#19929: GF(16) (without explicit variable name)
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-7.1
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
number fields | Work issues:
Keywords: | Commit:
Authors: | f96f09f848e3b9877aa50c4d4c26557e2181a9fd
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
public/19929 |
Dependencies: |
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Comment (by was):
Replying to [comment:9 roed]:
> Replying to [comment:7 was]:
> > Some points:
> >
> > - Background: `conway=True` would be absurd, because computing the
conway polynomial representation of a finite field is *incredibly* hard in
general.
>
> Yes, that's why we use pseudo-Conway polynomials, which drop the
condition of lexicographically least. They're still nontrivial to
compute, especially when the exponent has lots of divisors. But, as Dima
mentions, at least we have lookup tables for small values.
>
OK, I see. For Fpbar do you always use pseudo-Conway polynomials?
> > - I am **strongly** against #17569 without some new idea. In the
first benchmark I tried, arithmetic in Fpbar was **10 times** slower than
in GF (that was going to be the punchline of the sage worksheet I linked
to). Do you really want `GF(3^2, 'a')` to be 30 times faster than
`GF(3^2)`? I didn't think so. Even in David Roe's less unfavorable
example, there was a factor of 2-3 difference.
>
> Was the difference in field creation time or in arithmetic time?
Because the resulting fields of these two processes should be essentially
the same (with different defining polynomial perhaps).
>
I was testing arithmetic. However, I definitely made a mistake, because I
just tried again, and the timing for arithmetic is *identical*, just as
you say (which is very cool).
https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-
a18c706e8bcd/files/support/2016-01-21-114547-GF-speed.sagews
Thus I reverse my position: instead, I'm personally fine with #17569, with
the caveat that I'm a little nervous about the pseudo-Conway
polynomials....
Did anybody write up how Fpbar works somewhere? (I'm teaching
computational number theory and it would be fun to talk about this.)
--
Ticket URL: <http://trac.sagemath.org/ticket/19929#comment:10>
Sage <http://www.sagemath.org>
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