#10963: Axioms and more functorial constructions
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Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: days54 | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King, Frédéric
Report Upstream: N/A | Chapoton
Branch: | Work issues: To be merged
public/ticket/10963-doc- | simultaneously with #15801
distributive | Commit:
Dependencies: #11224, #8327, | 72735421026786100353f4756b16874e73a9cfe6
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506, |
#15757, #15759, #16244 |
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Comment (by nthiery):
Replying to [comment:683 darij]:
> OK, I guess I don't understand the inner workings of `__mul__` and
`__rmul__`. Could you explain them to me?
I am not sure I can do better than:
https://docs.python.org/2/reference/datamodel.html
> If the Modules *category* is suited for nonsymmetric bimodules (without
having to manually override certain non-abstract methods in every
subcategory), then my edit on that file indeed should be reverted; thanks
for spotting that. But there still should be warning signs around this
class that it really allows for bimodules.
I reverted the change, and replaced it with a bunch of warnings.
> And I fear that the dispatching of Modules(field) to VectorSpaces(field)
is strictly speaking incorrect in this case.
Looking up wikipedia, VectorSpaces are actually defined as left-vector
spaces. So I guess that's not so bad. Really it's saying that you can
do all your usual linear algebra on the left or on the right at you
preference.
> EDIT: What about ModulesWithBasis in this case? Does this basis have to
be a basis for the left module structure or for the right one?
Both I guess. And in all practical use cases so far, multiplication on
the left and on the right are both more or less supposed to be
multiplication on the coefficients. In MuPAD we had started to explore
situations where this was not the case (e.g. with polynomials whose
monomials skew-commuted with their coefficients).
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:685>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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