On 8 October 2014 20:26, Kurt Pagani <[email protected]> wrote:
>
> Some more bricks ...
> attached is a first draft of the functions which IMO should be sufficient.
Thanks!
> Pull-back/push-forward have to be presumably in a higher-level domain as we
> need a mapping F:X -->Y between two DFORM domains (??)
>
We need a mapping between manifolds, e.g. between the set of
independent variables of one DFORM into the independent variables of
another DFORM.
My first thought is that maybe pullback and pushforward should be
exports of a package that is parameterized by a list of expressions.
Something sort of like this?
DiffForms_functions(R,X:DiffFormCat(R), m:List(R), Y:DiffFormCat(R)): with
pullback: Y -> X
pushforward: X -> Y
==
s:=matrix map(x+->[differentiate(y, x) for y in m], generators()$X )
termPull: (R,X) -> X
termPull(r, e) ==
pullback(g:Y):X ==
g = 0 => 0
termPull(leadingCoefficient g, leadingBasisTerm g) + pullback(reductum g)
termPush: (R,X) -> Y
termPush(r,e) ==
pushforward(f:X):Y ==
f = 0 => 0
termPush(leadingCoefficient f, leadingBasisTerm f) + pushback(reductum f)
--
DiffFormCat(R) is a category defining the exports of DiffForm.
Bill Page.
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