# Expression RΒΆ

Expressions involving symbolic functions.

0: % if R has AbelianSemiGroup

from AbelianMonoid

1: % if R has SemiGroup

from MagmaWithUnit

*: (%, %) -> % if R has SemiGroup

from LeftModule %

*: (%, Fraction Integer) -> % if R has IntegralDomain
*: (%, Integer) -> % if R has IntegralDomain and R has LinearlyExplicitOver Integer or R has LinearlyExplicitOver Integer and R has Ring
*: (%, R) -> % if R has Ring

from RightModule R

*: (Fraction Integer, %) -> % if R has IntegralDomain
*: (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 Group or R has IntegralDomain

from Field

/: (SparseMultivariatePolynomial(R, Kernel %), SparseMultivariatePolynomial(R, Kernel %)) -> % if R has IntegralDomain

from FunctionSpace R

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % if R has IntegralDomain
^: (%, Fraction Integer) -> % if R has IntegralDomain

^: (%, Integer) -> % if R has Group or R has IntegralDomain

from DivisionRing

^: (%, NonNegativeInteger) -> % if R has SemiGroup

from MagmaWithUnit

^: (%, PositiveInteger) -> % if R has SemiGroup

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if R has IntegralDomain
acos: % -> % if R has IntegralDomain
acosh: % -> % if R has IntegralDomain
acot: % -> % if R has IntegralDomain
acoth: % -> % if R has IntegralDomain
acsc: % -> % if R has IntegralDomain
acsch: % -> % if R has IntegralDomain
airyAi: % -> % if R has IntegralDomain
airyAiPrime: % -> % if R has IntegralDomain
airyBi: % -> % if R has IntegralDomain
airyBiPrime: % -> % if R has IntegralDomain
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
annihilate?: (%, %) -> Boolean if R has Ring

from Rng

antiCommutator: (%, %) -> % if R has Ring
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
asech: % -> % if R has IntegralDomain
asin: % -> % if R has IntegralDomain
asinh: % -> % if R has IntegralDomain
associates?: (%, %) -> Boolean if R has IntegralDomain

from EntireRing

associator: (%, %, %) -> % if R has Ring
atan: % -> % if R has IntegralDomain
atanh: % -> % if R has IntegralDomain
belong?: BasicOperator -> Boolean

from ExpressionSpace

besselI: (%, %) -> % if R has IntegralDomain
besselJ: (%, %) -> % if R has IntegralDomain
besselK: (%, %) -> % if R has IntegralDomain
besselY: (%, %) -> % if R has IntegralDomain
Beta: (%, %) -> % if R has IntegralDomain
Beta: (%, %, %) -> % if R has IntegralDomain
binomial: (%, %) -> % if R has IntegralDomain
box: % -> %

from ExpressionSpace

ceiling: % -> % if R has IntegralDomain
characteristic: () -> NonNegativeInteger if R has Ring
charlierC: (%, %, %) -> % if R has IntegralDomain
charthRoot: % -> Union(%, failed) if R has IntegralDomain and % has CharacteristicNonZero and R has PolynomialFactorizationExplicit or R has CharacteristicNonZero
Chi: % -> % if R has IntegralDomain
Ci: % -> % if R has IntegralDomain
coerce: % -> % if R has IntegralDomain

from Algebra %

coerce: % -> OutputForm
coerce: AlgebraicNumber -> % if R has IntegralDomain and R has RetractableTo Integer
coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer or R has IntegralDomain
coerce: Fraction Polynomial Fraction R -> % if R has IntegralDomain

from FunctionSpace R

coerce: Fraction Polynomial R -> % if R has IntegralDomain
coerce: Fraction R -> % if R has IntegralDomain

from FunctionSpace R

coerce: Integer -> % if R has RetractableTo Integer or R has Ring
coerce: Kernel % -> %

from CoercibleFrom Kernel %

coerce: Polynomial Fraction R -> % if R has IntegralDomain

from FunctionSpace R

coerce: Polynomial R -> % if R has Ring
coerce: R -> %

from CoercibleFrom R

coerce: SparseMultivariatePolynomial(R, Kernel %) -> % if R has Ring

from FunctionSpace R

coerce: Symbol -> %
commutator: (%, %) -> % if R has Ring or R has Group
conditionP: Matrix % -> Union(Vector %, failed) if R has IntegralDomain and % has CharacteristicNonZero and R has PolynomialFactorizationExplicit
conjugate: % -> % if R has IntegralDomain
conjugate: (%, %) -> % if R has Group

