#10963: More functorial constructions
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Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: categories | Resolution:
Keywords: days54 | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King, Frédéric
Report Upstream: N/A | Chapoton
Branch: | Work issues:
public/ticket/10963 | Commit:
Dependencies: #11224, #8327, | eb7b486c6fecac296052f980788e15e2ad1b59e4
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506 |
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Comment (by SimonKing):
Replying to [comment:413 vbraun]:
> At that point I think its fine to require that Wedderburn has to restart
Sage.
Sure, that's what I meant.
> I don't quite understand how Polybori solves this, `Z/2Z` has only
idempotents but `Z/2Z[x]` does not.
`x^2=x` is intrinsic in polybori. That's why I think polybori is the right
tool for implementing the model: It provides an efficient Gröbner basis
implementation for rings generated by idempotents.
{{{
sage: P.<magma, additive_magma, ring, distributive,
finite,division,commutative> = BooleanPolynomialRing()
sage: magma*magma
magma
sage: R = P*[ring*division*finite-ring*division*commutative*finite, ring-
magma*additive_magma*distributive]
sage: R.groebner_basis()
[magma*additive_magma*distributive + ring, magma*ring + ring,
additive_magma*ring + ring, ring*distributive + ring,
ring*finite*division*commutative + ring*finite*division]
sage:
(magma*additive_magma*distributive*finite*division).reduce(R.groebner_basis())
ring*finite*division
sage: (ring*commutative*finite*division).reduce(R.groebner_basis())
ring*finite*division
}}}
I think this is more or less what we want.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:414>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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