Expression(R)

expr.spad line 1 [edit on github]

Expressions involving symbolic functions.

* : (%, %) -> % if R has SemiGroup
from Magma
* : (%, R) -> % if R has Ring
from RightModule(R)
* : (%, Fraction(Integer)) -> % if R has IntegralDomain
from RightModule(Fraction(Integer))
* : (%, Integer) -> % if R has IntegralDomain and R has LinearlyExplicitOver(Integer) or R has LinearlyExplicitOver(Integer) and R has Ring
from RightModule(Integer)
* : (R, %) -> % if R has CommutativeRing
from LeftModule(R)
* : (Fraction(Integer), %) -> % if R has IntegralDomain
from LeftModule(Fraction(Integer))
* : (Integer, %) -> % if R has AbelianGroup
from AbelianGroup
* : (NonNegativeInteger, %) -> % if R has AbelianSemiGroup
from AbelianMonoid
* : (PositiveInteger, %) -> % if R has AbelianSemiGroup
from AbelianSemiGroup
+ : (%, %) -> % if R has AbelianSemiGroup
from AbelianSemiGroup
- : % -> % if R has AbelianGroup
from AbelianGroup
- : (%, %) -> % if R has AbelianGroup
from AbelianGroup
/ : (%, %) -> % if R has Group or R has IntegralDomain
from Group
/ : (SparseMultivariatePolynomial(R, Kernel(%)), SparseMultivariatePolynomial(R, Kernel(%))) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
0 : () -> % if R has AbelianSemiGroup
from AbelianMonoid
1 : () -> % if R has SemiGroup
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
Beta : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
Beta : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
Chi : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
Ci : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
D : (%, List(Symbol)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
D : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
D : (%, Symbol) -> % if R has Ring
from PartialDifferentialRing(Symbol)
D : (%, Symbol, NonNegativeInteger) -> % if R has Ring
from PartialDifferentialRing(Symbol)
Ei : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
Gamma : % -> % if R has IntegralDomain
from SpecialFunctionCategory
Gamma : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
Shi : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
Si : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
^ : (%, %) -> % if R has IntegralDomain
from ElementaryFunctionCategory
^ : (%, Fraction(Integer)) -> % if R has IntegralDomain
from RadicalCategory
^ : (%, Integer) -> % if R has Group or R has IntegralDomain
from Group
^ : (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
^ : (%, PositiveInteger) -> % if R has SemiGroup
from Magma
abs : % -> % if R has IntegralDomain
from SpecialFunctionCategory
acos : % -> % if R has IntegralDomain
from ArcTrigonometricFunctionCategory
acosh : % -> % if R has IntegralDomain
from ArcHyperbolicFunctionCategory
acot : % -> % if R has IntegralDomain
from ArcTrigonometricFunctionCategory
acoth : % -> % if R has IntegralDomain
from ArcHyperbolicFunctionCategory
acsc : % -> % if R has IntegralDomain
from ArcTrigonometricFunctionCategory
acsch : % -> % if R has IntegralDomain
from ArcHyperbolicFunctionCategory
airyAi : % -> % if R has IntegralDomain
from SpecialFunctionCategory
airyAiPrime : % -> % if R has IntegralDomain
from SpecialFunctionCategory
airyBi : % -> % if R has IntegralDomain
from SpecialFunctionCategory
airyBiPrime : % -> % if R has IntegralDomain
from SpecialFunctionCategory
algtower : % -> List(Kernel(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
algtower : List(%) -> List(Kernel(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
angerJ : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
annihilate? : (%, %) -> Boolean if R has Ring
from Rng
antiCommutator : (%, %) -> % if R has Ring
from NonAssociativeSemiRng
applyQuote : (Symbol, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, %, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, %, %, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, %, %, %, %) -> %
from FunctionSpace2(R, Kernel(%))
applyQuote : (Symbol, List(%)) -> %
from FunctionSpace2(R, Kernel(%))
asec : % -> % if R has IntegralDomain
from ArcTrigonometricFunctionCategory
asech : % -> % if R has IntegralDomain
from ArcHyperbolicFunctionCategory
asin : % -> % if R has IntegralDomain
from ArcTrigonometricFunctionCategory
asinh : % -> % if R has IntegralDomain
from ArcHyperbolicFunctionCategory
associates? : (%, %) -> Boolean if R has IntegralDomain
