Expression RΒΆ

expr.spad line 1

Expressions involving symbolic functions.

0: % if R has AbelianSemiGroup
from AbelianMonoid
1: % if R has SemiGroup
from MagmaWithUnit
*: (%, %) -> % if R has SemiGroup
from Magma
*: (%, Fraction Integer) -> % if R has IntegralDomain
from RightModule Fraction Integer
*: (%, R) -> % if R has CommutativeRing
from RightModule 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
*: (R, %) -> % if R has CommutativeRing
from LeftModule R
+: (%, %) -> % if R has AbelianSemiGroup
from AbelianSemiGroup
-: % -> % if R has AbelianGroup
from AbelianGroup
-: (%, %) -> % if R has AbelianGroup
from AbelianGroup
/: (%, %) -> % if R has IntegralDomain or R has Group
from Group
/: (SparseMultivariatePolynomial(R, Kernel %), SparseMultivariatePolynomial(R, Kernel %)) -> % if R has IntegralDomain
from FunctionSpace R
=: (%, %) -> Boolean
from BasicType
^: (%, %) -> % if R has IntegralDomain
from ElementaryFunctionCategory
^: (%, Fraction Integer) -> % if R has IntegralDomain
from RadicalCategory
^: (%, Integer) -> % if R has IntegralDomain or R has Group
from Group
^: (%, NonNegativeInteger) -> % if R has SemiGroup
from MagmaWithUnit
^: (%, PositiveInteger) -> % if R has SemiGroup
from Magma
~=: (%, %) -> Boolean
from BasicType
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 FunctionSpace R
algtower: List % -> List Kernel % if R has IntegralDomain
from FunctionSpace R
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 FunctionSpace R
applyQuote: (Symbol, %, %) -> %
from FunctionSpace R
applyQuote: (Symbol, %, %, %) -> %
from FunctionSpace R
applyQuote: (Symbol, %, %, %, %) -> %
from FunctionSpace R
applyQuote: (Symbol, List %) -> %
from FunctionSpace R
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 ExpressionSpace
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
Beta: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
binomial: (%, %) -> % if R has IntegralDomain
from CombinatorialFunctionCategory
box: % -> %
from ExpressionSpace
box: List % -> %
from ExpressionSpace
characteristic: () -> NonNegativeInteger if R has Ring
from NonAssociativeRing
charlierC: (%, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
from CharacteristicNonZero
Chi: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
Ci: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
coerce: % -> % if R has IntegralDomain
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: AlgebraicNumber -> % if R has RetractableTo Integer and R has IntegralDomain
from RetractableTo AlgebraicNumber
coerce: Fraction Integer -> % if R has IntegralDomain or R has RetractableTo Fraction Integer
from Algebra Fraction Integer
coerce: Fraction Polynomial Fraction R -> % if R has IntegralDomain
from FunctionSpace R
coerce: Fraction Polynomial R -> % if R has IntegralDomain
from RetractableTo Fraction Polynomial R
coerce: Fraction R -> % if R has IntegralDomain
from FunctionSpace R
coerce: Integer -> % if R has RetractableTo Integer or R has Ring
from NonAssociativeRing
coerce: Kernel % -> %
from RetractableTo Kernel %
coerce: Polynomial Fraction R -> % if R has IntegralDomain
from FunctionSpace R
coerce: Polynomial R -> % if R has Ring
from RetractableTo Polynomial R
coerce: R -> %
from RetractableTo R
coerce: SparseMultivariatePolynomial(R, Kernel %) -> % if R has Ring
from FunctionSpace R
coerce: Symbol -> %
from RetractableTo Symbol
commutator: (%, %) -> % if R has Ring or R has Group
from NonAssociativeRng
conjugate: (%, %) -> % if R has Group
from Group
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
convert: Factored % -> % if R has IntegralDomain
from FunctionSpace R
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
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
denom: % -> SparseMultivariatePolynomial(R, Kernel %) if R has IntegralDomain
from FunctionSpace R
denominator: % -> % if R has IntegralDomain
from FunctionSpace R
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
distribute: % -> %
from ExpressionSpace
distribute: (%, %) -> %
from ExpressionSpace
divide: (%, %) -> Record(quotient: %, remainder: %) if R has IntegralDomain
from EuclideanDomain
Ei: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
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 ExpressionSpace
elt: (BasicOperator, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %, %, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, %, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace
elt: (BasicOperator, List %) -> %
from ExpressionSpace
