On Thursday 11 September 2008, Martin Albrecht wrote:
> > Did you check how fast singular is for the Lewis-Wester determinants?
>
> Are these some kind of benchmark(et)ing examples? Where can I find the
> input matrices? Sorry, never heard that name before ... which isn't that
> surprising, since I never thought about this computation before the bug
> report on [sage-support]. :-)
>
> Cheers,
> Martin
Okay, found it:
# the original benchmark is over ZZ, but that's really slow in Sage
---------------
P.<x1,x2,x3,x4,x5> = PolynomialRing(QQ, 5)
M = MatrixSpace(P, 26)
w = [ [ 1, 1, 1, 7, x4, 12, x3, 17, x2, 22, x1 ],
[ 2, 2, 1, 8, x4, 13, x3, 18, x2, 23, x1 ],
[ 3, 3, 1, 9, x4, 14, x3, 19, x2, 24, x1 ],
[ 4, 4, 1, 10, x4, 15, x3, 20, x2, 25, x1 ],
[ 5, 5, 1, 26, 1, 1, 0, 1, 0, 1, 0 ],
[ 6, 2, x5, 6, 1, 12, x3, 17, x2, 22, x1 ],
[ 7, 3, x5, 7, 1, 13, x3, 18, x2, 23, x1 ],
[ 8, 4, x5, 8, 1, 14, x3, 19, x2, 24, x1 ],
[ 9, 5, x5, 9, 1, 15, x3, 20, x2, 25, x1 ],
[10, 10, 1, 26, 1, 1, 0, 1, 0, 1, 0 ],
[11, 2, x5, 7, x4, 11, 1, 17, x2, 22, x1 ],
[12, 3, x5, 8, x4, 12, 1, 18, x2, 23, x1 ],
[13, 4, x5, 9, x4, 13, 1, 19, x2, 24, x1 ],
[14, 5, x5, 10, x4, 14, 1, 20, x2, 25, x1 ],
[15, 15, 1, 26, 1, 1, 0, 1, 0, 1, 0 ],
[16, 2, x5, 7, x4, 12, x3, 16, 1, 22, x1 ],
[17, 3, x5, 8, x4, 13, x3, 17, 1, 23, x1 ],
[18, 4, x5, 9, x4, 14, x3, 18, 1, 24, x1 ],
[19, 5, x5, 10, x4, 15, x3, 19, 1, 25, x1 ],
[20, 20, 1, 26, 1, 1, 0, 1, 0, 1, 0 ],
[21, 2, x5, 7, x4, 12, x3, 17, x2, 21, 1 ],
[22, 3, x5, 8, x4, 13, x3, 18, x2, 22, 1 ],
[23, 4, x5, 9, x4, 14, x3, 19, x2, 23, 1 ],
[24, 5, x5, 10, x4, 15, x3, 20, x2, 24, 1 ],
[25, 25, 1, 26, 1, 1, 0, 1, 0, 1, 0 ],
[26, 1, x5, 6, x4, 11, x3, 16, x2, 21, x1 ] ]
m = M.matrix()
for i in range(0,26):
for j in range(0,5):
m[i, (w[i][2*j+1])-1] = w[i][2*j+2]
tinit = cputime()
qqq = m.determinant()
print "M1 =", cputime(tinit), "(SAGE)";
del P, M, w, m, qqq
---------------
This takes 0.001 seconds on my notebook, Magma is in the same ballpark, i.e.
the example is way too small for a comparison.
M2 (again, over QQ) takes 2.2 seconds in Sage 3.1.2.rc2 and 2.02 seconds in
Magma (over ZZ).
Cheers,
Martin
Cheers,
Martin
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
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