Expression R

expr.spad line 1 [edit on github]

• R: Comparable

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

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

from RightModule Integer

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

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 Group or R has IntegralDomain

from Group

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

from FunctionSpace2(R, Kernel %)

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % 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

~=: (%, %) -> 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 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

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

from SpecialFunctionCategory

Beta: (%, %, %) -> % 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 PolynomialFactorizationExplicit and R has IntegralDomain or R has CharacteristicNonZero

from PolynomialFactorizationExplicit

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 CoercibleFrom AlgebraicNumber

coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer or R has IntegralDomain

from CoercibleFrom Fraction Integer

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

from FunctionSpace2(R, Kernel %)

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

from CoercibleFrom Fraction Polynomial R

coerce: Fraction R -> % if R has IntegralDomain

from FunctionSpace2(R, Kernel %)

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

from NonAssociativeRing

coerce: Kernel % -> %

from CoercibleFrom Kernel %

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

from FunctionSpace2(R, Kernel %)

coerce: Polynomial R -> % if R has Ring

from CoercibleFrom Polynomial R

coerce: R -> %

from Algebra R

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

from FunctionSpace2(R, Kernel %)

coerce: Symbol -> %

from CoercibleFrom Symbol

commutator: (%, %) -> % if R has Group or R has Ring

from NonAssociativeRng

conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and R has PolynomialFactorizationExplicit and R has IntegralDomain

from PolynomialFactorizationExplicit

conjugate: % -> % if R has IntegralDomain

from SpecialFunctionCategory

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 FunctionSpace2(R, Kernel %)

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

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

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 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, % -> %) -> %

from ExpressionSpace2 Kernel %

eval: (%, BasicOperator, %, Symbol) -> % if R has ConvertibleTo InputForm

from FunctionSpace2(R, Kernel %)

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

from ExpressionSpace2 Kernel %

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

from ExpressionSpace2 Kernel %

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

from Evalable %

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

from InnerEvalable(Kernel %, %)

eval: (%, List Symbol, List NonNegativeInteger, List(% -> %)) -> % if R has Ring

from FunctionSpace2(R, Kernel %)

eval: (%, List Symbol, List NonNegativeInteger, List(List % -> %)) -> % if R has Ring

from FunctionSpace2(R, Kernel %)

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

from ExpressionSpace2 Kernel %

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

from ExpressionSpace2 Kernel %

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

from ExpressionSpace2 Kernel %

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

from ExpressionSpace2 Kernel %

eval: (%, Symbol, NonNegativeInteger, % -> %) -> % if R has Ring

from FunctionSpace2(R, Kernel %)

eval: (%, Symbol, NonNegativeInteger, 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

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

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

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 PolynomialFactorizationExplicit

getSimplifyDenomsFlag: () -> Boolean if R has IntegralDomain

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

ground?: % -> Boolean

from FunctionSpace2(R, Kernel %)

ground: % -> R

from FunctionSpace2(R, Kernel %)

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

hahnS: (%, %, %, %, %) -> % 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: (% -> %, 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 %

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 %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if R has IntegralDomain and R has LinearlyExplicitOver Integer or R has Ring and R has LinearlyExplicitOver Integer

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

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 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: % -> 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 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(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 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.

Shi: % -> % if R has IntegralDomain

from LiouvillianFunctionCategory

Si: % -> % if R has IntegralDomain

from LiouvillianFunctionCategory

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 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 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: (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

CoercibleFrom AlgebraicNumber if R has RetractableTo Integer and R has IntegralDomain

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

CoercibleFrom Fraction Polynomial R if R has IntegralDomain

CoercibleFrom Integer if R has RetractableTo Integer

CoercibleFrom Kernel %

CoercibleFrom Polynomial R if R has Ring

CoercibleFrom R

CoercibleFrom Symbol

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

ExpressionSpace2 Kernel %

Field if R has IntegralDomain

FullyLinearlyExplicitOver R if R has Ring

FullyPatternMatchable R

FullyRetractableTo R

FunctionSpace R

FunctionSpace2(R, Kernel %)

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

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

NonAssociativeAlgebra % if R has IntegralDomain

NonAssociativeAlgebra Fraction Integer 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

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 Integer and R has IntegralDomain or R has RetractableTo Fraction Integer

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

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

SpecialFunctionCategory if R has IntegralDomain

TranscendentalFunctionCategory if R has IntegralDomain

TrigonometricFunctionCategory if R has IntegralDomain

TwoSidedRecip if R has Group or R has IntegralDomain

UniqueFactorizationDomain if R has IntegralDomain

unitsKnown if R has Group or R has Ring