erf: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
erfi: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
euclideanSize: % -> NonNegativeInteger if R has IntegralDomain
from EuclideanDomain
eval: % -> % if R has ConvertibleTo InputForm
from FunctionSpace R
eval: (%, %, %) -> %
from InnerEvalable(%, %)
eval: (%, BasicOperator, % -> %) -> %
from ExpressionSpace
eval: (%, BasicOperator, %, Symbol) -> % if R has ConvertibleTo InputForm
from FunctionSpace R
eval: (%, BasicOperator, List % -> %) -> %
from ExpressionSpace
eval: (%, Equation %) -> %
from Evalable %
eval: (%, Kernel %, %) -> %
from InnerEvalable(Kernel %, %)
eval: (%, List %, List %) -> %
from InnerEvalable(%, %)
eval: (%, List BasicOperator, List % -> %) -> %
from ExpressionSpace
eval: (%, List BasicOperator, List %, Symbol) -> % if R has ConvertibleTo InputForm
from FunctionSpace R
eval: (%, List BasicOperator, List List % -> %) -> %
from ExpressionSpace
eval: (%, List Equation %) -> %
from Evalable %
eval: (%, List Kernel %, List %) -> %
from InnerEvalable(Kernel %, %)
eval: (%, List Symbol) -> % if R has ConvertibleTo InputForm
from FunctionSpace R
eval: (%, List Symbol, List % -> %) -> %
from ExpressionSpace
eval: (%, List Symbol, List List % -> %) -> %
from ExpressionSpace
eval: (%, List Symbol, List NonNegativeInteger, List % -> %) -> % if R has Ring
from FunctionSpace R
eval: (%, List Symbol, List NonNegativeInteger, List List % -> %) -> % if R has Ring
from FunctionSpace R
eval: (%, Symbol) -> % if R has ConvertibleTo InputForm
from FunctionSpace R
eval: (%, Symbol, % -> %) -> %
from ExpressionSpace
eval: (%, Symbol, List % -> %) -> %
from ExpressionSpace
eval: (%, Symbol, NonNegativeInteger, % -> %) -> % if R has Ring
from FunctionSpace R
eval: (%, Symbol, NonNegativeInteger, List % -> %) -> % if R has Ring
from FunctionSpace R
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
factorial: % -> % if R has IntegralDomain
from CombinatorialFunctionCategory
factorials: % -> % if R has IntegralDomain
from CombinatorialOpsCategory
factorials: (%, Symbol) -> % if R has IntegralDomain
from CombinatorialOpsCategory
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit and R has IntegralDomain
from PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit and R has IntegralDomain
from PolynomialFactorizationExplicit
freeOf?: (%, %) -> Boolean
from ExpressionSpace
freeOf?: (%, Symbol) -> Boolean
from ExpressionSpace
fresnelC: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
fresnelS: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
Gamma: % -> % if R has IntegralDomain
from SpecialFunctionCategory
Gamma: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
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 FunctionSpace R
ground?: % -> Boolean
from FunctionSpace R
hankelH1: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hankelH2: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
height: % -> NonNegativeInteger
from ExpressionSpace
hermiteH: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
integral: (%, SegmentBinding %) -> % if R has IntegralDomain
from PrimitiveFunctionCategory
integral: (%, Symbol) -> % if R has IntegralDomain
from PrimitiveFunctionCategory
inv: % -> % if R has IntegralDomain or R has Group
from Group
is?: (%, BasicOperator) -> Boolean
from ExpressionSpace
is?: (%, Symbol) -> Boolean
from ExpressionSpace
isExpt: % -> Union(Record(var: Kernel %, exponent: Integer), failed) if R has SemiGroup
from FunctionSpace R
isExpt: (%, BasicOperator) -> Union(Record(var: Kernel %, exponent: Integer), failed) if R has Ring
from FunctionSpace R
isExpt: (%, Symbol) -> Union(Record(var: Kernel %, exponent: Integer), failed) if R has Ring
from FunctionSpace R
isMult: % -> Union(Record(coef: Integer, var: Kernel %), failed) if R has AbelianSemiGroup
from FunctionSpace R
isPlus: % -> Union(List %, failed) if R has AbelianSemiGroup
from FunctionSpace R
isPower: % -> Union(Record(val: %, exponent: Integer), failed) if R has Ring
from FunctionSpace R
isTimes: % -> Union(List %, failed) if R has SemiGroup
from FunctionSpace R
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 ExpressionSpace
kernel: (BasicOperator, List %) -> %
from ExpressionSpace
kernels: % -> List Kernel %
from ExpressionSpace
kernels: List % -> List Kernel %
from ExpressionSpace
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 ExpressionSpace
map: (% -> %, Kernel %) -> %
from ExpressionSpace
meixnerM: (%, %, %, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