from Group

convert: % -> InputForm if R has ConvertibleTo InputForm
convert: % -> Pattern Float if R has ConvertibleTo Pattern Float
convert: % -> Pattern Integer if R has ConvertibleTo Pattern Integer
convert: Factored % -> % if R has IntegralDomain

from FunctionSpace R

cos: % -> % if R has IntegralDomain
cosh: % -> % if R has IntegralDomain
cot: % -> % if R has IntegralDomain
coth: % -> % if R has IntegralDomain
csc: % -> % if R has IntegralDomain
csch: % -> % if R has IntegralDomain
D: (%, List Symbol) -> % if R has Ring
D: (%, List Symbol, List NonNegativeInteger) -> % if R has Ring
D: (%, Symbol) -> % if R has Ring
D: (%, Symbol, NonNegativeInteger) -> % if R has Ring
definingPolynomial: % -> % if % has Ring

from ExpressionSpace

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
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if R has Ring
differentiate: (%, Symbol) -> % if R has Ring
differentiate: (%, Symbol, NonNegativeInteger) -> % if R has Ring
digamma: % -> % if R has IntegralDomain
dilog: % -> % if R has IntegralDomain
diracDelta: % -> % if R has IntegralDomain
distribute: % -> %

from ExpressionSpace

distribute: (%, %) -> %

from ExpressionSpace

divide: (%, %) -> Record(quotient: %, remainder: %) if R has IntegralDomain

from EuclideanDomain

Ei: % -> % if R has IntegralDomain
ellipticE: % -> % if R has IntegralDomain
ellipticE: (%, %) -> % if R has IntegralDomain
ellipticF: (%, %) -> % if R has IntegralDomain
ellipticK: % -> % if R has IntegralDomain
ellipticPi: (%, %, %) -> % if R has IntegralDomain
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
erfi: % -> % if R has IntegralDomain
euclideanSize: % -> NonNegativeInteger if R has IntegralDomain

from EuclideanDomain

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 %, Symbol) -> % if R has ConvertibleTo InputForm

from FunctionSpace R

eval: (%, List BasicOperator, List(% -> %)) -> %

from ExpressionSpace

eval: (%, List BasicOperator, List(List % -> %)) -> %

from ExpressionSpace

eval: (%, List Equation %) -> %

from Evalable %

eval: (%, List Kernel %, List %) -> %

from InnerEvalable(Kernel %, %)

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: (%, List Symbol, List(% -> %)) -> %

from ExpressionSpace

eval: (%, List Symbol, List(List % -> %)) -> %

from ExpressionSpace

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

even?: % -> Boolean if % has RetractableTo Integer

from ExpressionSpace

exp: % -> % if R has IntegralDomain
expressIdealMember: (List %, %) -> Union(List %, failed) if R has IntegralDomain
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
factorial: % -> % if R has IntegralDomain
factorials: % -> % if R has IntegralDomain
factorials: (%, Symbol) -> % if R has IntegralDomain
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has IntegralDomain and R has PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has IntegralDomain and R has PolynomialFactorizationExplicit
floor: % -> % if R has IntegralDomain
fractionPart: % -> % if R has IntegralDomain
freeOf?: (%, %) -> Boolean

from ExpressionSpace

freeOf?: (%, Symbol) -> Boolean

from ExpressionSpace

fresnelC: % -> % if R has IntegralDomain
fresnelS: % -> % if R has IntegralDomain
Gamma: % -> % if R has IntegralDomain
Gamma: (%, %) -> % if R has IntegralDomain
gcd: (%, %) -> % if R has IntegralDomain

from GcdDomain

gcd: List % -> % if R has IntegralDomain

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has IntegralDomain
getSimplifyDenomsFlag: () -> Boolean if R has IntegralDomain

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

ground?: % -> Boolean

from FunctionSpace R

ground: % -> R

from FunctionSpace R

hankelH1: (%, %) -> % if R has IntegralDomain
hankelH2: (%, %) -> % if R has IntegralDomain
height: % -> NonNegativeInteger

from ExpressionSpace

hermiteH: (%, %) -> % if R has IntegralDomain
hypergeometricF: (List %, List %, %) -> % if R has IntegralDomain and % has RetractableTo Integer
integral: (%, SegmentBinding %) -> % if R has IntegralDomain
integral: (%, Symbol) -> % if R has IntegralDomain
inv: % -> % if R has Group or R has IntegralDomain

