JetDifferential(JB, D)

jet.spad line 3591 [edit on github]

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

* : (%, D) -> %
from RightModule(D)
* : (D, %) -> %
from LeftModule(D)
* : (Integer, %) -> %
from AbelianGroup
* : (NonNegativeInteger, %) -> %
from AbelianMonoid
* : (PositiveInteger, %) -> %
from AbelianSemiGroup
+ : (%, %) -> %
from AbelianSemiGroup
- : % -> %
from AbelianGroup
- : (%, %) -> %
from AbelianGroup
0 : () -> %
from AbelianMonoid
= : (%, %) -> 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.

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).

differentials : % -> List(JB)

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

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
~= : (%, %) -> Boolean
from BasicType

RightModule(D)

BasicType

SetCategory

BiModule(D, D)

CoercibleTo(OutputForm)

AbelianMonoid

AbelianGroup

AbelianSemiGroup

CancellationAbelianMonoid

LeftModule(D)

Module(D)