JetVectorField(JB, D)

jet.spad line 3319 [edit on github]

• JB: JetBundleCategory

• D: JetBundleFunctionCategory JB

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

from CoercibleTo 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)

from CancellationAbelianMonoid

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

CoercibleTo OutputForm

LeftModule D

Module D

RightModule D

SetCategory