from DivisionRing

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
jacobiDn: (%, %) -> % if R has IntegralDomain
jacobiP: (%, %, %, %) -> % if R has IntegralDomain
jacobiSn: (%, %) -> % if R has IntegralDomain
jacobiTheta: (%, %) -> % if R has IntegralDomain
jacobiZeta: (%, %) -> % if R has IntegralDomain
kelvinBei: (%, %) -> % if R has IntegralDomain
kelvinBer: (%, %) -> % if R has IntegralDomain
kelvinKei: (%, %) -> % if R has IntegralDomain
kelvinKer: (%, %) -> % if R has IntegralDomain
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
kummerU: (%, %, %) -> % if R has IntegralDomain
laguerreL: (%, %, %) -> % if R has IntegralDomain
lambertW: % -> % if R has IntegralDomain
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
legendreQ: (%, %, %) -> % if R has IntegralDomain
lerchPhi: (%, %, %) -> % if R has IntegralDomain
li: % -> % if R has IntegralDomain
log: % -> % if R has IntegralDomain
lommelS1: (%, %, %) -> % if R has IntegralDomain
lommelS2: (%, %, %) -> % if R has IntegralDomain
mainKernel: % -> Union(Kernel %, failed)

from ExpressionSpace

map: (% -> %, Kernel %) -> %

from ExpressionSpace

meijerG: (List %, List %, List %, List %, %) -> % if R has IntegralDomain and % has RetractableTo Integer
meixnerM: (%, %, %, %) -> % if R has IntegralDomain
minPoly: Kernel % -> SparseUnivariatePolynomial % if % has Ring

from ExpressionSpace

multiEuclidean: (List %, %) -> Union(List %, failed) if R has IntegralDomain

from EuclideanDomain

nthRoot: (%, Integer) -> % if R has IntegralDomain

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

odd?: % -> Boolean if % has RetractableTo Integer

from ExpressionSpace

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

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if R has PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if R has PatternMatchable Integer
permutation: (%, %) -> % if R has IntegralDomain
pi: () -> % if R has IntegralDomain
plenaryPower: (%, PositiveInteger) -> % if R has CommutativeRing
polygamma: (%, %) -> % if R has IntegralDomain
polylog: (%, %) -> % if R has IntegralDomain
prime?: % -> Boolean if R has IntegralDomain
principalIdeal: List % -> Record(coef: List %, generator: %) if R has IntegralDomain
product: (%, SegmentBinding %) -> % if R has IntegralDomain
product: (%, Symbol) -> % if R has IntegralDomain
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 IntegralDomain and R has LinearlyExplicitOver Integer or R has LinearlyExplicitOver Integer and R has Ring
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix R, vec: Vector 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
reducedSystem: Matrix % -> Matrix R if R has Ring

from LinearlyExplicitOver R

rem: (%, %) -> % if R has IntegralDomain

from EuclideanDomain

retract: % -> AlgebraicNumber if R has IntegralDomain and R has RetractableTo Integer
retract: % -> Fraction Integer if R has IntegralDomain and R has RetractableTo Integer or R has RetractableTo Fraction Integer
retract: % -> Fraction Polynomial R if R has IntegralDomain
retract: % -> Integer if R has RetractableTo Integer
retract: % -> Kernel %

from RetractableTo Kernel %

retract: % -> Polynomial R if R has Ring
retract: % -> R

from RetractableTo R

retract: % -> Symbol
retractIfCan: % -> Union(AlgebraicNumber, failed) if R has IntegralDomain and R has RetractableTo Integer
retractIfCan: % -> Union(Fraction Integer, failed) if R has IntegralDomain and R has RetractableTo Integer or R has RetractableTo Fraction Integer
retractIfCan: % -> Union(Fraction Polynomial R, failed) if R has IntegralDomain
retractIfCan: % -> Union(Integer, failed) if R has RetractableTo Integer
retractIfCan: % -> Union(Kernel %, failed)

from RetractableTo Kernel %

retractIfCan: % -> Union(Polynomial R, failed) if R has Ring
retractIfCan: % -> Union(R, failed)

from RetractableTo R

retractIfCan: % -> Union(Symbol, failed)
riemannZeta: % -> % if R has IntegralDomain
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
rootOf: (%, Symbol) -> % if R has IntegralDomain
rootOf: (SparseUnivariatePolynomial %, Symbol) -> % if R has IntegralDomain
rootOf: Polynomial % -> % if R has IntegralDomain
rootOf: SparseUnivariatePolynomial % -> % if R has IntegralDomain
rootsOf: % -> List % if R has IntegralDomain
rootsOf: (%, Symbol) -> List % if R has IntegralDomain
rootsOf: (SparseUnivariatePolynomial %, Symbol) -> List % if R has IntegralDomain
rootsOf: Polynomial % -> List % if R has IntegralDomain
rootsOf: SparseUnivariatePolynomial % -> List % if R has IntegralDomain
rootSum: (%, SparseUnivariatePolynomial %, Symbol) -> % if R has IntegralDomain
sample: % if R has SemiGroup or R has AbelianSemiGroup

