# JetVectorField(JB, D)ΒΆ

`JetVectorField(JB, D)` implements vector fields over the jet bundle `JB` with coefficients from `D`. The fields operate on functions from `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(v, jb)` returns the coefficient of `v` in direction `jb`.

coefficients: % -> List D

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

coerce: % -> OutputForm
commutator: (%, %) -> %

`commutator(v, w)` calculates the commutator of two vector fields.

copy: % -> %

`copy(v)` returns a copy of the vector field `v`.

diff: JB -> %

`diff(jb)` returns the base vector field in direction `jb`.

diffP: (PositiveInteger, List NonNegativeInteger) -> %

`diffP(i, mu)` returns the base vector field in direction `P(i, mu)`.

diffU: PositiveInteger -> %

`diffU(i)` returns the base vector field in direction `U(i)`.

diffX: PositiveInteger -> %

`diffX(i)` returns the base vector field in direction `X(i)`.

directions: % -> List JB

`directions(v)` yields the directions of the base vectors where `v` has non-vanishing coefficients.

eval: (%, D) -> D

`eval(v, f)` applies the vector field `v` to the function `f`.

latex: % -> String

from SetCategory

lie: (%, %) -> %

`lie(v, w)` calculates the Lie derivative of `w` with respect to `v`. (This yields the commutator of the fields.)

opposite?: (%, %) -> Boolean

from AbelianMonoid

prolong: (%, NonNegativeInteger) -> %

`prolong(v, q)` prolongs a vector field `v` defined on the base space into the jet bundle of order `q`.

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
table: List % -> TwoDimensionalArray %

`table(lv)` computes the commutator table for a given list of vector fields.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(D, D)

CancellationAbelianMonoid

SetCategory