JetDifferential(JB, D)ΒΆ

jet.spad line 3593

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.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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