# JetBundleLinearFunction(JB, D)ΒΆ

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: (%, %) -> %
associates?: (%, %) -> Boolean

from EntireRing

associator: (%, %, %) -> %
autoReduce: List % -> List %
characteristic: () -> NonNegativeInteger
class: % -> NonNegativeInteger
coerce: % -> %

from Algebra %

coerce: % -> OutputForm

coerce: D -> %

coerce: Integer -> %
coerce: JB -> %

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

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

coercion to matrices over ground domain.

commutator: (%, %) -> %
const?: % -> Boolean
D: (%, List Symbol) -> %
D: (%, List Symbol, List NonNegativeInteger) -> %
D: (%, Symbol) -> %
D: (%, Symbol, NonNegativeInteger) -> %
denominator: % -> %
differentiate: (%, JB) -> %
differentiate: (%, List Symbol) -> %
differentiate: (%, List Symbol, List NonNegativeInteger) -> %
differentiate: (%, Symbol) -> %
differentiate: (%, Symbol, NonNegativeInteger) -> %
dimension: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger
dSubst: (%, JB, %) -> %
exquo: (%, %) -> Union(%, failed)

from EntireRing

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

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

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 -> %
plenaryPower: (%, PositiveInteger) -> %
recip: % -> Union(%, failed)

from MagmaWithUnit

reduceMod: (List %, List %) -> List %
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
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: % -> %
solveFor: (%, JB) -> Union(%, failed)
sortLD: List % -> List %
subst: (%, JB, %) -> %
subtractIfCan: (%, %) -> Union(%, failed)
symbol: List % -> SparseEchelonMatrix(JB, %)
U: () -> %
U: PositiveInteger -> %
unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

X: () -> %
X: PositiveInteger -> %
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

BiModule(D, D)

CancellationAbelianMonoid

CommutativeRing

CommutativeStar

EntireRing

GcdDomain

IntegralDomain

LeftOreRing

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

unitsKnown