from AbelianMonoid

sec: % -> % if R has IntegralDomain
sech: % -> % if R has IntegralDomain
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
Si: % -> % if R has IntegralDomain
sign: % -> % if R has IntegralDomain
sin: % -> % if R has IntegralDomain
sinh: % -> % if R has IntegralDomain
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
sqrt: % -> % if R has IntegralDomain

squareFree: % -> Factored % if R has IntegralDomain
squareFreePart: % -> % if R has IntegralDomain
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has IntegralDomain and R has PolynomialFactorizationExplicit
struveH: (%, %) -> % if R has IntegralDomain
struveL: (%, %) -> % if R has IntegralDomain
subst: (%, Equation %) -> %

from ExpressionSpace

subst: (%, List Equation %) -> %

from ExpressionSpace

subst: (%, List Kernel %, List %) -> %

from ExpressionSpace

subtractIfCan: (%, %) -> Union(%, failed) if R has AbelianGroup
summation: (%, SegmentBinding %) -> % if R has IntegralDomain
summation: (%, Symbol) -> % if R has IntegralDomain
tan: % -> % if R has IntegralDomain
tanh: % -> % if R has IntegralDomain
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

unitStep: % -> % if R has IntegralDomain
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
weierstrassP: (%, %, %) -> % if R has IntegralDomain
weierstrassPInverse: (%, %, %) -> % if R has IntegralDomain
weierstrassPPrime: (%, %, %) -> % if R has IntegralDomain
weierstrassSigma: (%, %, %) -> % if R has IntegralDomain
weierstrassZeta: (%, %, %) -> % if R has IntegralDomain
whittakerM: (%, %, %) -> % if R has IntegralDomain
whittakerW: (%, %, %) -> % if R has IntegralDomain
zero?: % -> Boolean if R has AbelianSemiGroup

from AbelianMonoid

zeroOf: % -> % if R has IntegralDomain
zeroOf: (%, Symbol) -> % if R has IntegralDomain
zeroOf: (SparseUnivariatePolynomial %, Symbol) -> % if R has IntegralDomain
zeroOf: Polynomial % -> % if R has IntegralDomain
zeroOf: SparseUnivariatePolynomial % -> % if R has IntegralDomain
zerosOf: % -> List % if R has IntegralDomain
zerosOf: (%, Symbol) -> List % if R has IntegralDomain
zerosOf: (SparseUnivariatePolynomial %, Symbol) -> List % if R has IntegralDomain
zerosOf: Polynomial % -> List % if R has IntegralDomain
zerosOf: SparseUnivariatePolynomial % -> List % if R has IntegralDomain

AbelianGroup if R has AbelianGroup

AbelianMonoid if R has AbelianSemiGroup

AbelianSemiGroup if R has AbelianSemiGroup

Algebra % if R has IntegralDomain

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %) if R has Ring

BiModule(R, R) if R has CommutativeRing

canonicalsClosed if R has IntegralDomain

CoercibleFrom AlgebraicNumber if R has IntegralDomain and R has RetractableTo Integer

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

CoercibleFrom Polynomial R if R has Ring

CommutativeRing if R has IntegralDomain

CommutativeStar if R has IntegralDomain

Comparable

DivisionRing if R has IntegralDomain

EntireRing if R has IntegralDomain

EuclideanDomain if R has IntegralDomain

ExpressionSpace

Field if R has IntegralDomain

FullyLinearlyExplicitOver R if R has Ring

GcdDomain if R has IntegralDomain

Group if R has Group

InnerEvalable(%, %)

InnerEvalable(Kernel %, %)

IntegralDomain if R has IntegralDomain

LeftModule % if R has Ring

LeftModule R if R has CommutativeRing

LeftOreRing if R has IntegralDomain

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

LinearlyExplicitOver R if R has Ring

Magma if R has SemiGroup

MagmaWithUnit if R has SemiGroup

Module % if R has IntegralDomain

Module R if R has CommutativeRing

Monoid if R has SemiGroup

NonAssociativeAlgebra % if R has IntegralDomain

NonAssociativeAlgebra R if R has CommutativeRing

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

RetractableTo AlgebraicNumber if R has IntegralDomain and R has RetractableTo Integer

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

RetractableTo Polynomial R if R has Ring

RightModule % if R has Ring

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

RightModule R if R has Ring

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

TwoSidedRecip if R has Group or R has IntegralDomain

unitsKnown if R has Ring or R has Group