Here is an example of an ambitious development in Sage that overlaps
some your objectives for FriCAS:

http://sagemanifolds.obspm.fr/

http://trac.sagemath.org/ticket/14865


On 7 October 2014 13:15, Bill Page <[email protected]> wrote:
> On 7 October 2014 12:13, Kurt Pagani <[email protected]> wrote:
> ...
>> What I have in mind is first to complete this by functions like proj
>> (projection on homogeneous parts, subspaces), push forward/pull
>> back, interior product i_X and Lie derivative L_X which is possible
>> which little effort, second to have simplicial homology (e.g. a type Simplex)
>> then using FreeAbelianGroup(Simplex), defining boundaryOperator and
>> so on such that one can deal with integration of differential forms over
>> simplicial complexes (Stokes theorem, Hodge pairing and so on you
>> know). It's almost all there but one has to organize it. It should be a
>> teamwork to becoming really useful, so any suggestions welcome.
>
> Yes!  I think your orientation and objectives are perfect. I would be
> very glad to help where I can.
>

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