Categories for FreeModule's

[nthiery]

Put FreeModule? in the category ModulesWithBasis?(), and implement all the related methods. This should make FreeModule? and CombinatorialFreeModule? compatible and consistent.

There might be some compatibility issues to handle.

[tscrim]

I put VectorSpaces in the category ModulesWithBasis because FreeModules is already an alias for ModulesWithBasis. There doesn't seem to be any compatibility issues that I noticed.

[nthiery]

Thanks for working on this! A big part of the ticket is in "and implement all the related methods". The point is to have all the zillion little utilities of ModulesWithBasis? (term, monomial, sum_of_terms, leading_term, iter, ...) also work for plain FreeModules?.

My guess is that the main incompatibility that needs to be discussed is about iter. Indeed, as far as I remember:

      for x in v:
          ...

iterates over pairs for "Combinatorial" free modules(like a iteritems of dictionaries), whereas it iterates over coefficients for plain free modules. So we have to decide on which interface we want and how to handle backward compatibility.

Cheers

Granted: ModulesWithBasis? should have appropriate abstract methods and tests so that, if an implementation does not provide the required methods, the testsuite barks.

[ncohen]

As the patchbot indicates, this patch does not pass tests. Though it seems good otherwise :-P

Nathann

[nthiery]

See also ​http://trac.sagemath.org/ticket/18310#comment:13 for a few issues we will need to double check for.

[tscrim]

There is still a minor issue with __iter__, however we can avoid those in code by using monomial_coefficients() which give the consistent behavior. I also think we can leave the issues raised in #18310 to be handled there and once submodule supports coordinate rings...

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Last 10 new commits:

​4a9fd81	Trac 18411: merge Sage 6.10.beta0
​525d038	Trac 18411: Fix doctest in colored_permutations.py
​41af762	Trac 18411: pass keywords in __call__
​6e27dde	Trac 18411: merge sage-6.10.beta1
​b21396c	Merge branch '18411' into HEAD
​b32e479	further changes (mostly doc)
​dbb5789	Further fixes
​e2fb14a	remove _test_keytype since submodules of free modules are currently failing it
​96004df	Darij...
​d94f997	Some last compatibility issues with modules with basis (hopefully).

[darij]

LGTM (it is really just the last commit; everything else is from #18066).

The heisenberg.py part of #16820 relies on this patch, so that'll serve as a doctest.

[vbraun]

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