#8327: Implement the universal cyclotomic field, using Zumbroich basis
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Reporter: nthiery | Owner:
Type: enhancement | Status:
needs_review
Priority: major | Milestone: sage-5.6
Component: number fields | Resolution:
Keywords: Cyclotomic field, Zumbroich basis | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Christian Stump, Simon King | Merged in:
Dependencies: #13765 | Stopgaps:
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Comment (by nbruin):
Replying to [comment:160 stumpc5]:
> Right, but there is a {{{__hash__}}} function returning the id, that's
why I wasn't quite sure... I now do test the hash by functionality, do you
think it's better now?
I guess for parents that would be OK, because they are unique. Otherwise,
most elements in sage can be equal to non-identical elements, so `id`
doesn't make for a valid hash on them. Using `id` as a hash isn't
consistent across sessions and won't survive pickling, but I'd hope that's
OK.
> Btw: As with the hash for elements in the !CyclotomicField, it does not
depend on the embedding of the parent. Do you think this might cause
problems?
No. The constant function would make a valid hash function. It would just
lead to horrible performance on dictionaries and sets.
> Finally, some functionalities become slower (e.g. matrix multiplication
where addition or multiplication of UCF elements are done multiple times).
Do you think, it is appropriate to cache (in the parent) the
multipliciation or addition in UCF.Elements ?
??? I hope you're not proposing caching by essentially building up
addition and multiplication tables. That'll be horrible on memory and
rarely result in speedup.
I'd say this is all optimization. First you want to have the functionality
in (that'll already be great!). Once you have a stable platform, you can
test where the bottlenecks are and optimize those, if required (with a
minimum of caching).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8327#comment:161>
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