#10963: Axioms and more functorial constructions
-------------------------------------+-------------------------------------
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, | f7e1a6bba29372bd197de88c9db3a6e866b001a2
#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:678 git]:
> Branch pushed to git repo; I updated commit sha1. New commits:
>
||[http://git.sagemath.org/sage.git/commit/?id=f7e1a6bba29372bd197de88c9db3a6e866b001a2
f7e1a6b]||{{{clarifying symmetry requirement on modules, which is
absolutely necessary seeing that __mul__ and __rmul__ are defined to be
the same thing}}}||
They are not defined the same way! And indeed:
{{{
sage: F = FreeAlgebra(QQ,2,'a')
sage: a0,a1 = F.gens()
sage: V = CombinatorialFreeModule(F, [1,2,3])
sage: v = V.an_element()
sage: (a0*v)*a1
2*a0*a1*B[1] + 2*a0*a1*B[2] + 3*a0*a1*B[3]
sage: a1*(a0*v)
2*a1*a0*B[1] + 2*a1*a0*B[2] + 3*a1*a0*B[3]
}}}
Beware that '__rmul__' in Python takes its arguments in reverse order
which can indeed be confusing.
I am not claiming that all modules implemented in Sage are clean in
this respect, but the category code by itself does not prevent non
symmetry.
With this in mind, I'd rather revert this piece of the last commit.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:682>
Sage <http://www.sagemath.org>
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