JetVectorField(JB, D)

jet.spad line 3319 [edit on github]

JetVectorField(JB, D) implements vector fields over the jet bundle JB with coefficients from D. The fields operate on functions from 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(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
~= : (%, %) -> Boolean
from BasicType

RightModule(D)

BasicType

CoercibleTo(OutputForm)

BiModule(D, D)

AbelianMonoid

AbelianGroup

AbelianSemiGroup

Module(D)

LeftModule(D)

CancellationAbelianMonoid

SetCategory