DistributedJetBundlePolynomial(R, JB, LJV, E)ΒΆ

jet.spad line 6529 [edit on github]

DistributedJetBundlePolynomial implements polynomials in a distributed representation. The unknowns come from a finite list of jet variables. The implementation is basically a copy of the one of GeneralDistributedMultivariatePolynomial.

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, E)

=: (%, %) -> 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, E)

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from CharacteristicNonZero

coefficient: (%, E) -> R

from AbelianMonoidRing(R, E)

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

from MaybeSkewPolynomialCategory(R, E, JB)

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

from MaybeSkewPolynomialCategory(R, E, JB)

coefficients: % -> List R

from FreeModuleCategory(R, E)

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: JB -> %

from CoercibleFrom JB

coerce: R -> %

from Algebra R

commutator: (%, %) -> %

from NonAssociativeRng

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

from PolynomialFactorizationExplicit

const: % -> R

const(p) coerces a polynomial into an element of the coefficient ring, if it is constant. Otherwise an error occurs.

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

from IndexedProductCategory(R, E)

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

from IndexedProductCategory(R, E)

content: % -> R if R has GcdDomain

from FiniteAbelianMonoidRing(R, E)

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

from PolynomialCategory(R, E, JB)

convert: % -> InputForm if R has ConvertibleTo InputForm and JB has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> JetBundlePolynomial(R, JB)

convert(p) converts a polynomial p in distributive representation into a polynomial in recursive representation.

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

from ConvertibleTo Pattern Float

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

from ConvertibleTo Pattern Integer

convert: JetBundlePolynomial(R, JB) -> %

convert(p) converts a polynomial p in recursive representation into a polynomial in distributive representation.

D: (%, JB) -> %

from PartialDifferentialRing JB

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

from PartialDifferentialRing JB

D: (%, List JB) -> %

from PartialDifferentialRing JB

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

from PartialDifferentialRing JB

degree: % -> E

from AbelianMonoidRing(R, E)

degree: (%, JB) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, E, JB)

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

from MaybeSkewPolynomialCategory(R, E, JB)

differentiate: (%, JB) -> %

from PartialDifferentialRing JB

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

from PartialDifferentialRing JB

differentiate: (%, List JB) -> %

from PartialDifferentialRing JB

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

from PartialDifferentialRing JB

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

from PolynomialCategory(R, E, JB)

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

from InnerEvalable(%, %)

eval: (%, Equation %) -> %

from Evalable %

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

from InnerEvalable(JB, %)

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

from InnerEvalable(JB, R)

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

from InnerEvalable(%, %)

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

from Evalable %

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

from InnerEvalable(JB, %)

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

from InnerEvalable(JB, R)

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

from EntireRing

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

from FiniteAbelianMonoidRing(R, E)

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

from FiniteAbelianMonoidRing(R, E)

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

groebner: List % -> List % if R has GcdDomain

groebner(lp) computes a Groebner basis for the ideal generated by the list of polynomials lp.

ground?: % -> Boolean

from FiniteAbelianMonoidRing(R, E)

ground: % -> R

from FiniteAbelianMonoidRing(R, E)

hash: % -> SingleInteger if JB has Hashable and R has Hashable

from Hashable

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

from Hashable

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

from PolynomialCategory(R, E, JB)

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

from PolynomialCategory(R, E, JB)

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

from PolynomialCategory(R, E, JB)

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, E)

leadingMonomial: % -> %

from IndexedProductCategory(R, E)

leadingSupport: % -> E

from IndexedProductCategory(R, E)

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

from IndexedProductCategory(R, E)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

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

from FreeModuleCategory(R, E)

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

from IndexedDirectProductCategory(R, E)

mainVariable: % -> Union(JB, failed)

from MaybeSkewPolynomialCategory(R, E, JB)

