#8800: Doctest coverage of categories
--------------------------+-------------------------------------------------
Reporter: SimonKing | Owner: Simon King
Type: defect | Status: new
Priority: major | Milestone: sage-4.4.2
Component: categories | Keywords: categories doctests
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
--------------------------+-------------------------------------------------
Comment(by SimonKing):
Currently, the construction functors for free modules and for matrix
spaces have the same rank, but they do not commute and do not merge.
Hence, the following goes boom:
{{{
sage: from sage.categories.pushout import pushout
sage: pushout(QQ^3,MatrixSpace(QQ,3))
---------------------------------------------------------------------------
CoercionException Traceback (most recent call
last)
...
CoercionException: ('Ambiguous Base Extension', Vector space of dimension
3 over Rational Field, Full MatrixSpace of 3 by 3 dense matrices over
Rational Field)
}}}
I think this pushout should exist. But what should result?
1. ``MatrixSpace(QQ,3)^3^`` resp. ``FreeModule(MatrixSpace(QQ,3),3)``.
This is currently not possible, since ``MatrixSpace_generic`` has no
attribute ``is_commutative``.
2. ``MatrixSpace(QQ^3^,3)`` makes no sense, as ``QQ^3^`` is no ring.
3. ``MatrixSpace(QQ,27)`` makes not much sense, as I don't see coercion
maps.
So, probably it is solution number 1, which at least requires to implement
an ``is_commutative`` method, resp. to first test for the presence of such
method in ``FreeModule``. I think I'll go for it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8800#comment:20>
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