SparseMultivariatePolynomialExpressions R

ssolve.spad line 22 [edit on github]

• R: Ring

undocumented

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> % if R has Algebra Fraction Integer

from RightModule Fraction Integer

*: (%, Integer) -> % if R has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, R) -> %

from RightModule R

*: (Fraction Integer, %) -> % if R has Algebra Fraction Integer

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, R) -> % if R has Field

from AbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % if R has TranscendentalFunctionCategory

from ElementaryFunctionCategory

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

acos: % -> % if R has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acosh: % -> % if R has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acot: % -> % if R has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acoth: % -> % if R has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acsc: % -> % if R has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acsch: % -> % if R has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

asec: % -> % if R has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asech: % -> % if R has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

asin: % -> % if R has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asinh: % -> % if R has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean if R has EntireRing

from EntireRing

associator: (%, %, %) -> %

from NonAssociativeRng

atan: % -> % if R has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

atanh: % -> % if R has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

binomThmExpt: (%, %, NonNegativeInteger) -> % if % has CommutativeRing

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

charthRoot: % -> Union(%, failed) if % has CharacteristicNonZero and R has PolynomialFactorizationExplicit or R has CharacteristicNonZero

from PolynomialFactorizationExplicit

coefficient: (%, IndexedExponents NonNegativeInteger) -> R

from AbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

coefficient: (%, List NonNegativeInteger, List NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

coefficient: (%, NonNegativeInteger, NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

coefficients: % -> List R

from FreeModuleCategory(R, IndexedExponents NonNegativeInteger)

coerce: % -> % if R has CommutativeRing

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

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

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: NonNegativeInteger -> %

from CoercibleFrom NonNegativeInteger

coerce: R -> %

from Algebra R

commutator: (%, %) -> %

from NonAssociativeRng

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

from PolynomialFactorizationExplicit

construct: List Record(k: IndexedExponents NonNegativeInteger, c: R) -> %

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

constructOrdered: List Record(k: IndexedExponents NonNegativeInteger, c: R) -> %

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

content: % -> R if R has GcdDomain

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

content: (%, NonNegativeInteger) -> % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

convert: % -> InputForm if R has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float if R has ConvertibleTo Pattern Float and NonNegativeInteger has ConvertibleTo Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if R has ConvertibleTo Pattern Integer and NonNegativeInteger has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

cos: % -> % if R has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

cosh: % -> % if R has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

cot: % -> % if R has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

coth: % -> % if R has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

csc: % -> % if R has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

csch: % -> % if R has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

D: (%, List NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

D: (%, List NonNegativeInteger, List NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

D: (%, NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

D: (%, NonNegativeInteger, NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

degree: % -> IndexedExponents NonNegativeInteger

from AbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

degree: (%, List NonNegativeInteger) -> List NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

degree: (%, NonNegativeInteger) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

differentiate: (%, List NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

differentiate: (%, List NonNegativeInteger, List NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

differentiate: (%, NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

differentiate: (%, NonNegativeInteger, NonNegativeInteger) -> %

from PartialDifferentialRing NonNegativeInteger

discriminant: (%, NonNegativeInteger) -> % if R has CommutativeRing

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

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

from InnerEvalable(%, %)

eval: (%, Equation %) -> %

from Evalable %

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

from InnerEvalable(%, %)

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

from Evalable %

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

from InnerEvalable(NonNegativeInteger, %)

eval: (%, List NonNegativeInteger, List R) -> %

from InnerEvalable(NonNegativeInteger, R)

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

from InnerEvalable(NonNegativeInteger, %)

eval: (%, NonNegativeInteger, R) -> %

from InnerEvalable(NonNegativeInteger, R)

exp: % -> % if R has TranscendentalFunctionCategory

from ElementaryFunctionCategory

exquo: (%, %) -> Union(%, failed) if R has EntireRing

from EntireRing

exquo: (%, R) -> Union(%, failed) if R has EntireRing

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

factor: % -> Factored % if R has PolynomialFactorizationExplicit

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

fmecg: (%, IndexedExponents NonNegativeInteger, R, %) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

gcd: (%, %) -> % if R has GcdDomain

from GcdDomain

gcd: List % -> % if R has GcdDomain

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GcdDomain

from PolynomialFactorizationExplicit

ground?: % -> Boolean

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

ground: % -> R

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

hash: % -> SingleInteger if R has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if R has Hashable

from Hashable

isExpt: % -> Union(Record(var: NonNegativeInteger, exponent: NonNegativeInteger), failed)