from EntireRing
associator : (%, %, %) -> % if R has Ring
from NonAssociativeRng
atan : % -> % if R has IntegralDomain
from ArcTrigonometricFunctionCategory
atanh : % -> % if R has IntegralDomain
from ArcHyperbolicFunctionCategory
belong? : BasicOperator -> Boolean
from ExpressionSpace2(Kernel(%))
besselI : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
besselJ : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
besselK : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
besselY : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
binomial : (%, %) -> % if R has IntegralDomain
from CombinatorialFunctionCategory
box : % -> %
from ExpressionSpace2(Kernel(%))
ceiling : % -> % if R has IntegralDomain
from SpecialFunctionCategory
characteristic : () -> NonNegativeInteger if R has Ring
from NonAssociativeRing
charlierC : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
charthRoot : % -> Union(%, "failed") if % has CharacteristicNonZero and R has IntegralDomain and R has PolynomialFactorizationExplicit or R has CharacteristicNonZero
from CharacteristicNonZero
coerce : % -> % if R has IntegralDomain
from Algebra(%)
coerce : R -> %
from CoercibleFrom(R)
coerce : AlgebraicNumber -> % if R has RetractableTo(Integer) and R has IntegralDomain
from CoercibleFrom(AlgebraicNumber)
coerce : Fraction(R) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
coerce : Fraction(Integer) -> % if R has RetractableTo(Fraction(Integer)) or R has IntegralDomain
from CoercibleFrom(Fraction(Integer))
coerce : Fraction(Polynomial(R)) -> % if R has IntegralDomain
from CoercibleFrom(Fraction(Polynomial(R)))
coerce : Fraction(Polynomial(Fraction(R))) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
coerce : Integer -> % if R has RetractableTo(Integer) or R has Ring
from CoercibleFrom(Integer)
coerce : Kernel(%) -> %
from CoercibleFrom(Kernel(%))
coerce : Polynomial(R) -> % if R has Ring
from CoercibleFrom(Polynomial(R))
coerce : Polynomial(Fraction(R)) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
coerce : SparseMultivariatePolynomial(R, Kernel(%)) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
coerce : Symbol -> %
from CoercibleFrom(Symbol)
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
commutator : (%, %) -> % if R has Group or R has Ring
from NonAssociativeRng
conditionP : Matrix(%) -> Union(Vector(%), "failed") if % has CharacteristicNonZero and R has IntegralDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
conjugate : % -> % if R has IntegralDomain
from SpecialFunctionCategory
conjugate : (%, %) -> % if R has Group
from Group
convert : Factored(%) -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
convert : % -> InputForm if R has ConvertibleTo(InputForm)
from ConvertibleTo(InputForm)
convert : % -> Pattern(Float) if R has ConvertibleTo(Pattern(Float))
from ConvertibleTo(Pattern(Float))
convert : % -> Pattern(Integer) if R has ConvertibleTo(Pattern(Integer))
from ConvertibleTo(Pattern(Integer))
cos : % -> % if R has IntegralDomain
from TrigonometricFunctionCategory
cosh : % -> % if R has IntegralDomain
from HyperbolicFunctionCategory
cot : % -> % if R has IntegralDomain
from TrigonometricFunctionCategory
coth : % -> % if R has IntegralDomain
from HyperbolicFunctionCategory
csc : % -> % if R has IntegralDomain
from TrigonometricFunctionCategory
csch : % -> % if R has IntegralDomain
from HyperbolicFunctionCategory
definingPolynomial : % -> % if % has Ring
from ExpressionSpace2(Kernel(%))
denom : % -> SparseMultivariatePolynomial(R, Kernel(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
denominator : % -> % if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
differentiate : (%, List(Symbol)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
differentiate : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has Ring
from PartialDifferentialRing(Symbol)
differentiate : (%, Symbol) -> % if R has Ring
from PartialDifferentialRing(Symbol)
differentiate : (%, Symbol, NonNegativeInteger) -> % if R has Ring
from PartialDifferentialRing(Symbol)
digamma : % -> % if R has IntegralDomain
from SpecialFunctionCategory
dilog : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
diracDelta : % -> % if R has IntegralDomain
from SpecialFunctionCategory
distribute : % -> %
from ExpressionSpace2(Kernel(%))
distribute : (%, %) -> %
from ExpressionSpace2(Kernel(%))
