OrderlyDifferentialPolynomial RΒΆ

dpolcat.spad line 450

OrderlyDifferentialPolynomial implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates, with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain Polynomial.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Fraction Integer) -> % if R has Algebra Fraction Integer
from RightModule Fraction 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 OrderlyDifferentialVariable Symbol)
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associates?: (%, %) -> Boolean if R has EntireRing
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
binomThmExpt: (%, %, NonNegativeInteger) -> % if % has CommutativeRing
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
charthRoot: % -> Union(%, failed) if % has CharacteristicNonZero and R has PolynomialFactorizationExplicit or R has CharacteristicNonZero
from CharacteristicNonZero
coefficient: (%, IndexedExponents OrderlyDifferentialVariable Symbol) -> R
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
coefficient: (%, List OrderlyDifferentialVariable Symbol, List NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
coefficient: (%, OrderlyDifferentialVariable Symbol, NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
coefficients: % -> List R
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
coerce: % -> % if R has CommutativeRing
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer or R has Algebra Fraction Integer
from Algebra Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
coerce: OrderlyDifferentialVariable Symbol -> %
from RetractableTo OrderlyDifferentialVariable Symbol
coerce: R -> %
from Algebra R
coerce: SparseMultivariatePolynomial(R, Symbol) -> %
from RetractableTo SparseMultivariatePolynomial(R, Symbol)
coerce: Symbol -> %
from RetractableTo Symbol
commutator: (%, %) -> %
from NonAssociativeRng
conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
content: % -> R if R has GcdDomain
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
content: (%, OrderlyDifferentialVariable Symbol) -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
convert: % -> InputForm if OrderlyDifferentialVariable Symbol has ConvertibleTo InputForm and R has ConvertibleTo InputForm
from ConvertibleTo InputForm
convert: % -> Pattern Float if OrderlyDifferentialVariable Symbol has ConvertibleTo Pattern Float and R has ConvertibleTo Pattern Float
from ConvertibleTo Pattern Float
convert: % -> Pattern Integer if OrderlyDifferentialVariable Symbol has ConvertibleTo Pattern Integer and R has ConvertibleTo Pattern Integer
from ConvertibleTo Pattern Integer
D: % -> % if R has DifferentialRing
from DifferentialRing
D: (%, List OrderlyDifferentialVariable Symbol) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
D: (%, List OrderlyDifferentialVariable Symbol, List NonNegativeInteger) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
D: (%, List Symbol) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
D: (%, List Symbol, List NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
D: (%, NonNegativeInteger) -> % if R has DifferentialRing
from DifferentialRing
D: (%, OrderlyDifferentialVariable Symbol) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
D: (%, OrderlyDifferentialVariable Symbol, NonNegativeInteger) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
D: (%, R -> R) -> %
from DifferentialExtension R
D: (%, R -> R, NonNegativeInteger) -> %
from DifferentialExtension R
D: (%, Symbol) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
D: (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
degree: % -> IndexedExponents OrderlyDifferentialVariable Symbol
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
degree: (%, List OrderlyDifferentialVariable Symbol) -> List NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
degree: (%, OrderlyDifferentialVariable Symbol) -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
degree: (%, Symbol) -> NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
differentialVariables: % -> List Symbol
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
differentiate: % -> % if R has DifferentialRing
from DifferentialRing
differentiate: (%, List OrderlyDifferentialVariable Symbol) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
differentiate: (%, List OrderlyDifferentialVariable Symbol, List NonNegativeInteger) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
differentiate: (%, List Symbol) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
differentiate: (%, NonNegativeInteger) -> % if R has DifferentialRing
from DifferentialRing
differentiate: (%, OrderlyDifferentialVariable Symbol) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
differentiate: (%, OrderlyDifferentialVariable Symbol, NonNegativeInteger) -> %
from PartialDifferentialRing OrderlyDifferentialVariable Symbol
differentiate: (%, R -> R) -> %
from DifferentialExtension R
differentiate: (%, R -> R, NonNegativeInteger) -> %
from DifferentialExtension R
differentiate: (%, Symbol) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol
from PartialDifferentialRing Symbol
discriminant: (%, OrderlyDifferentialVariable Symbol) -> % if R has CommutativeRing
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
eval: (%, %, %) -> %
from InnerEvalable(%, %)
eval: (%, Equation %) -> %
from Evalable %
eval: (%, List %, List %) -> %
from InnerEvalable(%, %)
eval: (%, List Equation %) -> %
from Evalable %
eval: (%, List OrderlyDifferentialVariable Symbol, List %) -> %
from InnerEvalable(OrderlyDifferentialVariable Symbol, %)
eval: (%, List OrderlyDifferentialVariable Symbol, List R) -> %
from InnerEvalable(OrderlyDifferentialVariable Symbol, R)
eval: (%, List Symbol, List %) -> % if R has DifferentialRing
from InnerEvalable(Symbol, %)
eval: (%, List Symbol, List R) -> % if R has DifferentialRing
from InnerEvalable(Symbol, R)
eval: (%, OrderlyDifferentialVariable Symbol, %) -> %
from InnerEvalable(OrderlyDifferentialVariable Symbol, %)
eval: (%, OrderlyDifferentialVariable Symbol, R) -> %
from InnerEvalable(OrderlyDifferentialVariable Symbol, R)
eval: (%, Symbol, %) -> % if R has DifferentialRing
from InnerEvalable(Symbol, %)
eval: (%, Symbol, R) -> % if R has DifferentialRing
from InnerEvalable(Symbol, R)
exquo: (%, %) -> Union(%, failed) if R has EntireRing
from EntireRing
exquo: (%, R) -> Union(%, failed) if R has EntireRing
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
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 OrderlyDifferentialVariable Symbol, R, %) -> %
