JetBundleLinearFunction(JB, D)ΒΆ

jet.spad line 2889

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

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
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
=: (%, %) -> 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: % -> %
ground(l) returns the ground part of l.
ground?: % -> Boolean
ground?(l) yields true, if l is an element of the ground domain D.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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
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

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

EntireRing

GcdDomain

IntegralDomain

JetBundleFunctionCategory JB

lazyRepresentation if D has lazyRepresentation

LeftModule %

LeftModule D

LeftOreRing

Magma

MagmaWithUnit

Module %

Module D

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol

RetractableTo D

RetractableTo JB

RightModule %

RightModule D

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown