DistributedJetBundlePolynomial(R, JB, LJV, E)

jet.spad line 6529 [edit on github]

• R : Ring
• JB : JetBundleCategory
• LJV : List(JB)
• E : DirectProductCategory(#(LJV), NonNegativeInteger)

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.

* : (%, %) -> %

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, E)

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

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)

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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 : (%, JB, NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(R, E, JB)

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

from MaybeSkewPolynomialCategory(R, E, JB)

coefficient : (%, E) -> R

from AbelianMonoidRing(R, E)

coefficients : % -> List(R)

from FreeModuleCategory(R, E)

coerce : % -> % if R has CommutativeRing

from Algebra(%)

coerce : JB -> %

from CoercibleFrom(JB)

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 : % -> OutputForm

from CoercibleTo(OutputForm)

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

from PolynomialCategory(R, E, JB)

content : % -> R if R has GcdDomain

from FiniteAbelianMonoidRing(R, E)

convert : JetBundlePolynomial(R, JB) -> %

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

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))

degree : % -> E

from AbelianMonoidRing(R, E)

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

from MaybeSkewPolynomialCategory(R, E, JB)

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

from InnerEvalable(JB, %)

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

from InnerEvalable(JB, R)

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

from Evalable(%)

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

from InnerEvalable(%, %)

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

from InnerEvalable(JB, %)

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

from InnerEvalable(JB, R)

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

from Evalable(%)

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 : % -> R

from FiniteAbelianMonoidRing(R, E)

ground? : % -> Boolean

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

from IndexedProductCategory(R, E)

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

from FiniteAbelianMonoidRing(R, E)

minimumDegree : % -> E

from FiniteAbelianMonoidRing(R, E)

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

from PolynomialCategory(R, E, JB)

minimumDegree : (%, JB) -> NonNegativeInteger

from PolynomialCategory(R, E, JB)

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

from PolynomialCategory(R, E, JB)

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)

monomial? : % -> Boolean

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(%) -> 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, E)

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

from PolynomialCategory(R, E, JB)

retract : % -> JB

from RetractableTo(JB)

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)

retractIfCan : % -> Union(JB, "failed")

from RetractableTo(JB)

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)

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

from PolynomialCategory(R, E, JB)

univariate : % -> SparseUnivariatePolynomial(R)

from PolynomialCategory(R, E, JB)

variables : % -> List(JB)

from MaybeSkewPolynomialCategory(R, E, JB)

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

PolynomialCategory(R, E, JB)

CharacteristicNonZero

Module(Fraction(Integer))

NonAssociativeSemiRing

LeftModule(R)

BiModule(%, %)

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

TwoSidedRecip

FullyRetractableTo(R)

SemiRing

EntireRing

NonAssociativeAlgebra(Fraction(Integer))

unitsKnown

FullyLinearlyExplicitOver(R)

AbelianMonoidRing(R, E)

noZeroDivisors

CoercibleFrom(JB)

UniqueFactorizationDomain

InnerEvalable(%, %)

SemiGroup

Magma

GcdDomain

IntegralDomain

ConvertibleTo(InputForm)

LeftModule(%)

NonAssociativeRing

PatternMatchable(Float)

IndexedProductCategory(R, E)

CharacteristicZero

MaybeSkewPolynomialCategory(R, E, JB)

BasicType

Module(R)

CoercibleFrom(Fraction(Integer))

Algebra(%)

BiModule(R, R)

RightModule(Fraction(Integer))

Algebra(R)

FreeModuleCategory(R, E)

RightModule(R)

CommutativeRing

NonAssociativeSemiRng

CancellationAbelianMonoid

Comparable

RetractableTo(Integer)

RetractableTo(JB)

CommutativeStar

VariablesCommuteWithCoefficients

AbelianMonoid

RetractableTo(Fraction(Integer))

MagmaWithUnit

RightModule(%)

AbelianProductCategory(R)

Hashable

Evalable(%)

LinearlyExplicitOver(R)

Module(%)

CoercibleTo(OutputForm)

FiniteAbelianMonoidRing(R, E)

ConvertibleTo(Pattern(Float))

SemiRng

LinearlyExplicitOver(Integer)

Monoid

PolynomialFactorizationExplicit

NonAssociativeAlgebra(R)

LeftOreRing

NonAssociativeAlgebra(%)

Algebra(Fraction(Integer))

IndexedDirectProductCategory(R, E)

Ring

RightModule(Integer)

AbelianSemiGroup

SetCategory

InnerEvalable(JB, %)

PartialDifferentialRing(JB)

LeftModule(Fraction(Integer))

NonAssociativeRng

CoercibleFrom(R)

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

InnerEvalable(JB, R)

RetractableTo(R)

PatternMatchable(Integer)

ConvertibleTo(Pattern(Integer))

AbelianGroup