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.

* : (%, %) -> %

from Magma

* : (%, D) -> %

from RightModule(D)

* : (D, %) -> %

from LeftModule(D)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

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)

P : List(NonNegativeInteger) -> %

from JetBundleFunctionCategory(JB)

P : NonNegativeInteger -> %

from JetBundleFunctionCategory(JB)

P : (PositiveInteger, List(NonNegativeInteger)) -> %

from JetBundleFunctionCategory(JB)

P : (PositiveInteger, NonNegativeInteger) -> %

from JetBundleFunctionCategory(JB)

U : () -> %

from JetBundleFunctionCategory(JB)

U : PositiveInteger -> %

from JetBundleFunctionCategory(JB)

X : () -> %

from JetBundleFunctionCategory(JB)

X : PositiveInteger -> %

from JetBundleFunctionCategory(JB)

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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 : D -> %

coerce : JB -> %

from JetBundleFunctionCategory(JB)

coerce : Integer -> %

from NonAssociativeRing

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

coercion to matrices over ground domain.

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

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

commutator : (%, %) -> %

from NonAssociativeRng

const? : % -> Boolean

from JetBundleFunctionCategory(JB)

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

from JetBundleFunctionCategory(JB)

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)

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

from EntireRing

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

from JetBundleFunctionCategory(JB)

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

from JetBundleFunctionCategory(JB)

formalDiff : (%, PositiveInteger) -> %

from JetBundleFunctionCategory(JB)

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

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)

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 : % -> %

ground(l) returns the ground part of l.

ground? : % -> Boolean

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

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

from JetBundleFunctionCategory(JB)

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

numIndVar : () -> PositiveInteger

from JetBundleFunctionCategory(JB)

numerator : % -> %

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)

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

recip : % -> Union(%, "failed")

from MagmaWithUnit

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

from JetBundleFunctionCategory(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.

retract : % -> D

from RetractableTo(D)

retract : % -> JB

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.

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

from RetractableTo(D)

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

from RetractableTo(JB)

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

setNotation : Symbol -> Void

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)

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

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)

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

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

from EntireRing

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

IntegralDomain

noZeroDivisors

SetCategory

RetractableTo(D)

RightModule(%)

RetractableTo(JB)

GcdDomain

RightModule(D)

AbelianMonoid

Monoid

Algebra(%)

CancellationAbelianMonoid

MagmaWithUnit

Module(%)

Module(D)

BasicType

BiModule(D, D)

LeftModule(%)

JetBundleFunctionCategory(JB)

LeftOreRing

CoercibleFrom(D)

PartialDifferentialRing(Symbol)

LeftModule(D)

CommutativeRing

Magma

NonAssociativeRing

SemiGroup

NonAssociativeRng

BiModule(%, %)

CoercibleFrom(JB)

AbelianGroup

AbelianSemiGroup

CommutativeStar

NonAssociativeSemiRing

Rng

NonAssociativeAlgebra(%)

unitsKnown

Ring

SemiRng

EntireRing

NonAssociativeSemiRng

lazyRepresentation

CoercibleTo(OutputForm)

SemiRing

TwoSidedRecip