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

isPlus: % -> Union(List %, failed)

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

isTimes: % -> Union(List %, failed)

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

latex: % -> String

from SetCategory

lcm: (%, %) -> % if R has GcdDomain

from GcdDomain

lcm: List % -> % if R has GcdDomain

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if R has GcdDomain

from LeftOreRing

leadingCoefficient: % -> R

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

leadingMonomial: % -> %

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

leadingSupport: % -> IndexedExponents NonNegativeInteger

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

leadingTerm: % -> Record(k: IndexedExponents NonNegativeInteger, c: R)

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

linearExtend: (IndexedExponents NonNegativeInteger -> R, %) -> R if R has CommutativeRing

from FreeModuleCategory(R, IndexedExponents NonNegativeInteger)

listOfTerms: % -> List Record(k: IndexedExponents NonNegativeInteger, c: R)

from IndexedDirectProductCategory(R, IndexedExponents NonNegativeInteger)

log: % -> % if R has TranscendentalFunctionCategory

from ElementaryFunctionCategory

mainVariable: % -> Union(NonNegativeInteger, failed)

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

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

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

mapExponents: (IndexedExponents NonNegativeInteger -> IndexedExponents NonNegativeInteger, %) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

minimumDegree: % -> IndexedExponents NonNegativeInteger

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

minimumDegree: (%, List NonNegativeInteger) -> List NonNegativeInteger

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

minimumDegree: (%, NonNegativeInteger) -> NonNegativeInteger

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

monicDivide: (%, %, NonNegativeInteger) -> Record(quotient: %, remainder: %)

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

monomial?: % -> Boolean

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

monomial: (%, List NonNegativeInteger, List NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

monomial: (%, NonNegativeInteger, NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

monomial: (R, IndexedExponents NonNegativeInteger) -> %

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

monomials: % -> List %

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

multivariate: (SparseUnivariatePolynomial %, NonNegativeInteger) -> %

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

multivariate: (SparseUnivariatePolynomial R, NonNegativeInteger) -> %

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(R, IndexedExponents NonNegativeInteger)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if R has PatternMatchable Float and NonNegativeInteger has PatternMatchable Float

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if R has PatternMatchable Integer and NonNegativeInteger has PatternMatchable Integer

from PatternMatchable Integer

pi: () -> % if R has TranscendentalFunctionCategory

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> % if R has Algebra Fraction Integer or R has CommutativeRing

from NonAssociativeAlgebra %

pomopo!: (%, R, IndexedExponents NonNegativeInteger, %) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

prime?: % -> Boolean if R has PolynomialFactorizationExplicit

from UniqueFactorizationDomain

primitiveMonomials: % -> List %

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

primitivePart: % -> % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

primitivePart: (%, NonNegativeInteger) -> % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if R has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix R, vec: Vector R)

from LinearlyExplicitOver R

reducedSystem: Matrix % -> Matrix Integer if R has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix R

from LinearlyExplicitOver R

reductum: % -> %

from IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

resultant: (%, %, NonNegativeInteger) -> % if R has CommutativeRing

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

retract: % -> Fraction Integer if R has RetractableTo Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer if R has RetractableTo Integer

from RetractableTo Integer

retract: % -> NonNegativeInteger

from RetractableTo NonNegativeInteger

retract: % -> R

from RetractableTo R

retractIfCan: % -> Union(Fraction Integer, failed) if R has RetractableTo Fraction Integer

