SparseMultivariatePolynomialExpressions(R)

ssolve.spad line 22 [edit on github]

undocumented

* : (%, %) -> %
from Magma
* : (%, R) -> %
from RightModule(R)
* : (%, Fraction(Integer)) -> % if R has Algebra(Fraction(Integer))
from RightModule(Fraction(Integer))
* : (%, Integer) -> % if R has LinearlyExplicitOver(Integer)
from RightModule(Integer)
* : (R, %) -> %
from LeftModule(R)
* : (Fraction(Integer), %) -> % if R has Algebra(Fraction(Integer))
from LeftModule(Fraction(Integer))
* : (Integer, %) -> %
from AbelianGroup
* : (NonNegativeInteger, %) -> %
from AbelianMonoid
* : (PositiveInteger, %) -> %
from AbelianSemiGroup
+ : (%, %) -> %
from AbelianSemiGroup
- : % -> %
from AbelianGroup
- : (%, %) -> %
from AbelianGroup
/ : (%, R) -> % if R has Field
from AbelianMonoidRing(R, IndexedExponents(NonNegativeInteger))
0 : () -> %
from AbelianMonoid
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
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)
^ : (%, %) -> % if R has TranscendentalFunctionCategory
from ElementaryFunctionCategory
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
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 : (%, List(NonNegativeInteger), List(NonNegativeInteger)) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
coefficient : (%, NonNegativeInteger, NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
coefficient : (%, IndexedExponents(NonNegativeInteger)) -> R
from AbelianMonoidRing(R, IndexedExponents(NonNegativeInteger))
coefficients : % -> List(R)
from FreeModuleCategory(R, IndexedExponents(NonNegativeInteger))
coerce : % -> % if R has CommutativeRing
from Algebra(%)
coerce : R -> %
from Algebra(R)
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 : % -> OutputForm
from CoercibleTo(OutputForm)
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 : (%, NonNegativeInteger) -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
content : % -> R if R has GcdDomain
from FiniteAbelianMonoidRing(R, IndexedExponents(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
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 : % -> R
from FiniteAbelianMonoidRing(R, IndexedExponents(NonNegativeInteger))
ground? : % -> Boolean
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 : (Mapping(R, IndexedExponents(NonNegativeInteger)), %) -> 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 : (Mapping(R, R), %) -> %
from IndexedProductCategory(R, IndexedExponents(NonNegativeInteger))
mapExponents : (Mapping(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 : (%, 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))
monomial? : % -> Boolean
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 NonNegativeInteger has PatternMatchable(Float) and R has PatternMatchable(Float)
from PatternMatchable(Float)
patternMatch : (%, Pattern(Integer), PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if NonNegativeInteger has PatternMatchable(Integer) and R has PatternMatchable(Integer)
from PatternMatchable(Integer)
pi : () -> % if R has TranscendentalFunctionCategory
from TranscendentalFunctionCategory
plenaryPower : (%, PositiveInteger) -> % if R has CommutativeRing or R has Algebra(Fraction(Integer))
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(%) -> Matrix(R)
from LinearlyExplicitOver(R)
reducedSystem : Matrix(%) -> Matrix(Integer) if R has LinearlyExplicitOver(Integer)
from LinearlyExplicitOver(Integer)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(R), vec : Vector(R))
from LinearlyExplicitOver(R)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(Integer), vec : Vector(Integer)) if R has LinearlyExplicitOver(Integer)
from LinearlyExplicitOver(Integer)
reductum : % -> %
from IndexedProductCategory(R, IndexedExponents(NonNegativeInteger))
resultant : (%, %, NonNegativeInteger) -> % if R has CommutativeRing
from PolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
retract : % -> R
from RetractableTo(R)
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)
retractIfCan : % -> Union(R, "failed")
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)
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 : (%, NonNegativeInteger) -> SparseUnivariatePolynomial(%)
from PolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
univariate : % -> SparseUnivariatePolynomial(R)
from PolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
variables : % -> List(NonNegativeInteger)
from MaybeSkewPolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)
zero? : % -> Boolean
from AbelianMonoid
~= : (%, %) -> Boolean
from BasicType

Algebra(Fraction(Integer))

CharacteristicNonZero

Module(Fraction(Integer))

FullyLinearlyExplicitOver(R)

NonAssociativeSemiRing

LeftModule(R)

BiModule(%, %)

ConvertibleTo(InputForm)

canonicalUnitNormal

Rng

TrigonometricFunctionCategory

ArcTrigonometricFunctionCategory

CoercibleFrom(Integer)

TwoSidedRecip

FullyRetractableTo(R)

TranscendentalFunctionCategory

SemiRing

EntireRing

NonAssociativeAlgebra(Fraction(Integer))

FreeModuleCategory(R, IndexedExponents(NonNegativeInteger))

unitsKnown

MaybeSkewPolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)

PatternMatchable(Float)

NonAssociativeSemiRng

MagmaWithUnit

IndexedProductCategory(R, IndexedExponents(NonNegativeInteger))

AbelianSemiGroup

noZeroDivisors

UniqueFactorizationDomain

SemiGroup

Magma

GcdDomain

IntegralDomain

LeftModule(%)

RetractableTo(NonNegativeInteger)

ArcHyperbolicFunctionCategory

NonAssociativeAlgebra(%)

CoercibleFrom(NonNegativeInteger)

CharacteristicZero

Algebra(%)

Module(R)

CoercibleFrom(Fraction(Integer))

PolynomialFactorizationExplicit

BiModule(R, R)

RightModule(Fraction(Integer))

Algebra(R)

RightModule(R)

NonAssociativeRng

CommutativeRing

LeftOreRing

CancellationAbelianMonoid

Comparable

SetCategory

AbelianMonoidRing(R, IndexedExponents(NonNegativeInteger))

CommutativeStar

VariablesCommuteWithCoefficients

AbelianMonoid

RetractableTo(Fraction(Integer))

NonAssociativeRing

PartialDifferentialRing(NonNegativeInteger)

RightModule(%)

AbelianProductCategory(R)

Hashable

NonAssociativeAlgebra(R)

Evalable(%)

Module(%)

InnerEvalable(%, %)

LinearlyExplicitOver(Integer)

CoercibleTo(OutputForm)

SemiRng

FiniteAbelianMonoidRing(R, IndexedExponents(NonNegativeInteger))

ConvertibleTo(Pattern(Float))

RetractableTo(Integer)

Monoid

PolynomialCategory(R, IndexedExponents(NonNegativeInteger), NonNegativeInteger)

InnerEvalable(NonNegativeInteger, %)

HyperbolicFunctionCategory

BasicType

Ring

RightModule(Integer)

IndexedDirectProductCategory(R, IndexedExponents(NonNegativeInteger))

LinearlyExplicitOver(R)

LeftModule(Fraction(Integer))

PatternMatchable(Integer)

InnerEvalable(NonNegativeInteger, R)

CoercibleFrom(R)

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

RetractableTo(R)

ConvertibleTo(Pattern(Integer))

AbelianGroup

ElementaryFunctionCategory