On Sep 5, 10:14 am, Martin Albrecht <[EMAIL PROTECTED]>
wrote:
>
> sage: %time d2 = R(C._singular_().det())
> CPU times: user 0.04 s, sys: 0.01 s, total: 0.05 s
> Wall time: 0.15 s
This seems to scale very poorly with the number of variables.
Basically, it's impractical to compute determinants when there are
more than 4 variables.
Variables Time (seconds)
2 0.05
3 0.71
4 11.65
5 252.53
Sage commands / output:
sage: R.<a,b> = QQ[]
sage: C = random_matrix(R,8,8)
sage: %time d = R(C._singular_().det())
CPU times: user 0.05 s, sys: 0.00 s, total: 0.06 s
Wall time: 0.17 s
sage: R.<a,b,c> = QQ[]
sage: C = random_matrix(R,8,8)
sage: %time d = R(C._singular_().det())
CPU times: user 0.71 s, sys: 0.00 s, total: 0.72 s
Wall time: 1.54 s
sage: R.<a,b,c,d> = QQ[]
sage: C = random_matrix(R,8,8)
sage: %time d = R(C._singular_().det())
CPU times: user 11.65 s, sys: 0.05 s, total: 11.70 s
Wall time: 18.53 s
sage: R.<a,b,c,d,e> = QQ[]
sage: C = random_matrix(R,8,8)
sage: %time d = R(C._singular_().det())
CPU times: user 252.53 s, sys: 0.07 s, total: 252.60 s
Wall time: 329.91 s
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