JetBundleLinearFunction(JB, D)

jet.spad line 2888 [edit on github]

• JB: JetBundleCategory

• D: JetBundleBaseFunctionCategory JB

JetBundleLinearFunction implements linear functions over a jet bundle. The coefficients are functions of the independent variables only.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, D) -> %

from RightModule D

*: (D, %) -> %

from LeftModule D

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> 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

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

class: % -> NonNegativeInteger

from JetBundleFunctionCategory JB

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: D -> %

coerce: Integer -> %

from NonAssociativeRing

coerce: JB -> %

from JetBundleFunctionCategory JB

coerce: List % -> SparseEchelonMatrix(JB, D)

coerce: SparseEchelonMatrix(JB, D) -> List %

coercion to matrices over ground domain.

commutator: (%, %) -> %

from NonAssociativeRng

const?: % -> Boolean

from JetBundleFunctionCategory 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

denominator: % -> %

from JetBundleFunctionCategory JB

differentiate: (%, JB) -> %

from JetBundleFunctionCategory 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

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

from JetBundleFunctionCategory JB

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

from EntireRing

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

from JetBundleFunctionCategory 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

ground?: % -> Boolean

ground?(l) yields true, if l is an element of the ground domain D.

ground: % -> %

ground(l) returns the ground part of l.

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

leadingDer: % -> JB

from JetBundleFunctionCategory JB

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

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

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from JetBundleFunctionCategory JB

retract: % -> D

from RetractableTo D

retract: % -> JB

from RetractableTo JB

retract: JetBundleExpression JB -> % if D has retractIfCan: JetBundleExpression JB -> Union(D, failed)

retract(p) is like retractIfCan(p) put yields a hard error, if p contains further jet variables.

retractIfCan: % -> Union(D, failed)

from RetractableTo D

retractIfCan: % -> Union(JB, failed)

from RetractableTo JB

retractIfCan: JetBundleExpression JB -> Union(%, failed) if D has retractIfCan: JetBundleExpression JB -> Union(D, failed)

retractIfCan(p) tries to write a general expression as a linear function.

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

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

from JetBundleFunctionCategory JB

sortLD: List % -> List %

from JetBundleFunctionCategory JB

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

from JetBundleFunctionCategory JB

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

from CancellationAbelianMonoid

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

from JetBundleFunctionCategory JB

U: () -> %

from JetBundleFunctionCategory JB

U: PositiveInteger -> %

from JetBundleFunctionCategory JB

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

X: () -> %

from JetBundleFunctionCategory JB

X: PositiveInteger -> %

from JetBundleFunctionCategory JB

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

BasicType

BiModule(%, %)

BiModule(D, D)

CancellationAbelianMonoid

CoercibleFrom D

CoercibleFrom JB

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

EntireRing

GcdDomain

IntegralDomain

JetBundleFunctionCategory JB

lazyRepresentation if D has lazyRepresentation

LeftModule %

LeftModule D

LeftOreRing

Magma

MagmaWithUnit

Module %

Module D

Monoid

NonAssociativeAlgebra %

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol

RetractableTo D

RetractableTo JB

RightModule %

RightModule D

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

unitsKnown