divide : (%, %) -> Record(quotient : %, remainder : %) if R has IntegralDomain
from EuclideanDomain
ellipticE : % -> % if R has IntegralDomain
from SpecialFunctionCategory
ellipticE : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
ellipticF : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
ellipticK : % -> % if R has IntegralDomain
from SpecialFunctionCategory
ellipticPi : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
elt : (BasicOperator, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, %, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace2(Kernel(%))
elt : (BasicOperator, List(%)) -> %
from ExpressionSpace2(Kernel(%))
erf : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
erfi : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
euclideanSize : % -> NonNegativeInteger if R has IntegralDomain
from EuclideanDomain
eval : (%, %, %) -> %
from InnerEvalable(%, %)
eval : (%, BasicOperator, %, Symbol) -> % if R has ConvertibleTo(InputForm)
from FunctionSpace2(R, Kernel(%))
eval : (%, BasicOperator, Mapping(%, %)) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, BasicOperator, Mapping(%, List(%))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, Equation(%)) -> %
from Evalable(%)
eval : (%, Kernel(%), %) -> %
from InnerEvalable(Kernel(%), %)
eval : (%, List(%), List(%)) -> %
from InnerEvalable(%, %)
eval : (%, List(BasicOperator), List(%), Symbol) -> % if R has ConvertibleTo(InputForm)
from FunctionSpace2(R, Kernel(%))
eval : (%, List(BasicOperator), List(Mapping(%, %))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(BasicOperator), List(Mapping(%, List(%)))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(Equation(%))) -> %
from Evalable(%)
eval : (%, List(Kernel(%)), List(%)) -> %
from InnerEvalable(Kernel(%), %)
eval : (%, List(Symbol), List(Mapping(%, %))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(Symbol), List(Mapping(%, List(%)))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, List(Symbol), List(NonNegativeInteger), List(Mapping(%, %))) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
eval : (%, List(Symbol), List(NonNegativeInteger), List(Mapping(%, List(%)))) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
eval : (%, Symbol, Mapping(%, %)) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, Symbol, Mapping(%, List(%))) -> %
from ExpressionSpace2(Kernel(%))
eval : (%, Symbol, NonNegativeInteger, Mapping(%, %)) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
eval : (%, Symbol, NonNegativeInteger, Mapping(%, List(%))) -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
even? : % -> Boolean if % has RetractableTo(Integer)
from ExpressionSpace2(Kernel(%))
exp : % -> % if R has IntegralDomain
from ElementaryFunctionCategory
expressIdealMember : (List(%), %) -> Union(List(%), "failed") if R has IntegralDomain
from PrincipalIdealDomain
exquo : (%, %) -> Union(%, "failed") if R has IntegralDomain
from EntireRing
extendedEuclidean : (%, %) -> Record(coef1 : %, coef2 : %, generator : %) if R has IntegralDomain
from EuclideanDomain
extendedEuclidean : (%, %, %) -> Union(Record(coef1 : %, coef2 : %), "failed") if R has IntegralDomain
from EuclideanDomain
factor : % -> Factored(%) if R has IntegralDomain
from UniqueFactorizationDomain
factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has IntegralDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has IntegralDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
factorial : % -> % if R has IntegralDomain
from CombinatorialFunctionCategory
factorials : % -> % if R has IntegralDomain
from CombinatorialOpsCategory
factorials : (%, Symbol) -> % if R has IntegralDomain
from CombinatorialOpsCategory
floor : % -> % if R has IntegralDomain
from SpecialFunctionCategory
fractionPart : % -> % if R has IntegralDomain
from SpecialFunctionCategory
freeOf? : (%, %) -> Boolean
from ExpressionSpace2(Kernel(%))
freeOf? : (%, Symbol) -> Boolean
from ExpressionSpace2(Kernel(%))
fresnelC : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
fresnelS : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
gcd : (%, %) -> % if R has IntegralDomain
from GcdDomain
gcd : List(%) -> % if R has IntegralDomain
from GcdDomain
gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has IntegralDomain
from GcdDomain
getSimplifyDenomsFlag : () -> Boolean if R has IntegralDomain