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
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 OrderlyDifferentialVariable Symbol)
ground?: % -> Boolean
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
initial: % -> %
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
isExpt: % -> Union(Record(var: OrderlyDifferentialVariable Symbol, exponent: NonNegativeInteger), failed)
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
isobaric?: % -> Boolean
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
isPlus: % -> Union(List %, failed)
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
isTimes: % -> Union(List %, failed)
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
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
leader: % -> OrderlyDifferentialVariable Symbol
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
leadingCoefficient: % -> R
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
leadingMonomial: % -> %
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
mainVariable: % -> Union(OrderlyDifferentialVariable Symbol, failed)
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
makeVariable: % -> NonNegativeInteger -> % if R has DifferentialRing
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
makeVariable: Symbol -> NonNegativeInteger -> %
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
map: (R -> R, %) -> %
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
mapExponents: (IndexedExponents OrderlyDifferentialVariable Symbol -> IndexedExponents OrderlyDifferentialVariable Symbol, %) -> %
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
minimumDegree: % -> IndexedExponents OrderlyDifferentialVariable Symbol
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
minimumDegree: (%, List OrderlyDifferentialVariable Symbol) -> List NonNegativeInteger
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
minimumDegree: (%, OrderlyDifferentialVariable Symbol) -> NonNegativeInteger
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
monicDivide: (%, %, OrderlyDifferentialVariable Symbol) -> Record(quotient: %, remainder: %)
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
monomial: (%, List OrderlyDifferentialVariable Symbol, List NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
monomial: (%, OrderlyDifferentialVariable Symbol, NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
monomial: (R, IndexedExponents OrderlyDifferentialVariable Symbol) -> %
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
monomial?: % -> Boolean
from AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
monomials: % -> List %
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
multivariate: (SparseUnivariatePolynomial %, OrderlyDifferentialVariable Symbol) -> %
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
multivariate: (SparseUnivariatePolynomial R, OrderlyDifferentialVariable Symbol) -> %
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
numberOfMonomials: % -> NonNegativeInteger
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
order: % -> NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
order: (%, Symbol) -> NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if OrderlyDifferentialVariable Symbol has PatternMatchable Float and R has PatternMatchable Float
from PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if OrderlyDifferentialVariable Symbol has PatternMatchable Integer and R has PatternMatchable Integer
from PatternMatchable Integer
pomopo!: (%, R, IndexedExponents OrderlyDifferentialVariable Symbol, %) -> %
from FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
prime?: % -> Boolean if R has PolynomialFactorizationExplicit
from UniqueFactorizationDomain
primitiveMonomials: % -> List %
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
primitivePart: % -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
primitivePart: (%, OrderlyDifferentialVariable Symbol) -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
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 AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)
resultant: (%, %, OrderlyDifferentialVariable Symbol) -> % if R has CommutativeRing
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
retract: % -> Fraction Integer if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
retract: % -> Integer if R has RetractableTo Integer
from RetractableTo Integer
retract: % -> OrderlyDifferentialVariable Symbol
from RetractableTo OrderlyDifferentialVariable Symbol
retract: % -> R
from RetractableTo R
retract: % -> SparseMultivariatePolynomial(R, Symbol)
from RetractableTo SparseMultivariatePolynomial(R, Symbol)
retract: % -> Symbol
from RetractableTo Symbol
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(OrderlyDifferentialVariable Symbol, failed)
from RetractableTo OrderlyDifferentialVariable Symbol
retractIfCan: % -> Union(R, failed)
from RetractableTo R
retractIfCan: % -> Union(SparseMultivariatePolynomial(R, Symbol), failed)
from RetractableTo SparseMultivariatePolynomial(R, Symbol)
retractIfCan: % -> Union(Symbol, failed)
from RetractableTo Symbol
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
separant: % -> %
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
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 OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
squareFreePart: % -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
totalDegree: % -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
totalDegree: (%, List OrderlyDifferentialVariable Symbol) -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
totalDegreeSorted: (%, List OrderlyDifferentialVariable Symbol) -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
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 OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
univariate: (%, OrderlyDifferentialVariable Symbol) -> SparseUnivariatePolynomial %
from PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
variables: % -> List OrderlyDifferentialVariable Symbol
from MaybeSkewPolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)
weight: % -> NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
weight: (%, Symbol) -> NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
weights: % -> List NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
weights: (%, Symbol) -> List NonNegativeInteger
from DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)

