#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):
PS:
Replying to [comment:409 vbraun]:
> There is also a consistency issue about user-supplied axioms: They must
not induce further relations for the categories and axioms that Sage ships
with.
Why?
Imagine Wedderburn lived today. We wouldn't know that all finite division
rings are commutative. Hence, `Rings.Division().Finite()` and
`Fields().Finite()` would be distinct categories. Then, Wedderburn proves
his theorem. We add his theorem as a relation, and as a result we have a
new relation between previously distinct categories in Sage. I don't think
this would be a problem.
The only requirement: When adding a new axiom or a new basic category, the
original commutative monoid must be extended, and the ordering of the
enlarged monoid must be compatible with the ordering of the original
monoid; The original monoid must be an ordered submonoid of the enlarged
monoid. By this requirement, we can keep using the Gröbner basis we had
for the relations in the original monoid.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:411>
Sage <http://www.sagemath.org>
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