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed) if R has RetractableTo Integer

from RetractableTo Integer

retractIfCan: % -> Union(NonNegativeInteger, failed)

from RetractableTo NonNegativeInteger

retractIfCan: % -> Union(R, failed)

from RetractableTo R

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if R has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sech: % -> % if R has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

sin: % -> % if R has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sinh: % -> % if R has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

smaller?: (%, %) -> Boolean if R has Comparable

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if R has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

squareFree: % -> Factored % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

squareFreePart: % -> % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

support: % -> List IndexedExponents NonNegativeInteger

from FreeModuleCategory(R, IndexedExponents NonNegativeInteger)

tan: % -> % if R has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

tanh: % -> % if R has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

totalDegree: % -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

totalDegree: (%, List NonNegativeInteger) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

totalDegreeSorted: (%, List NonNegativeInteger) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

unit?: % -> Boolean if R has EntireRing

from EntireRing

unitCanonical: % -> % if R has EntireRing

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %) if R has EntireRing

from EntireRing

univariate: % -> SparseUnivariatePolynomial R

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

univariate: (%, NonNegativeInteger) -> SparseUnivariatePolynomial %

from PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

variables: % -> List NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

AbelianProductCategory R

AbelianSemiGroup

Algebra % if R has CommutativeRing

Algebra Fraction Integer if R has Algebra Fraction Integer

Algebra R if R has CommutativeRing

ArcHyperbolicFunctionCategory if R has TranscendentalFunctionCategory

ArcTrigonometricFunctionCategory if R has TranscendentalFunctionCategory

BasicType

BiModule(%, %)

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

BiModule(R, R)

CancellationAbelianMonoid

canonicalUnitNormal if R has canonicalUnitNormal

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleFrom Fraction Integer if R has RetractableTo Fraction Integer

CoercibleFrom Integer if R has RetractableTo Integer

CoercibleFrom NonNegativeInteger

CoercibleFrom R

CoercibleTo OutputForm

CommutativeRing if R has CommutativeRing

CommutativeStar if R has CommutativeRing

Comparable if R has Comparable

ConvertibleTo InputForm if R has ConvertibleTo InputForm

ConvertibleTo Pattern Float if R has ConvertibleTo Pattern Float and NonNegativeInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if R has ConvertibleTo Pattern Integer and NonNegativeInteger has ConvertibleTo Pattern Integer

ElementaryFunctionCategory if R has TranscendentalFunctionCategory

EntireRing if R has EntireRing

Evalable %

FiniteAbelianMonoidRing(R, IndexedExponents NonNegativeInteger)

FreeModuleCategory(R, IndexedExponents NonNegativeInteger)

FullyLinearlyExplicitOver R

FullyRetractableTo R

GcdDomain if R has GcdDomain

Hashable if R has Hashable

HyperbolicFunctionCategory if R has TranscendentalFunctionCategory

IndexedDirectProductCategory(R, IndexedExponents NonNegativeInteger)

IndexedProductCategory(R, IndexedExponents NonNegativeInteger)

InnerEvalable(%, %)

InnerEvalable(NonNegativeInteger, %)

InnerEvalable(NonNegativeInteger, R)

IntegralDomain if R has IntegralDomain

LeftModule %

LeftModule Fraction Integer if R has Algebra Fraction Integer

LeftModule R

LeftOreRing if R has GcdDomain

LinearlyExplicitOver Integer if R has LinearlyExplicitOver Integer

LinearlyExplicitOver R

Magma

MagmaWithUnit

MaybeSkewPolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

Module % if R has CommutativeRing

Module Fraction Integer if R has Algebra Fraction Integer

Module R if R has CommutativeRing

Monoid

NonAssociativeAlgebra % if R has CommutativeRing

NonAssociativeAlgebra Fraction Integer if R has Algebra Fraction Integer

NonAssociativeAlgebra R if R has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has EntireRing

PartialDifferentialRing NonNegativeInteger

PatternMatchable Float if R has PatternMatchable Float and NonNegativeInteger has PatternMatchable Float

PatternMatchable Integer if R has PatternMatchable Integer and NonNegativeInteger has PatternMatchable Integer

PolynomialCategory(R, IndexedExponents NonNegativeInteger, NonNegativeInteger)

PolynomialFactorizationExplicit if R has PolynomialFactorizationExplicit

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer

RetractableTo NonNegativeInteger

RetractableTo R

RightModule %

RightModule Fraction Integer if R has Algebra Fraction Integer

RightModule Integer if R has LinearlyExplicitOver Integer

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory if R has TranscendentalFunctionCategory

TrigonometricFunctionCategory if R has TranscendentalFunctionCategory

TwoSidedRecip if R has CommutativeRing

UniqueFactorizationDomain if R has PolynomialFactorizationExplicit

unitsKnown

VariablesCommuteWithCoefficients