JetVectorField(JB, D)ΒΆ

jet.spad line 3321

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