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 FunctionSpace R
numerator: % -> % if R has Ring
from FunctionSpace R
one?: % -> Boolean if R has SemiGroup
from MagmaWithUnit
operator: BasicOperator -> BasicOperator
from ExpressionSpace
operators: % -> List BasicOperator
from ExpressionSpace
opposite?: (%, %) -> Boolean if R has AbelianSemiGroup
from AbelianMonoid
paren: % -> %
from ExpressionSpace
paren: List % -> %
from ExpressionSpace
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
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
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 %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if R has LinearlyExplicitOver Integer and R has IntegralDomain 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 % -> Matrix Integer if R has LinearlyExplicitOver Integer and R has IntegralDomain or R has LinearlyExplicitOver Integer and R has Ring
from LinearlyExplicitOver Integer
reducedSystem: Matrix % -> Matrix R if R has Ring
from LinearlyExplicitOver R
rem: (%, %) -> % if R has IntegralDomain
from EuclideanDomain
retract: % -> AlgebraicNumber if R has RetractableTo Integer and R has IntegralDomain
from RetractableTo AlgebraicNumber
retract: % -> Fraction Integer if R has RetractableTo Integer and R has IntegralDomain or R has RetractableTo Fraction Integer
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: % -> R
from RetractableTo R
retract: % -> Symbol
from RetractableTo Symbol
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 Integer and R has IntegralDomain or R has RetractableTo Fraction Integer
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(R, failed)
from RetractableTo 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: (SparseUnivariatePolynomial %, Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedField
rootOf: Polynomial % -> % if R has IntegralDomain
from AlgebraicallyClosedField
rootOf: SparseUnivariatePolynomial % -> % if R has IntegralDomain
from AlgebraicallyClosedField
rootsOf: % -> List % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace R
rootsOf: (%, Symbol) -> List % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace R
rootsOf: (SparseUnivariatePolynomial %, Symbol) -> List % if R has IntegralDomain
from AlgebraicallyClosedField
rootsOf: Polynomial % -> List % if R has IntegralDomain
from AlgebraicallyClosedField
rootsOf: SparseUnivariatePolynomial % -> List % if R has IntegralDomain
from AlgebraicallyClosedField
rootSum: (%, SparseUnivariatePolynomial %, Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedFunctionSpace R
sample: % if R has AbelianSemiGroup or R has SemiGroup
from MagmaWithUnit
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.
Shi: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
Si: % -> % if R has IntegralDomain
from LiouvillianFunctionCategory
simplifyPower: (%, Integer) -> % if R has IntegralDomain
simplifyPower(f, n) is undocumented.
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 PolynomialFactorizationExplicit and R has IntegralDomain
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 PolynomialFactorizationExplicit and R has IntegralDomain
from PolynomialFactorizationExplicit
struveH: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
struveL: (%, %) -> % if R has IntegralDomain
from SpecialFunctionCategory
subst: (%, Equation %) -> %
from ExpressionSpace
subst: (%, List Equation %) -> %
from ExpressionSpace
subst: (%, List Kernel %, List %) -> %
from ExpressionSpace
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 ExpressionSpace
tower: List % -> List Kernel %
from ExpressionSpace
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
univariate: (%, Kernel %) -> Fraction SparseUnivariatePolynomial % if R has IntegralDomain
from FunctionSpace R
variables: % -> List Symbol
from FunctionSpace R
variables: List % -> List Symbol
from FunctionSpace R
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
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: (SparseUnivariatePolynomial %, Symbol) -> % if R has IntegralDomain
from AlgebraicallyClosedField
zeroOf: Polynomial % -> % if R has IntegralDomain
from AlgebraicallyClosedField
zeroOf: SparseUnivariatePolynomial % -> % 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: (SparseUnivariatePolynomial %, Symbol) -> List % if R has IntegralDomain
from AlgebraicallyClosedField
zerosOf: Polynomial % -> List % if R has IntegralDomain
from AlgebraicallyClosedField
zerosOf: SparseUnivariatePolynomial % -> List % if R has IntegralDomain
from AlgebraicallyClosedField

