JetBundlePolynomial(R, JB)ΒΆ

jet.spad line 6453 [edit on github]

JetBundlePolynomial implements polynomial sections over a jet bundle. The order is not fixed, thus jet variables of any order can appear.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, 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 JB)

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

autoReduce: List % -> List %

from JetBundleFunctionCategory JB

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

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from CharacteristicNonZero

class: % -> NonNegativeInteger

from JetBundleFunctionCategory JB

coefficient: (%, IndexedExponents JB) -> R

from FreeModuleCategory(R, IndexedExponents JB)

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

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

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

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

coefficients: % -> List R

from FreeModuleCategory(R, IndexedExponents JB)

coerce: % -> %

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 JetBundleFunctionCategory JB

coerce: R -> %

from Algebra R

commutator: (%, %) -> %

from NonAssociativeRng

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

from PolynomialFactorizationExplicit

const?: % -> Boolean

from JetBundleFunctionCategory JB

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

from IndexedProductCategory(R, IndexedExponents JB)

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

from IndexedProductCategory(R, IndexedExponents JB)

content: % -> R if R has GcdDomain

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

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

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from ConvertibleTo InputForm

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

from ConvertibleTo Pattern Float

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

from ConvertibleTo Pattern Integer

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

D: (%, List Symbol) -> %

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

D: (%, Symbol) -> %

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

degree: % -> IndexedExponents JB

from AbelianMonoidRing(R, IndexedExponents JB)

degree: (%, JB) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

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

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

denominator: % -> %

from JetBundleFunctionCategory JB

differentiate: (%, JB) -> %

from JetBundleFunctionCategory JB

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

from PartialDifferentialRing JB

differentiate: (%, List JB) -> %

from PartialDifferentialRing JB

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

from PartialDifferentialRing JB

differentiate: (%, List Symbol) -> %

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

differentiate: (%, Symbol) -> %

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

dimension: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger

from JetBundleFunctionCategory JB

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

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from JetBundleFunctionCategory 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)

from EntireRing

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

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

extractSymbol: SparseEchelonMatrix(JB, %) -> SparseEchelonMatrix(JB, %)

from JetBundleFunctionCategory JB

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 JB, R, %) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

formalDiff2: (%, PositiveInteger, SparseEchelonMatrix(JB, %)) -> Record(DPhi: %, JVars: List JB)

from JetBundleFunctionCategory JB

formalDiff2: (List %, PositiveInteger, SparseEchelonMatrix(JB, %)) -> Record(DSys: List %, JVars: List List JB)

from JetBundleFunctionCategory JB

formalDiff: (%, List NonNegativeInteger) -> %

from JetBundleFunctionCategory JB

formalDiff: (%, PositiveInteger) -> %

from JetBundleFunctionCategory JB

formalDiff: (List %, PositiveInteger) -> List %

from JetBundleFunctionCategory JB

freeOf?: (%, JB) -> Boolean

from JetBundleFunctionCategory JB

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

getNotation: () -> Symbol

from JetBundleFunctionCategory JB

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

groebner(lp) computes a Groebner basis for the ideal generated by lp wrt a lexicographic ordering.

ground?: % -> Boolean

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

ground: % -> R

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

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, IndexedExponents JB, JB)

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

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from PolynomialCategory(R, IndexedExponents JB, JB)

jacobiMatrix: (List %, List List JB) -> SparseEchelonMatrix(JB, %)

from JetBundleFunctionCategory JB

jacobiMatrix: List % -> SparseEchelonMatrix(JB, %)

from JetBundleFunctionCategory JB

jetVariables: % -> List JB

from JetBundleFunctionCategory JB

latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)

from LeftOreRing

leadingCoefficient: % -> R

from IndexedProductCategory(R, IndexedExponents JB)

leadingDer: % -> JB

from JetBundleFunctionCategory JB

leadingMonomial: % -> %

from IndexedProductCategory(R, IndexedExponents JB)

leadingSupport: % -> IndexedExponents JB

from IndexedProductCategory(R, IndexedExponents JB)

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

from IndexedProductCategory(R, IndexedExponents JB)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

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

from FreeModuleCategory(R, IndexedExponents JB)

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

from IndexedDirectProductCategory(R, IndexedExponents JB)

mainVariable: % -> Union(JB, failed)

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

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

from IndexedProductCategory(R, IndexedExponents JB)

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

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

minimumDegree: % -> IndexedExponents JB

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

minimumDegree: (%, JB) -> NonNegativeInteger

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from PolynomialCategory(R, IndexedExponents JB, JB)

monomial?: % -> Boolean

from IndexedProductCategory(R, IndexedExponents JB)

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

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

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

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

monomial: (R, IndexedExponents JB) -> %

from IndexedProductCategory(R, IndexedExponents JB)

monomials: % -> List %

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

multivariate: (SparseUnivariatePolynomial %, JB) -> %

from PolynomialCategory(R, IndexedExponents JB, JB)

multivariate: (SparseUnivariatePolynomial R, JB) -> %

from PolynomialCategory(R, IndexedExponents JB, JB)

