#16718: Create a category for Cartesian products of groups
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-6.3
Component: group theory | Resolution:
Keywords: cartesian | Merged in:
product, generators, categories | Reviewers: Nathann Cohen
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 8db0f5138914ddd7a9da9e2a57d26c8f45091c93
public/groups/cartesian_product_category-16718| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by tscrim):
* status: needs_review => positive_review
* reviewer: => Nathann Cohen
Comment:
Replying to [comment:12 ncohen]:
> It is also more costly. Really it would all be okay if this was compiled
code, but I keep thinking of what happens when a line like
> {{{
> if all(M.monoid_generators() in FiniteEnumeratedSets()
> or isinstance(M.monoid_generators(), (tuple, list)) for M in F):
> ret = [lift(i, gen) for i,M in enumerate(F) for gen in
M.monoid_generators()]
> }}}
> is executed and it really is awful... `monoid_generators()` is called
once or twice per factor, the caching mechanism does its job to return the
pre-computed generators if necessary, `FiniteEnumeratedSets()` is also
created at each turn and because it is a `UniqueRepresentation` of
something there is a lookup going on there too....
I changed it to create `FiniteEnumeratedSets()` outside of the loop (its a
micro-optimization: the result is cached and the number of factors is
small). However `*_generators` is very rarely to be called twice and not
short-circuit the `all` (because `*_generators` should return a `Family`),
and it should be cached.
> Don't know ... Then you would have stuff which is detected as
`FiniteEnumeratedSet` but does not inherit the methods... Well...
Another question for me to ask Nicolas next time I see him.
> Okay. Despite the fact that I really do not like categories and probably
never will, thank you for fixing that, your patch does the job. Can you
fix the broken doctests ? It can be set to `positive_review` afterwards.
Thanks Nathann!
--
Ticket URL: <http://trac.sagemath.org/ticket/16718#comment:16>
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