AbelianGroup if R has AbelianGroup

AbelianMonoid if R has AbelianSemiGroup

AbelianSemiGroup if R has AbelianSemiGroup

Algebra % if R has IntegralDomain

Algebra Fraction Integer if R has IntegralDomain

Algebra R if R has CommutativeRing

AlgebraicallyClosedField if R has IntegralDomain

AlgebraicallyClosedFunctionSpace R if R has IntegralDomain

ArcHyperbolicFunctionCategory if R has IntegralDomain

ArcTrigonometricFunctionCategory if R has IntegralDomain

BasicType

BiModule(%, %) if R has Ring

BiModule(Fraction Integer, Fraction Integer) if R has IntegralDomain

BiModule(R, R) if R has CommutativeRing

CancellationAbelianMonoid if R has AbelianGroup

canonicalsClosed if R has IntegralDomain

canonicalUnitNormal if R has IntegralDomain

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleTo OutputForm

CombinatorialFunctionCategory if R has IntegralDomain

CombinatorialOpsCategory if R has IntegralDomain

CommutativeRing if R has IntegralDomain

CommutativeStar if R has IntegralDomain

Comparable

ConvertibleTo InputForm if R has ConvertibleTo InputForm

ConvertibleTo Pattern Float if R has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if R has ConvertibleTo Pattern Integer

DivisionRing if R has IntegralDomain

ElementaryFunctionCategory if R has IntegralDomain

EntireRing if R has IntegralDomain

EuclideanDomain if R has IntegralDomain

Evalable %

ExpressionSpace

Field if R has IntegralDomain

FullyLinearlyExplicitOver R if R has Ring

FullyPatternMatchable R

FullyRetractableTo R

FunctionSpace R

GcdDomain if R has IntegralDomain

Group if R has Group

HyperbolicFunctionCategory if R has IntegralDomain

InnerEvalable(%, %)

InnerEvalable(Kernel %, %)

IntegralDomain if R has IntegralDomain

LeftModule % if R has Ring

LeftModule Fraction Integer if R has IntegralDomain

LeftModule R if R has CommutativeRing

LeftOreRing if R has IntegralDomain

LinearlyExplicitOver Integer if R has LinearlyExplicitOver Integer and R has IntegralDomain or R has LinearlyExplicitOver Integer and R has Ring

LinearlyExplicitOver R if R has Ring

LiouvillianFunctionCategory if R has IntegralDomain

Magma if R has SemiGroup

MagmaWithUnit if R has SemiGroup

Module % if R has IntegralDomain

Module Fraction Integer if R has IntegralDomain

Module R if R has CommutativeRing

Monoid if R has SemiGroup

NonAssociativeRing if R has Ring

NonAssociativeRng if R has Ring

NonAssociativeSemiRing if R has Ring

NonAssociativeSemiRng if R has Ring

noZeroDivisors if R has IntegralDomain

PartialDifferentialRing Symbol if R has Ring

Patternable R

PatternMatchable Float if R has PatternMatchable Float

PatternMatchable Integer if R has PatternMatchable Integer

PolynomialFactorizationExplicit if R has PolynomialFactorizationExplicit and R has IntegralDomain

PrimitiveFunctionCategory if R has IntegralDomain

PrincipalIdealDomain if R has IntegralDomain

RadicalCategory if R has IntegralDomain

RetractableTo AlgebraicNumber if R has RetractableTo Integer and R has IntegralDomain

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer or R has RetractableTo Integer and R has IntegralDomain

RetractableTo Fraction Polynomial R if R has IntegralDomain

RetractableTo Integer if R has RetractableTo Integer

RetractableTo Kernel %

RetractableTo Polynomial R if R has Ring

RetractableTo R

RetractableTo Symbol

RightModule % if R has Ring

RightModule Fraction Integer if R has IntegralDomain

RightModule R if R has CommutativeRing

Ring if R has Ring

Rng if R has Ring

SemiGroup if R has SemiGroup

SemiRing if R has Ring

SemiRng if R has Ring

SetCategory

SpecialFunctionCategory if R has IntegralDomain

TranscendentalFunctionCategory if R has IntegralDomain

TrigonometricFunctionCategory if R has IntegralDomain

UniqueFactorizationDomain if R has IntegralDomain

unitsKnown if R has Ring or R has Group