# JetBundlePolynomial(R, JB)ΒΆ

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
*: (%, Integer) -> % if R has LinearlyExplicitOver Integer
*: (%, R) -> %

from RightModule R

*: (Fraction Integer, %) -> % if R has Algebra 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: (%, %) -> %
associates?: (%, %) -> Boolean

from EntireRing

associator: (%, %, %) -> %
autoReduce: List % -> List %
binomThmExpt: (%, %, NonNegativeInteger) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

characteristic: () -> NonNegativeInteger
charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero or % has CharacteristicNonZero and R has PolynomialFactorizationExplicit
class: % -> NonNegativeInteger
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
coerce: Fraction Integer -> % if R has Algebra Fraction Integer or R has RetractableTo Fraction Integer
coerce: Integer -> %
coerce: JB -> %
coerce: R -> %

from Algebra R

commutator: (%, %) -> %
conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and R has PolynomialFactorizationExplicit
const?: % -> Boolean
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
convert: % -> Pattern Float if JB has ConvertibleTo Pattern Float and R has ConvertibleTo Pattern Float
convert: % -> Pattern Integer if JB has ConvertibleTo Pattern Integer and R has 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) -> %
D: (%, List Symbol, List NonNegativeInteger) -> %
D: (%, Symbol) -> %
D: (%, Symbol, NonNegativeInteger) -> %
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: % -> %
differentiate: (%, JB) -> %
differentiate: (%, JB, NonNegativeInteger) -> %

from PartialDifferentialRing JB

differentiate: (%, List JB) -> %

from PartialDifferentialRing JB

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

from PartialDifferentialRing JB

differentiate: (%, List Symbol) -> %
differentiate: (%, List Symbol, List NonNegativeInteger) -> %
differentiate: (%, Symbol) -> %
differentiate: (%, Symbol, NonNegativeInteger) -> %
dimension: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger
discriminant: (%, JB) -> % if R has CommutativeRing

from PolynomialCategory(R, IndexedExponents JB, JB)

dSubst: (%, 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, %)
factor: % -> Factored % if R has PolynomialFactorizationExplicit
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit
fmecg: (%, IndexedExponents JB, R, %) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

formalDiff2: (%, PositiveInteger, SparseEchelonMatrix(JB, %)) -> Record(DPhi: %, JVars: List JB)
formalDiff2: (List %, PositiveInteger, SparseEchelonMatrix(JB, %)) -> Record(DSys: List %, JVars: List List JB)
formalDiff: (%, List NonNegativeInteger) -> %
formalDiff: (%, PositiveInteger) -> %
formalDiff: (List %, PositiveInteger) -> List %
freeOf?: (%, JB) -> Boolean
gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

getNotation: () -> Symbol
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, %)
jacobiMatrix: List % -> SparseEchelonMatrix(JB, %)
jetVariables: % -> List JB
latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

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

from LeftOreRing

from IndexedProductCategory(R, IndexedExponents JB)

from IndexedProductCategory(R, 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)
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
numDepVar: () -> PositiveInteger
numerator: % -> %
numIndVar: () -> PositiveInteger
one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> NonNegativeInteger
orderDim: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger
P: (PositiveInteger, List NonNegativeInteger) -> %
P: (PositiveInteger, NonNegativeInteger) -> %
P: List NonNegativeInteger -> %
P: NonNegativeInteger -> %
patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if R has PatternMatchable Float and JB has PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if R has PatternMatchable Integer and JB has PatternMatchable Integer
plenaryPower: (%, PositiveInteger) -> %
pomopo!: (%, R, IndexedExponents JB, %) -> %

from FiniteAbelianMonoidRing(R, IndexedExponents JB)

prime?: % -> Boolean if R has PolynomialFactorizationExplicit
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
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix R, vec: Vector R)

from LinearlyExplicitOver R

reducedSystem: Matrix % -> Matrix Integer if R has LinearlyExplicitOver Integer
reducedSystem: Matrix % -> Matrix R

from LinearlyExplicitOver R

reduceMod: (List %, List %) -> List %
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
retract: % -> Integer if R has RetractableTo Integer
retract: % -> JB

from RetractableTo JB

retract: % -> R

from RetractableTo R

retractIfCan: % -> Union(Fraction Integer, failed) if R has RetractableTo Fraction Integer
retractIfCan: % -> Union(Integer, failed) if R has 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
simplify: (List %, SparseEchelonMatrix(JB, %)) -> Record(Sys: List %, JM: SparseEchelonMatrix(JB, %), Depend: Union(failed, List List NonNegativeInteger))
simpMod: (List %, List %) -> List %
simpMod: (List %, SparseEchelonMatrix(JB, %), List %) -> Record(Sys: List %, JM: SparseEchelonMatrix(JB, %), Depend: Union(failed, List List NonNegativeInteger))
simpOne: % -> %
smaller?: (%, %) -> Boolean if R has Comparable

from Comparable

solveFor: (%, JB) -> Union(%, failed)
solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if R has PolynomialFactorizationExplicit
sortLD: List % -> List %
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
subst: (%, JB, %) -> %
subtractIfCan: (%, %) -> Union(%, failed)
support: % -> List IndexedExponents JB

from FreeModuleCategory(R, IndexedExponents JB)

symbol: List % -> SparseEchelonMatrix(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: () -> %
U: PositiveInteger -> %
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: () -> %
X: PositiveInteger -> %
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

CommutativeRing

CommutativeStar

Comparable if R has Comparable

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

EntireRing

GcdDomain

Hashable if JB has Hashable and R has Hashable

InnerEvalable(%, %)

InnerEvalable(JB, %)

InnerEvalable(JB, R)

IntegralDomain

LeftOreRing

Magma

MagmaWithUnit

Module R if R has CommutativeRing

Monoid

NonAssociativeAlgebra R if R has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

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)

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

unitsKnown

VariablesCommuteWithCoefficients