicClosureOfRationalNumber
--R retract : % -> PseudoAlgebraicClosureOfRationalNumber
--R retractIfCan : % -> Union(PseudoAlgebraicClosureOfRationalNumber,"failed")
--R retractIfCan : % -> Union(PseudoAlgebraicClosureOfRationalNumber,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed")
---R retractIfCan : % -> Union(Fraction Integer,"failed")
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
+--R retractIfCan : % -> Union(Fraction(Integer),"failed")
--R retractIfCan : % -> Union(Integer,"failed")
--R subtractIfCan : (%,%) -> Union(%,"failed")
--R transcendenceDegree : () -> NonNegativeInteger
diff --git a/changelog b/changelog
index df33128..700f1e1 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20120303 tpd src/axiom-website/patches.html 20120303.01.tpd.patch
+20120303 tpd books/bookvol10.2 fix bug 7217
20120302 tpd src/axiom-website/patches.html 20120302.03.tpd.patch
20120302 tpd src/input/schaum9.input fix bug 7217
20120302 tpd src/input/schaum8.input fix bug 7217
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 6989d21..e4a2765 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -3838,5 +3838,7 @@ books/bookvol0 add )tangle and )regress commands
buglist add bugs found during regression test review
20120302.03.tpd.patch
src/input/* fix bug 7217
+20120303.01.tpd.patch
+books/bookvol10.2 fix bug 7217