#8212: arithmetic on GF(2^n) might be improved
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Reporter: zimmerma | Owner: zimmerma
Type: enhancement | Status: positive_review
Priority: minor | Milestone: sage-4.3.3
Component: basic arithmetic | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by zimmerma):
* status: needs_review => positive_review
Comment:
ok, I give a positive review for that ticket, and will review #8220
afterwards. Great work!
Paul
PS: a related question is the following over GF(2): when no irreducible
trinomial exists for a
given degree n, instead of using a pentanomial, one can use an "almost
irreducible" trinomial,
i.e., a trinomial x^n+d^+x^s^+1 which has an irreducible factor of degree
n. For example for
n=211, x^214^+x^103^+1 works. I tried this with QuotientRing, but it is
much slower:
{{{
R.<x> = PolynomialRing(GF(2),x)
T.<x> = QuotientRing(R, x^214 + x^103 + 1)
def bar(n):
f = x
for i in range(n):
f = f^2
return f
sage: %timeit bar(10000)
10 loops, best of 3: 191 ms per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8212#comment:9>
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