JetDifferential(JB, D)

jet.spad line 3591 [edit on github]

• JB: JetBundleCategory

• D: JetBundleFunctionCategory JB

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

from CoercibleTo 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)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(D, D)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule D

Module D

RightModule D

SetCategory