#10963: More functorial constructions
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Reporter: nthiery |
Owner: stumpc5
Type: enhancement |
Status: needs_work
Priority: major |
Milestone:
Component: categories |
Resolution:
Keywords: |
Work issues: Reduce startup time by 5%. Avoid "recursion depth exceeded
(ignored)". Trivial doctest fixes.
Report Upstream: N/A |
Reviewers: Simon King
Authors: Nicolas M. Thiéry |
Merged in:
Dependencies: #11224, #8327, #10193, #12895, #14516, #14722, #13589 |
Stopgaps:
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Comment (by SimonKing):
I guess I should re-think the above in a more concrete scenario. Let `D =
DivisionRings()`. What do we do with `D.Finite()`?
Would we agree on `D = Rings().WithMultiplicativeInverses()`? I guess we
would obtain `Fields()=D.Commutative()`. So, as in the situation above, we
have the rule that if `WithMultiplicativeInverses()` is applied to
`Rings()`, then the additional axiom `Finite()` implies the axiom
`Commutative()`.
Hence, `D.Finite()` yields `Fields().Finite()=FiniteFields()`. To be
discussed: Should this be created dynamically, or should there be a hard-
coded separate class definition?
So, what would `FiniteFields().super_categories()` return by the algorithm
I presented above?
- Omit `Commutative`: We still have the axioms
`WithMultiplicativeInverses` and `Finite`, hence, we recover
`FiniteFields()`, which is thus a duplicate and not part of
`FiniteFields().super_categories()`.
- Omit `Finite`: The remaining axioms are those of commutative division
rings, which yields `Fields()`.
- Omit `WithMultiplicativeInverses`: Yields finite commutative rings.
So, `FiniteFields().super_categories()`returns `[Fields(),
Rings().Commutative().Finite()]`. Do you think this answer makes sense?
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10963#comment:51>
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