[sage-support] Re: freeze on 36*36 integer determinant

[P Purkayastha]

On 11/14/2012 06:54 AM, David Harvey wrote:

sage: version()
'Sage Version 4.8, Release Date: 2012-01-20'

sage: L = [-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, -9, 9, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 9, 1, 0, 0, 0,
0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, -9, 9, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 9, 0, 0,
0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 1, 0, 0, 0, 18, 3, 0, 0, 0, 0, -4, 0, 0,
0, 0, 0, 0, 0, 0, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -12, 0, 0, 0,
9, 1, 0, 0, -9, 18, 3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -18, 9,
0, 0, 6, 0, 0, 0, 0, 0, 0, -4, 2, -12, 0, 0, -9, 9, 1, 0, 0, -9, 18, 3,
0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -18, 9, 0, 0, 6, 0, 0, 0, 0, 0,
0, -4, 2, -12, 0, 0, -9, 9, 1, 0, 0, -9, 18, 3, 0, 2, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, -18, 9, 0, 0, 6, 0, 0, 0, 0, 0, 0, -4, 2, -12, 0, 0, -9,
9, 0, 0, 0, -9, 18, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0,
0, 6, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, -9, 0, 0, 0, 0, -9, 0, 0, 0, 2,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0,
0, 0, 0, -12, 0, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
9, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -12, 0, 0, 0, 1, -12, 0, 0, 0, 18,
3, 0, 0, 0, -4, 0, 0, 0, 0, -4, 1, 0, 0, 0, -18, 9, 0, 0, 0, 0, 0, -6,
-6, 0, 0, 0, 2, -12, 0, 0, 0, 1, -12, 0, 0, -9, 18, 3, 0, 0, 0, -4, 0,
0, 0, 0, -4, 1, 0, 0, 0, -18, 9, 0, 6, 0, 0, 0, -6, -6, 0, 0, -4, 2,
-12, 0, 0, 0, 1, -12, 0, 0, -9, 18, 3, 2, 0, 0, 0, 0, 0, 0, 0, -4, 1, 0,
0, 0, -18, 9, 0, 6, 0, 0, 0, -6, -6, 0, 0, -4, 2, -12, 0, 0, 0, 1, -12,
0, 0, -9, 18, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 1, 0, 0, 0, -18, 0, 0, 6,
0, 0, 0, -6, -6, 0, 0, -4, 2, 0, 0, 0, 0, 1, 0, 0, 0, -9, 0, 0, 2, 0, 0,
0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -4, -2,
0, 0, 0, 0, -12, 0, 0, 0, 3, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0,
9, 0, 0, -12, 0, 0, 0, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 1, -12, 0, 0, 18,
3, 0, 0, -4, 0, 0, -2, 0, 0, 0, -4, 1, 0, 0, -18, 9, 0, 0, -12, 0, 0, 0,
-6, -6, 0, 0, 0, 0, -2, 0, 0, 0, 1, -12, 0, -9, 18, 3, 0, 0, 0, 0, 0,
-2, 0, 0, 0, -4, 1, 0, 0, -18, 9, 0, 0, -12, 0, 0, 0, -6, -6, 0, 0, 0,
0, -2, 0, 0, 0, 1, -12, 0, -9, 18, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 1,
0, 0, -18, 0, 0, 0, -12, 0, 0, 0, -6, -6, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0,
0, -9, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12,
0, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, -12, 0, 0, 3, 0, -4, 0, 0, 0,
0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0,
0, -2, 0, 0, 1, -12, 0, 18, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 1, 0,
0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, -12, -9,
18, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 1, 0, 0, 0, 0, 0, 0, 0, -12,
0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, -9, 2, 0, 0, 0, 0, 0, 0, 0,
0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-2, 0, 0, -12, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -12, 18, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, -2, 0, 1, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -12, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

sage: M = Matrix(ZZ, 36, 36, L)
sage: M.rref().det()
1
sage: M.det()
[..... still no answer after one minute .....]

But sage is perfectly happy to compute an integer determinant of a random 
matrix of that size. So my matrix must be very special!

And it can compute the characteristic polynomial of my matrix almost instantly 
(so at least I can get on with my work).

Same thing happens with version 5.3 on sage.math.

Any ideas?

david

Looks like a bug in PARI?

sage: M._det_pari(flag=1)
-117676753399256830377657976750080

This works. But flag=0 doesn't work.


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