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

from IndexedProductCategory(R, E)

mapExponents: (E -> E, %) -> %

from FiniteAbelianMonoidRing(R, E)

minimumDegree: % -> E

from FiniteAbelianMonoidRing(R, E)

minimumDegree: (%, JB) -> NonNegativeInteger

from PolynomialCategory(R, E, JB)

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

from PolynomialCategory(R, E, JB)

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

from PolynomialCategory(R, E, JB)

monomial?: % -> Boolean

from IndexedProductCategory(R, E)

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

from MaybeSkewPolynomialCategory(R, E, JB)

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

from MaybeSkewPolynomialCategory(R, E, JB)

monomial: (R, E) -> %

from IndexedProductCategory(R, E)

monomials: % -> List %

from MaybeSkewPolynomialCategory(R, E, JB)

multivariate: (SparseUnivariatePolynomial %, JB) -> %

from PolynomialCategory(R, E, JB)

multivariate: (SparseUnivariatePolynomial R, JB) -> %

from PolynomialCategory(R, E, JB)

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(R, E)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

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

from PatternMatchable Float

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

from PatternMatchable Integer

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

from NonAssociativeAlgebra %

pomopo!: (%, R, E, %) -> %

from FiniteAbelianMonoidRing(R, E)

prime?: % -> Boolean if R has PolynomialFactorizationExplicit

from UniqueFactorizationDomain

primitiveMonomials: % -> List %

from MaybeSkewPolynomialCategory(R, E, JB)

primitivePart: % -> % if R has GcdDomain

from PolynomialCategory(R, E, JB)

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

from PolynomialCategory(R, E, JB)

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, E)

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

from PolynomialCategory(R, E, JB)

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

from RetractableTo Fraction Integer

retract: % -> Integer if R has RetractableTo Integer

from RetractableTo Integer

retract: % -> JB

from RetractableTo JB

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(JB, failed)

from RetractableTo JB

retractIfCan: % -> Union(R, failed)

from RetractableTo R

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

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, E, JB)

squareFreePart: % -> % if R has GcdDomain

from PolynomialCategory(R, E, JB)

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

from PolynomialFactorizationExplicit

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

from CancellationAbelianMonoid

support: % -> List E

from FreeModuleCategory(R, E)

totalDegree: % -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, E, JB)

totalDegree: (%, List JB) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, E, JB)

totalDegreeSorted: (%, List JB) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, E, JB)

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, E, JB)

univariate: (%, JB) -> SparseUnivariatePolynomial %

from PolynomialCategory(R, E, JB)

variables: % -> List JB

from MaybeSkewPolynomialCategory(R, E, JB)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, E)

AbelianProductCategory R

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

CoercibleFrom Fraction Integer if R has RetractableTo Fraction Integer

CoercibleFrom Integer if R has RetractableTo Integer

CoercibleFrom JB

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 and JB has ConvertibleTo InputForm

ConvertibleTo Pattern Float if R has ConvertibleTo Pattern Float and JB has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if R has ConvertibleTo Pattern Integer and JB has ConvertibleTo Pattern Integer

EntireRing if R has EntireRing

Evalable %

FiniteAbelianMonoidRing(R, E)

FreeModuleCategory(R, E)

FullyLinearlyExplicitOver R

FullyRetractableTo R

GcdDomain if R has GcdDomain

Hashable if JB has Hashable and R has Hashable

IndexedDirectProductCategory(R, E)

IndexedProductCategory(R, E)

InnerEvalable(%, %)

InnerEvalable(JB, %)

InnerEvalable(JB, 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, E, JB)

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 JB

PatternMatchable Float if JB has PatternMatchable Float and R has PatternMatchable Float

PatternMatchable Integer if JB has PatternMatchable Integer and R has PatternMatchable Integer

PolynomialCategory(R, E, JB)

PolynomialFactorizationExplicit if R has PolynomialFactorizationExplicit

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer

RetractableTo JB

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

TwoSidedRecip if R has CommutativeRing

UniqueFactorizationDomain if R has PolynomialFactorizationExplicit

unitsKnown

VariablesCommuteWithCoefficients