#11684: Obtaining coefficients of polynomials over finite fields is extremely
slow
----------------------------------------+-----------------------------------
Reporter: johanbosman | Owner: tbd
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.7.2
Component: performance | Keywords: polynomials, finite
fields
Work_issues: | Upstream: N/A
Reviewer: Simon King, Johan Bosman | Author: Johan Bosman, Simon
King
Merged: | Dependencies: #11685
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Old description:
> If we have a polynomial over a finite field and we want to obtain its
> coefficients, then there seems to be a lot of conversion overhead. It is
> a lot slower than multiplying such polynomials:
> {{{
> sage: K.<a> = GF(5^3)
> sage: P = PolynomialRing(K, 'x')
> sage: f = P.random_element(100)
> sage: timeit('f.list()')
> 5 loops, best of 3: 115 ms per loop
> sage: timeit('f * f')
> 625 loops, best of 3: 794 µs per loop
> }}}
>
> If, on the other hand, we do not use NTL, then we can obtain the
> coefficient list without any delays, though in that case multiplication
> is a lot slower:
> {{{
> sage: P = PolynomialRing(K, 'x', implementation='not NTL')
> sage: f = P(f)
> sage: timeit('f.list()')
> 625 loops, best of 3: 968 ns per loop
> sage: timeit('f * f')
> 25 loops, best of 3: 12.3 ms per loop
> }}}
> This performance issue occurs in both 4.7 and 4.7.1.rc1.
New description:
If we have a polynomial over a finite field and we want to obtain its
coefficients, then there seems to be a lot of conversion overhead. It is
a lot slower than multiplying such polynomials:
{{{
sage: K.<a> = GF(5^3)
sage: P = PolynomialRing(K, 'x')
sage: f = P.random_element(100)
sage: timeit('f.list()')
5 loops, best of 3: 115 ms per loop
sage: timeit('f * f')
625 loops, best of 3: 794 µs per loop
}}}
If, on the other hand, we do not use NTL, then we can obtain the
coefficient list without any delays, though in that case multiplication is
a lot slower:
{{{
sage: P = PolynomialRing(K, 'x', implementation='not NTL')
sage: f = P(f)
sage: timeit('f.list()')
625 loops, best of 3: 968 ns per loop
sage: timeit('f * f')
25 loops, best of 3: 12.3 ms per loop
}}}
This performance issue occurs in both 4.7 and 4.7.1.rc1.
----
Apply
1. [attachment:trac_11684_coefficient_speedup.patch]
1. [attachment:trac_11684_list_speedup.patch]
to the Sage library.
--
Comment(by leif):
Make someone review #11685... ;-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11684#comment:13>
Sage <http://www.sagemath.org>
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