JetDifferential(JB, D)
jet.spad line 3591
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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)