(Combinatorial) Free modules: cleanup, abstraction into categories, and functorial constructions

[nthiery]

• Deprecates CombinatorialAlgebra
• Abstracts some of the generic code into ModulesWithBasis, Algebras, ...
• Implements the functorial constructions: tensor and cartesian product
• Stronger type checking, use UniqueRepresentation
• Disabled dangerous conversions (see doc of _element_constructor), strict __contains__
• Naming cleanup: _term -> term, __repr__ -> _repr_, _element_class -> element_class
  _combinatorial_class -> _basis_keys
• New methods: monomial, sum_of_terms, sum_of_monomials, term_or_zero_if_none, from_vector,
  _repr_term, _repr_option_bracket
• More interesting an_element, using heuristics
• Handle non sortable objects in repr
• Implements sage.categories.poor_man_map.PoorManMap for maps between
  sets which are not modelled by parents.
• This is used to make term and sum_of_monomial into maps, with
  codomain and composition.

Depends on the category patches.
See http://trac.sagemath.org/sage_trac/wiki/CategoriesRoadMap.

CC: @sagetrac-sage-combinat

Component: algebra

Keywords: free modules, tensor, direct sum

Author: Nicolas M. Thiéry

Reviewer: Florent Hivert

Merged: sage-4.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/6136

[nthiery]

Attachment: categories-freemodule-6136-nt.patch.gz

[nthiery]

Reviewer: Florent Hivert

[nthiery]

Author: Nicolas M. Thiéry

[nthiery]

Attachment: trac_6136-categories-freemodule-nt.patch.gz

Adds TestSuite.run call, and implements equality for PoorManMap's. Apply only this one.

[hivert]

Last version of the file from combinat patch server.

[hivert]

comment:3

Attachment: trac_6136-categories-freemodule-nt.2.patch.gz

[hivert]

comment:4

Apply only the last patch trac_6136-categories-freemodule-nt.2.patch

Note: it breaks some doctests which are corrected in #6137 (See http://sagetrac.org/sage_trac/wiki/CategoriesRoadMap)

Ready to go.

Cheers,

Florent

[hivert]

Attachment: trac_6136-categories-freemodule-nt.3.patch.gz

Correct version

[mwhansen]

Merged: sage-4.3.alpha0