On 28/08/16 01:27, Waldek Hebisch wrote:
'cochainComplex' in ChainComplex is doing this. I think
that ATM it is best to delete this routine. Of course
if you later work out working version, then we can re-add it.
Agreed, I have removed this for now.
You could obtain cochain complex by transposing matrices,
or more generally applying HOM functor with fixed second
argument, but that is not the only way to produce
cochain complexes.
How can I work with hom functors in FriCAS?
Let me take a very simple example of a cochain complex.
Thank you very much for taking the time to do this, it will take me a
while to think through.
One initial thought is that I think, from what you are saying, that it
is best to continue to represent (co)chains as a sequence of matrices as
opposed to a sequence of functions?
As an experiment I took the simpler case of graph and used functions in
its Rep to make it more general and match theoretical definitions:
https://github.com/martinbaker/multivector/blob/master/graphexperiment.spad
This seems to work very well, although in the finite case, I am just
hiding a lookup table inside the function. Do you think there would be
any advantages in extending this to simplicial complexes and (co)chains?
What I am trying to achieve is to get code that can do practical
examples (like electrical circuits and linking up with existing
differential forms stuff) and also work and experiment with the
mathematical concepts like:
* Image and kernel of these mappings.
* ext and tor.
* morphisms between (co)chains, short and long exact sequences.
Do you think it is best to explore these concepts purely in terms of
matrix sequences?
Thanks,
Martin B
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