getSimplifyDenomsFlag() gets values of flag affecting simplification of denominators. See setSimplifyDenomsFlag.

ground : % -> R
from FunctionSpace2(R, Kernel(%))
ground? : % -> Boolean
from FunctionSpace2(R, Kernel(%))
hahnQ : (%, %, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hahnR : (%, %, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hahnS : (%, %, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hahn_p : (%, %, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hankelH1 : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hankelH2 : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
height : % -> NonNegativeInteger
from ExpressionSpace2(Kernel(%))
hermiteH : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hypergeometricF : (List(%), List(%), %) -> % if R has IntegralDomain and % has RetractableTo(Integer)
from SpecialFunctionCategory
integral : (%, SegmentBinding(%)) -> % if R has IntegralDomain
from PrimitiveFunctionCategory
integral : (%, Symbol) -> % if R has IntegralDomain
from PrimitiveFunctionCategory
inv : % -> % if R has Group or R has IntegralDomain
from Group
is? : (%, BasicOperator) -> Boolean
from ExpressionSpace2(Kernel(%))
is? : (%, Symbol) -> Boolean
from ExpressionSpace2(Kernel(%))
isExpt : % -> Union(Record(var : Kernel(%), exponent : Integer), "failed") if R has SemiGroup
from FunctionSpace2(R, Kernel(%))
isExpt : (%, BasicOperator) -> Union(Record(var : Kernel(%), exponent : Integer), "failed") if R has Ring
from FunctionSpace2(R, Kernel(%))
isExpt : (%, Symbol) -> Union(Record(var : Kernel(%), exponent : Integer), "failed") if R has Ring
from FunctionSpace2(R, Kernel(%))
isMult : % -> Union(Record(coef : Integer, var : Kernel(%)), "failed") if R has AbelianSemiGroup
from FunctionSpace2(R, Kernel(%))
isPlus : % -> Union(List(%), "failed") if R has AbelianSemiGroup
from FunctionSpace2(R, Kernel(%))
isPower : % -> Union(Record(val : %, exponent : Integer), "failed") if R has Ring
from FunctionSpace2(R, Kernel(%))
isTimes : % -> Union(List(%), "failed") if R has SemiGroup
from FunctionSpace2(R, Kernel(%))
jacobiCn : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
jacobiDn : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
jacobiP : (%, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
jacobiSn : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
jacobiTheta : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
jacobiZeta : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kelvinBei : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kelvinBer : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kelvinKei : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kelvinKer : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kernel : (BasicOperator, %) -> %
from ExpressionSpace2(Kernel(%))
kernel : (BasicOperator, List(%)) -> %
from ExpressionSpace2(Kernel(%))
kernels : % -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
kernels : List(%) -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
krawtchoukK : (%, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kummerM : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
kummerU : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
laguerreL : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
lambertW : % -> % if R has IntegralDomain
from SpecialFunctionCategory
latex : % -> String
from SetCategory
lcm : (%, %) -> % if R has IntegralDomain
from GcdDomain
lcm : List(%) -> % if R has IntegralDomain
from GcdDomain
lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %) if R has IntegralDomain
from LeftOreRing
leftPower : (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
leftPower : (%, PositiveInteger) -> % if R has SemiGroup
from Magma
leftRecip : % -> Union(%, "failed") if R has SemiGroup
from MagmaWithUnit
legendreP : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
legendreQ : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
lerchPhi : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
li : % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
log : % -> % if R has IntegralDomain
from ElementaryFunctionCategory
lommelS1 : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
lommelS2 : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
mainKernel : % -> Union(Kernel(%), "failed")
from ExpressionSpace2(Kernel(%))
map : (Mapping(%, %), Kernel(%)) -> %
from ExpressionSpace2(Kernel(%))
meijerG : (List(%), List(%), List(%), List(%), %) -> % if R has IntegralDomain and % has RetractableTo(Integer)
from SpecialFunctionCategory
meixnerM : (%, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
meixnerP : (%, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if % has Ring
from ExpressionSpace2(Kernel(%))
multiEuclidean : (List(%), %) -> Union(List(%), "failed") if R has IntegralDomain
from EuclideanDomain
nthRoot : (%, Integer) -> % if R has IntegralDomain
from RadicalCategory
number? : % -> Boolean if R has IntegralDomain

