PullBack
Author: Kurt Pagani
Date Created: Wed Jun 10 19:16:01 CEST 2020
License: BSD
References:
Description:
Given a mapping f:S->T, where S,T are presumed vector spaces,
represented by the list of coordinate symbols S:=[u_1,..,u_m] and
T:=[x_1,..,x_n], this package "PullBack(S,T)" provides functions
that pull elements from DeRhamComplex(INT,T) back to elements
of DeRhamComplex(INT,S) by the usual rules of exterior calculus.
Instead of a mapping f, one can also provide a list of equations of
the form [x_1=x_1(u),..,x_n=x_n(u)].
pullBack : (VX->VX, DRCT) -> DRCS
pullBack(f,w) returns the pulled back form f*(w).
pullBack : (List Equation X, DRCT) -> DRCS
pullBack([x=f(u)],w) returns the pulled back form f*(w).
pullBack : (VX->VX, X) -> X
pullBack(f,g(x)) returns the expression g(f(u)).
basisForms : Record(bs:List DRCS, bt:List DRCT)
basisForms() returns a record containing the list of basis
forms of DeRhamComplex(INT,S) and DeRhamComplex(INT,T).