Singular
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Dealing with big matrices
http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2559
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Author:  lkastner [ Thu Oct 27, 2016 4:24 pm ]
Post subject:  Dealing with big matrices

I am trying to compute Ext for two ideals as follows:
Code:
ring R = 0,(x(1),x(2),x(3),x(4),x(5),x(6),x(7)),dp;
ideal I = x(4)*x(6)-x(3)*x(7),
x(5)^2-x(3)*x(7),
x(4)*x(5)-x(2)*x(7),
x(3)*x(5)-x(2)*x(6),
x(1)*x(5)-x(6)*x(7),
x(3)*x(4)-x(2)*x(5),
x(1)*x(4)-x(5)*x(7),
x(1)*x(3)-x(5)*x(6),
x(1)*x(2)-x(3)*x(7),
x(2)*x(5)*x(6)-x(3)^2*x(7),
x(2)^2*x(6)^2-x(3)^3*x(7);
qring Q = std(I);
ideal D1 = x(7)^2, x(6)*x(7), x(5)*x(7), x(4)*x(7), x(1)*x(7), x(1)*x(6), x(1)^2, x(6)^3, x(5)*x(6)^2, x(4)^3;
ideal D2 = x(7)^2, x(4)*x(7), x(4)^2, x(2)*x(5)*x(7), x(2)^2*x(7), x(1)^2*x(7), x(2)^2*x(4), x(2)^3*x(5), x(2)^4, x(1)^4;
ideal CminD2 = x(4)^2, x(2)*x(7)^2, x(2)*x(5)*x(7), x(2)*x(4)*x(7), x(2)*x(3)*x(7), x(2)^2*x(7), x(3)*x(7)^3, x(3)^2*x(7)^2, x(3)^3*x(7), x(5)*x(6)*x(7)^3, x(2)*x(3)^2*x(6)^2, x(6)^2*x(7)^4, x(3)^4*x(6)^2;
ideal CminD1 = x(6)^3, x(3)*x(6)^2*x(7), x(3)^2*x(6)^2, x(3)^2*x(6)*x(7)^2, x(3)^3*x(6)*x(7), x(3)^4*x(6), x(3)^3*x(7)^3, x(3)^4*x(7)^2, x(3)^5*x(7), x(3)^6, x(2)^2*x(3)*x(6)*x(7)^3, x(2)^2*x(3)^2*x(7)^4, x(2)^4*x(6)*x(7)^4, x(2)^4*x(3)*x(7)^5, x(2)^5*x(5)*x(7)^5, x(2)^6*x(7)^6;
LIB "homolog.lib";
module M = Ext(5,syz(D1),syz(CminD2));

after quite some time this fails with the following error:
Code:
> module M = Ext(5,syz(D1),syz(CminD2));
   ? internal error: creating matrix[7647][38235]
Singular : signal 11 (v: 4020):
current line:>>   return(matrix(B));<<
Segment fault/Bus error occurred at 7f6dd04a25a0 because of 10246 (r:1477505230)
please inform the authors
trying to restart...
   ? error occurred in or before matrix.lib::concat line 106: `   return(matrix(B));`
   ? wrong type declaration. type 'help matrix;'
   ? leaving matrix.lib::concat
   skipping text from `;` error at token `)`
   ? leaving matrix.lib::concat
Auf Wiedersehen.

I suspect this matrix that Singular is creating might be too big. Is this correct? If so, is there any possibility to rebuild Singular in a way such that it can handle bigger matrices?

Author:  hannes [ Mon Oct 31, 2016 5:44 pm ]
Post subject:  Re: Dealing with big matrices

See http://www.singular.uni-kl.de:8002/trac ... 40e01a/git

Author:  lkastner [ Thu Nov 03, 2016 8:05 pm ]
Post subject:  Re: Dealing with big matrices

Thank you. Unfortunately it seems that this was just covering up another bottleneck, which I (and probably you as well) already feared :( :
Code:
> module M = Ext(5,syz(D1),syz(CminD2));

Singular error: no more memory
System 11919379k:17115977k Appl 11905349k/14029k Malloc 11880467k/0k Valloc 38912k/14029k Pages 9453/275 Regions 19:103 Internal: 9808

halt 14

I will try to find a smaller example.

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