# JetDifferential(JB, D)ΒΆ

`JetDifferential(JB, D)` implements differentials (one-forms) over the jet bundle `JB` with coefficients from `D`. The differentials operate on `JetVectorField(JB, D)`.

0: %

from AbelianMonoid

*: (%, 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

~=: (%, %) -> Boolean

from BasicType

coefficient: (%, JB) -> D

`coefficient(om, jb)` returns the coefficient of `om` for the differential of `jb`.

coefficients: % -> List D

`coefficients(om)` yields the coefficients of `om`.

coerce: % -> OutputForm
contract: (JetVectorField(JB, D), %) -> D

`contract(v, om)` computes the interior derivative of `om` with respect to `v`.

copy: % -> %

`copy(om)` returns a copy of the differential `om`.

d: D -> %

`d(f)` computes the differential of `f`.

d: JB -> %

`d(jb)` returns the differential of `jb`.

differentials: % -> List JB

`directions(om)` yields the differentials where `om` has non-vanishing coefficients.

dP: (PositiveInteger, List NonNegativeInteger) -> %

`dP(i, mu)` returns the differential of `P(i, mu)`.

dU: PositiveInteger -> %

`dU(i)` returns the differential of `U(i)`.

dX: PositiveInteger -> %

`dX(i)` returns the differential of `X(i)`.

eval: (%, JetVectorField(JB, D)) -> D

`eval(om, v)` applies the differential `om` to the vector field `v`.

latex: % -> String

from SetCategory

lie: (JetVectorField(JB, D), %) -> %

`lie(v, om)` calculates the Lie derivative of `om` with respect to `v`.

opposite?: (%, %) -> Boolean

from AbelianMonoid

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(D, D)

CancellationAbelianMonoid

SetCategory