number?(f) tests if f is rational

numer : % -> SparseMultivariatePolynomial(R, Kernel(%)) if R has Ring
from FunctionSpace2(R, Kernel(%))
numerator : % -> % if R has Ring
from FunctionSpace2(R, Kernel(%))
odd? : % -> Boolean if % has RetractableTo(Integer)
from ExpressionSpace2(Kernel(%))
one? : % -> Boolean if R has SemiGroup
from MagmaWithUnit
operator : BasicOperator -> BasicOperator
from ExpressionSpace2(Kernel(%))
operators : % -> List(BasicOperator)
from ExpressionSpace2(Kernel(%))
opposite? : (%, %) -> Boolean if R has AbelianSemiGroup
from AbelianMonoid
paren : % -> %
from ExpressionSpace2(Kernel(%))
patternMatch : (%, Pattern(Float), PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if R has PatternMatchable(Float)
from PatternMatchable(Float)
patternMatch : (%, Pattern(Integer), PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if R has PatternMatchable(Integer)
from PatternMatchable(Integer)
permutation : (%, %) -> % if R has IntegralDomain
from CombinatorialFunctionCategory
pi : () -> % if R has IntegralDomain
from TranscendentalFunctionCategory
plenaryPower : (%, PositiveInteger) -> % if R has CommutativeRing
from NonAssociativeAlgebra(R)
polygamma : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
polylog : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
prime? : % -> Boolean if R has IntegralDomain
from UniqueFactorizationDomain
principalIdeal : List(%) -> Record(coef : List(%), generator : %) if R has IntegralDomain
from PrincipalIdealDomain
product : (%, SegmentBinding(%)) -> % if R has IntegralDomain
from CombinatorialOpsCategory
product : (%, Symbol) -> % if R has IntegralDomain
from CombinatorialOpsCategory
quo : (%, %) -> % if R has IntegralDomain
from EuclideanDomain
racahR : (%, %, %, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
recip : % -> Union(%, "failed") if R has SemiGroup
from MagmaWithUnit
reduce : % -> % if R has IntegralDomain

reduce(f) simplifies all the unreduced algebraic quantities present in f by applying their defining relations.

reducedSystem : Matrix(%) -> Matrix(R) if R has Ring
from LinearlyExplicitOver(R)
reducedSystem : Matrix(%) -> Matrix(Integer) if R has IntegralDomain and R has LinearlyExplicitOver(Integer) or R has LinearlyExplicitOver(Integer) and R has Ring
from LinearlyExplicitOver(Integer)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(R), vec : Vector(R)) if R has Ring
from LinearlyExplicitOver(R)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(Integer), vec : Vector(Integer)) if R has IntegralDomain and R has LinearlyExplicitOver(Integer) or R has LinearlyExplicitOver(Integer) and R has Ring
from LinearlyExplicitOver(Integer)
rem : (%, %) -> % if R has IntegralDomain
from EuclideanDomain
retract : % -> R
from RetractableTo(R)
retract : % -> AlgebraicNumber if R has RetractableTo(Integer) and R has IntegralDomain
from RetractableTo(AlgebraicNumber)
retract : % -> Fraction(Integer) if R has RetractableTo(Fraction(Integer)) or R has RetractableTo(Integer) and R has IntegralDomain
from RetractableTo(Fraction(Integer))
retract : % -> Fraction(Polynomial(R)) if R has IntegralDomain
from RetractableTo(Fraction(Polynomial(R)))
retract : % -> Integer if R has RetractableTo(Integer)
from RetractableTo(Integer)
retract : % -> Kernel(%)
from RetractableTo(Kernel(%))
retract : % -> Polynomial(R) if R has Ring
from RetractableTo(Polynomial(R))
retract : % -> Symbol
from RetractableTo(Symbol)
retractIfCan : % -> Union(R, "failed")
from RetractableTo(R)
retractIfCan : % -> Union(AlgebraicNumber, "failed") if R has RetractableTo(Integer) and R has IntegralDomain
from RetractableTo(AlgebraicNumber)
retractIfCan : % -> Union(Fraction(Integer), "failed") if R has RetractableTo(Fraction(Integer)) or R has RetractableTo(Integer) and R has IntegralDomain
from RetractableTo(Fraction(Integer))
retractIfCan : % -> Union(Fraction(Polynomial(R)), "failed") if R has IntegralDomain
from RetractableTo(Fraction(Polynomial(R)))
retractIfCan : % -> Union(Integer, "failed") if R has RetractableTo(Integer)
from RetractableTo(Integer)
retractIfCan : % -> Union(Kernel(%), "failed")
from RetractableTo(Kernel(%))
retractIfCan : % -> Union(Polynomial(R), "failed") if R has Ring
from RetractableTo(Polynomial(R))
retractIfCan : % -> Union(Symbol, "failed")
from RetractableTo(Symbol)
riemannZeta : % -> % if R has IntegralDomain
from SpecialFunctionCategory
rightPower : (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
rightPower : (%, PositiveInteger) -> % if R has SemiGroup
from Magma
rightRecip : % -> Union(%, "failed") if R has SemiGroup
from MagmaWithUnit
rootOf : % -> % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
rootOf : (%, Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
rootOf : Polynomial(%) -> % if R has IntegralDomain
from AlgebraicallyClosedField
rootOf : SparseUnivariatePolynomial(%) -> % if R has IntegralDomain
from AlgebraicallyClosedField
rootOf : (SparseUnivariatePolynomial(%), Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedField
rootSum : (%, SparseUnivariatePolynomial(%), Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
rootsOf : % -> List(%) if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
rootsOf : (%, Symbol) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
rootsOf : Polynomial(%) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedField
rootsOf : SparseUnivariatePolynomial(%) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedField
rootsOf : (SparseUnivariatePolynomial(%), Symbol) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedField
sample : () -> % if R has AbelianSemiGroup or R has SemiGroup
from AbelianMonoid
sec : % -> % if R has IntegralDomain
from TrigonometricFunctionCategory
sech : % -> % if R has IntegralDomain
from HyperbolicFunctionCategory
setSimplifyDenomsFlag : Boolean -> Boolean if R has IntegralDomain

