Changes between Initial Version and Version 1 of Ticket #15647


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Timestamp:
01/19/14 20:41:43 (8 years ago)
Author:
nthiery
Comment:

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  • Ticket #15647

    • Property Type changed from task to defect
    • Property Summary changed from Docstring and probably also code is dangerously naive about duality to Make a proper distinction in the categories between dual and graded dual
  • Ticket #15647 – Description

    initial v1  
    4141
    4242I know this is not a big issue since the `dual()` of an algebra *is* a coalgebra in probably all cases in which `dual()` is implemented (not least because in the infinite-dimensional cases it usually means the graded dual). But at some point it probably *will* become an issue (maybe with the introduction of non-graded bases for graded algebras?), and I'm unhappy with the docstring lying in my face. And Nicolas suggests that "we need to clean up the distinction between dual and graded dual; this is not completely obvious to set the things up so that we can still share some code between the two".
     43
     44At this occasion, DualObjectsCategory should be made into a category
     45over base ring, if not just to inherit from the an_instance method.
     46Compare:
     47
     48{{{
     49sage: sage: ModulesWithBasis.Graded.an_instance()
     50Category of graded modules with basis over Rational Field
     51sage: ModulesWithBasis.DualObjects.an_instance()
     52Type error ...
     53}}}