#6136: (Combinatorial) Free modules: cleanup, abstraction into categories, and
functorial constructions
-------------------------------------------------------------+--------------
    Reporter:  nthiery                                       |         Owner:  
nthiery        
        Type:  enhancement                                   |        Status:  
closed         
    Priority:  major                                         |     Milestone:  
sage-4.3       
   Component:  algebra                                       |    Resolution:  
fixed          
    Keywords:  free modules, categories, tensor, direct sum  |   Work_issues:   
              
    Upstream:  N/A                                           |      Reviewer:  
Florent Hivert 
      Author:  Nicolas M. ThiƩry                             |        Merged:  
sage-4.3.alpha0
Dependencies:                                                |  
-------------------------------------------------------------+--------------
Changes (by ltw):

  * upstream:  => N/A


Old description:

> - 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://sagetrac.org/sage_trac/wiki/CategoriesRoadMap.

New description:

 - 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.

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6136#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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