setSimplifyDenomsFlag(x) sets flag affecting simplification of denominators. If true irrational algebraics are removed from denominators. If false they are kept.

sign : % -> % if R has IntegralDomain
from SpecialFunctionCategory
sin : % -> % if R has IntegralDomain
from TrigonometricFunctionCategory
sinh : % -> % if R has IntegralDomain
from HyperbolicFunctionCategory
sizeLess? : (%, %) -> Boolean if R has IntegralDomain
from EuclideanDomain
smaller? : (%, %) -> Boolean
from Comparable
solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)), SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)), "failed") if R has IntegralDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
sqrt : % -> % if R has IntegralDomain
from RadicalCategory
squareFree : % -> Factored(%) if R has IntegralDomain
from UniqueFactorizationDomain
squareFreePart : % -> % if R has IntegralDomain
from UniqueFactorizationDomain
squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has IntegralDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
struveH : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
struveL : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
subst : (%, Equation(%)) -> %
from ExpressionSpace2(Kernel(%))
subst : (%, List(Equation(%))) -> %
from ExpressionSpace2(Kernel(%))
subst : (%, List(Kernel(%)), List(%)) -> %
from ExpressionSpace2(Kernel(%))
subtractIfCan : (%, %) -> Union(%, "failed") if R has AbelianGroup
from CancellationAbelianMonoid
summation : (%, SegmentBinding(%)) -> % if R has IntegralDomain
from CombinatorialOpsCategory
summation : (%, Symbol) -> % if R has IntegralDomain
from CombinatorialOpsCategory
tan : % -> % if R has IntegralDomain
from TrigonometricFunctionCategory
tanh : % -> % if R has IntegralDomain
from HyperbolicFunctionCategory
tower : % -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
tower : List(%) -> List(Kernel(%))
from ExpressionSpace2(Kernel(%))
unit? : % -> Boolean if R has IntegralDomain
from EntireRing
unitCanonical : % -> % if R has IntegralDomain
from EntireRing
unitNormal : % -> Record(unit : %, canonical : %, associate : %) if R has IntegralDomain
from EntireRing
unitStep : % -> % if R has IntegralDomain
from SpecialFunctionCategory
univariate : (%, Kernel(%)) -> Fraction(SparseUnivariatePolynomial(%)) if R has IntegralDomain
from FunctionSpace2(R, Kernel(%))
variables : % -> List(Symbol)
from FunctionSpace2(R, Kernel(%))
variables : List(%) -> List(Symbol)
from FunctionSpace2(R, Kernel(%))
weberE : (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
weierstrassP : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
weierstrassPInverse : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
weierstrassPPrime : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
weierstrassSigma : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
weierstrassZeta : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
whittakerM : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
whittakerW : (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
wilsonW : (%, %, %, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
zero? : % -> Boolean if R has AbelianSemiGroup
from AbelianMonoid
zeroOf : % -> % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
zeroOf : (%, Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
zeroOf : Polynomial(%) -> % if R has IntegralDomain
from AlgebraicallyClosedField
zeroOf : SparseUnivariatePolynomial(%) -> % if R has IntegralDomain
from AlgebraicallyClosedField
zeroOf : (SparseUnivariatePolynomial(%), Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedField
zerosOf : % -> List(%) if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
zerosOf : (%, Symbol) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace(R)
zerosOf : Polynomial(%) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedField
zerosOf : SparseUnivariatePolynomial(%) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedField
zerosOf : (SparseUnivariatePolynomial(%), Symbol) -> List(%) if R has IntegralDomain
from AlgebraicallyClosedField
~= : (%, %) -> Boolean
from BasicType