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(R, IndexedExponents JB)

numDepVar: () -> PositiveInteger

from JetBundleFunctionCategory JB

numerator: % -> %

from JetBundleFunctionCategory JB

numIndVar: () -> PositiveInteger

from JetBundleFunctionCategory JB

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> NonNegativeInteger

from JetBundleFunctionCategory JB

orderDim: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger

from JetBundleFunctionCategory JB

P: (PositiveInteger, List NonNegativeInteger) -> %

from JetBundleFunctionCategory JB

P: (PositiveInteger, NonNegativeInteger) -> %

from JetBundleFunctionCategory JB

P: List NonNegativeInteger -> %

from JetBundleFunctionCategory JB

P: NonNegativeInteger -> %

from JetBundleFunctionCategory JB

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

from PatternMatchable Float

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

from PatternMatchable Integer

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

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

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

prime?: % -> Boolean if R has PolynomialFactorizationExplicit

from UniqueFactorizationDomain

primitiveMonomials: % -> List %

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

primitivePart: % -> % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from PolynomialCategory(R, IndexedExponents JB, 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

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

from JetBundleFunctionCategory JB

reductum: % -> %

from IndexedProductCategory(R, IndexedExponents JB)

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

from PolynomialCategory(R, IndexedExponents JB, 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

setNotation: Symbol -> Void

from JetBundleFunctionCategory JB

simplify: (List %, SparseEchelonMatrix(JB, %)) -> Record(Sys: List %, JM: SparseEchelonMatrix(JB, %), Depend: Union(failed, List List NonNegativeInteger))

from JetBundleFunctionCategory JB

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

from JetBundleFunctionCategory JB

simpMod: (List %, SparseEchelonMatrix(JB, %), List %) -> Record(Sys: List %, JM: SparseEchelonMatrix(JB, %), Depend: Union(failed, List List NonNegativeInteger))

from JetBundleFunctionCategory JB

simpOne: % -> %

from JetBundleFunctionCategory JB

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

from Comparable

solveFor: (%, JB) -> Union(%, failed)

from JetBundleFunctionCategory JB

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

from PolynomialFactorizationExplicit

sortLD: List % -> List %

from JetBundleFunctionCategory JB

squareFree: % -> Factored % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents JB, JB)

squareFreePart: % -> % if R has GcdDomain

from PolynomialCategory(R, IndexedExponents JB, JB)

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

from PolynomialFactorizationExplicit

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

from JetBundleFunctionCategory JB

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

from CancellationAbelianMonoid

support: % -> List IndexedExponents JB

from FreeModuleCategory(R, IndexedExponents JB)

symbol: List % -> SparseEchelonMatrix(JB, %)

from JetBundleFunctionCategory JB

totalDegree: % -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

totalDegree: (%, List JB) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

totalDegreeSorted: (%, List JB) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

U: () -> %

from JetBundleFunctionCategory JB

U: PositiveInteger -> %

from JetBundleFunctionCategory JB

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %)

from EntireRing

univariate: % -> SparseUnivariatePolynomial R

from PolynomialCategory(R, IndexedExponents JB, JB)

univariate: (%, JB) -> SparseUnivariatePolynomial %

from PolynomialCategory(R, IndexedExponents JB, JB)

variables: % -> List JB

from MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

X: () -> %

from JetBundleFunctionCategory JB

X: PositiveInteger -> %

from JetBundleFunctionCategory JB

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, IndexedExponents JB)

AbelianProductCategory R

AbelianSemiGroup

Algebra %

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

CommutativeStar

Comparable if R has Comparable

ConvertibleTo InputForm if JB has ConvertibleTo InputForm and R has ConvertibleTo InputForm

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

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

EntireRing

Evalable %

FiniteAbelianMonoidRing(R, IndexedExponents JB)

FreeModuleCategory(R, IndexedExponents JB)

FullyLinearlyExplicitOver R

FullyRetractableTo R

GcdDomain

Hashable if JB has Hashable and R has Hashable

IndexedDirectProductCategory(R, IndexedExponents JB)

IndexedProductCategory(R, IndexedExponents JB)

InnerEvalable(%, %)

InnerEvalable(JB, %)

InnerEvalable(JB, R)

IntegralDomain

JetBundleFunctionCategory JB

LeftModule %

LeftModule Fraction Integer if R has Algebra Fraction Integer

LeftModule R

LeftOreRing

LinearlyExplicitOver Integer if R has LinearlyExplicitOver Integer

LinearlyExplicitOver R

Magma

MagmaWithUnit

MaybeSkewPolynomialCategory(R, IndexedExponents JB, JB)

Module %

Module Fraction Integer if R has Algebra Fraction Integer

Module R if R has CommutativeRing

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer if R has Algebra Fraction Integer

NonAssociativeAlgebra R if R has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing JB

PartialDifferentialRing Symbol

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

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

PolynomialCategory(R, IndexedExponents JB, 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

UniqueFactorizationDomain if R has PolynomialFactorizationExplicit

unitsKnown

VariablesCommuteWithCoefficients