AbelianSemiGroup

Algebra % if R has CommutativeRing

Algebra Fraction Integer if R has Algebra Fraction Integer

Algebra R if R has CommutativeRing

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

CoercibleTo OutputForm

CommutativeRing if R has CommutativeRing

CommutativeStar if R has CommutativeRing

Comparable if R has Comparable

ConvertibleTo InputForm if OrderlyDifferentialVariable Symbol has ConvertibleTo InputForm and R has ConvertibleTo InputForm

ConvertibleTo Pattern Float if OrderlyDifferentialVariable Symbol has ConvertibleTo Pattern Float and R has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if OrderlyDifferentialVariable Symbol has ConvertibleTo Pattern Integer and R has ConvertibleTo Pattern Integer

DifferentialExtension R

DifferentialPolynomialCategory(R, Symbol, OrderlyDifferentialVariable Symbol, IndexedExponents OrderlyDifferentialVariable Symbol)

DifferentialRing if R has DifferentialRing

EntireRing if R has EntireRing

Evalable %

FiniteAbelianMonoidRing(R, IndexedExponents OrderlyDifferentialVariable Symbol)

FullyLinearlyExplicitOver R

FullyRetractableTo R

GcdDomain if R has GcdDomain

InnerEvalable(%, %)

InnerEvalable(OrderlyDifferentialVariable Symbol, %)

InnerEvalable(OrderlyDifferentialVariable Symbol, R)

InnerEvalable(Symbol, %) if R has DifferentialRing

InnerEvalable(Symbol, R) if R has DifferentialRing

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 OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)

Module % if R has CommutativeRing

Module Fraction Integer if R has Algebra Fraction Integer

Module R if R has CommutativeRing

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has EntireRing

PartialDifferentialRing OrderlyDifferentialVariable Symbol

PartialDifferentialRing Symbol if R has PartialDifferentialRing Symbol

PatternMatchable Float if OrderlyDifferentialVariable Symbol has PatternMatchable Float and R has PatternMatchable Float

PatternMatchable Integer if OrderlyDifferentialVariable Symbol has PatternMatchable Integer and R has PatternMatchable Integer

PolynomialCategory(R, IndexedExponents OrderlyDifferentialVariable Symbol, OrderlyDifferentialVariable Symbol)

PolynomialFactorizationExplicit if R has PolynomialFactorizationExplicit

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer

RetractableTo OrderlyDifferentialVariable Symbol

RetractableTo R

RetractableTo SparseMultivariatePolynomial(R, Symbol)

RetractableTo Symbol

RightModule %

RightModule Fraction Integer if R has Algebra Fraction Integer

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

UniqueFactorizationDomain if R has PolynomialFactorizationExplicit

unitsKnown

VariablesCommuteWithCoefficients