EntireRing

Ring

CoercibleFrom(AlgebraicNumber)

Algebra(%)

CoercibleFrom(Kernel(%))

Patternable(R)

CancellationAbelianMonoid

CommutativeStar

DivisionRing

ConvertibleTo(Pattern(Float))

Field

LinearlyExplicitOver(Integer)

FullyPatternMatchable(R)

SemiGroup

RetractableTo(Kernel(%))

AlgebraicallyClosedFunctionSpace(R)

LeftModule(%)

RightModule(R)

Monoid

InnerEvalable(Kernel(%), %)

CombinatorialFunctionCategory

BiModule(Fraction(Integer), Fraction(Integer))

SpecialFunctionCategory

RetractableTo(Polynomial(R))

Algebra(R)

TrigonometricFunctionCategory

Module(%)

LeftOreRing

CoercibleFrom(Fraction(Integer))

noZeroDivisors

ExpressionSpace2(Kernel(%))

FullyRetractableTo(R)

SemiRing

NonAssociativeAlgebra(%)

SetCategory

CharacteristicNonZero

NonAssociativeSemiRing

RetractableTo(AlgebraicNumber)

PolynomialFactorizationExplicit

TwoSidedRecip

EuclideanDomain

CoercibleFrom(Fraction(Polynomial(R)))

CombinatorialOpsCategory

NonAssociativeRing

CoercibleFrom(Symbol)

FunctionSpace(R)

NonAssociativeRng

CoercibleFrom(Polynomial(R))

BiModule(R, R)

RetractableTo(R)

PrincipalIdealDomain

canonicalsClosed

NonAssociativeAlgebra(R)

ArcTrigonometricFunctionCategory

CommutativeRing

ArcHyperbolicFunctionCategory

FunctionSpace2(R, Kernel(%))

unitsKnown

AbelianSemiGroup

LeftModule(R)

Rng

canonicalUnitNormal

LeftModule(Fraction(Integer))

IntegralDomain

ExpressionSpace

RightModule(Integer)

CoercibleFrom(R)

Evalable(%)

NonAssociativeAlgebra(Fraction(Integer))

FullyLinearlyExplicitOver(R)

AlgebraicallyClosedField

LinearlyExplicitOver(R)

RadicalCategory

Group

NonAssociativeSemiRng

GcdDomain

CharacteristicZero

PatternMatchable(Float)

PartialDifferentialRing(Symbol)

Algebra(Fraction(Integer))

HyperbolicFunctionCategory

AbelianGroup

LiouvillianFunctionCategory

BasicType

RetractableTo(Fraction(Polynomial(R)))

MagmaWithUnit

PrimitiveFunctionCategory

Comparable

CoercibleFrom(Integer)

AbelianMonoid

PatternMatchable(Integer)

CoercibleTo(OutputForm)

BiModule(%, %)

RetractableTo(Fraction(Integer))

SemiRng

ConvertibleTo(InputForm)

RetractableTo(Symbol)

RightModule(Fraction(Integer))

Module(R)

InnerEvalable(%, %)

UniqueFactorizationDomain

ElementaryFunctionCategory

TranscendentalFunctionCategory

ConvertibleTo(Pattern(Integer))

Module(Fraction(Integer))

RightModule(%)

RetractableTo(Integer)

Magma