#9713: Add toric Chow group
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   Reporter:  vbraun              |       Owner:  AlexGhitza
       Type:  enhancement         |      Status:  needs_work
   Priority:  major               |   Milestone:  sage-4.6.2
  Component:  algebraic geometry  |    Keywords:            
     Author:  Volker Braun        |    Upstream:  N/A       
   Reviewer:  Andrey Novoseltsev  |      Merged:            
Work_issues:                      |  
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Changes (by SimonKing):

  * status:  needs_review => needs_work


Comment:

 I am about to create a new ticket whose purpose is to implement the new
 parent and coercion framework not only for the base class
 `sage.modules.module.Module`, but also for the most derived classes. In
 that regard, it goes beyond what is done in the patches here.

 My to-be-created ticket will leave the `FGP_*` stuff almost unchanged. I
 suggest to include that to-be-created ticket as a new dependency
 (mentioning it in #9604 as well), so that the ticket here can concentrate
 on its "real" purpose, which is not coercion but toric Chow group.

 Then I would also provide a replacement of
 trac_9713_toric_chow_group.patch relative to the to-be-created ticket.

 A few words on trac_9713_toric_chow_group.patch: The `element_class`
 attribute of Parent is in fact a ''lazy'' attribute, that takes another
 attribute `Element` and mixes it with some category stuff before it turns
 `element_class` into an actual attribute. Hence, one should ''not''
 directly set `element_class` (which is done in the patch), but should
 provide an attribute `Element` instead.

 My to-be-created patch would actually preserve the `_element_class`
 (leading underscore) method, since it chooses the right element class and
 is already implemented for all sub-classes. But I would call it in the
 `__init__` method of the base class `sage.modules.module.Module` and
 assign its output to the `Element` attribute. In that way, it is most easy
 to implement the lazy `element_class` (no leading underscore) attribute as
 one is supposed to.

 Also, the `__call__` method of fgp morphisms should probably be replaces
 by `_call_`, `_call_with_args` and perhaps `pushforward` (likely depending
 on #10496).


 Best regards, Simon

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9713#comment:33>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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