Singular
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Bug in minAssGTZ with real coefficients?
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2777		 Page 1 of 1
Author:  uffish [ Fri Aug 17, 2018 7:29 pm ]
Post subject:  Bug in minAssGTZ with real coefficients?
Hi all,

The following program causes Singular to receive a segmentation fault and exit.

(background: if you replace the coefficient ring to Q, the program works, but is very slow: the std in the beginning takes about an hour. I guessed that the reason was the appearnace of very large coefficients and tried to switch to real coefficients. It really made the program faster, but...)

Thanks,

ring R=(real,200),(a,b,c,d,e,f),dp;
poly pxb=a+b*d-a*b*d+c*e-a*c*e-b*c*d*e+a*b*c*d*e+c*d*f-a*c*d*f-b*c*d*f+a*b*c*d*f+b*e*f-a*b*e*f-b*c*e*f+a*b*c*e*f-b*d*e*f+a*b*d*e*f-c*d*e*f+a*c*d*e*f+2b*c*d*e*f-2a*b*c*d*e*f;
poly pxA=a+b-a*b+c-a*c-b*c+a*b*c;
poly pab=a*b+d-a*b*d+b*c*e-a*b*c*e-b*c*d*e+a*b*c*d*e+a*c*f-a*b*c*f-a*c*d*f+a*b*c*d*f+e*f-a*b*e*f-a*c*e*f-b*c*e*f+2a*b*c*e*f-d*e*f+a*b*d*e*f+a*c*d*e*f+b*c*d*e*f-2a*b*c*d*e*f;
poly pa2b=a*c+b*c*d-a*b*c*d+e-a*c*e-b*c*d*e+a*b*c*d*e+a*b*f-a*b*c*f+d*f-a*b*d*f-a*c*d*f-b*c*d*f+2a*b*c*d*f-a*b*e*f+a*b*c*e*f-d*e*f+a*b*d*e*f+a*c*d*e*f+b*c*d*e*f-2a*b*c*d*e*f;
poly dpxb0=1-b*d-c*e+b*c*d*e-c*d*f+b*c*d*f-b*e*f+b*c*e*f+b*d*e*f+c*d*e*f-2b*c*d*e*f;
poly dpxA0=1-b-c+b*c;
poly dpab0=b-b*d-b*c*e+b*c*d*e+c*f-b*c*f-c*d*f+b*c*d*f-b*e*f-c*e*f+2b*c*e*f+b*d*e*f+c*d*e*f-2b*c*d*e*f;
poly dpxb1=d-a*d-c*d*e+a*c*d*e-c*d*f+a*c*d*f+e*f-a*e*f-c*e*f+a*c*e*f-d*e*f+a*d*e*f+2c*d*e*f-2a*c*d*e*f;
poly dpxA1=1-a-c+a*c;
poly dpab1=a-a*d+c*e-a*c*e-c*d*e+a*c*d*e-a*c*f+a*c*d*f-a*e*f-c*e*f+2a*c*e*f+a*d*e*f+c*d*e*f-2a*c*d*e*f;
poly dpxb2=e-a*e-b*d*e+a*b*d*e+d*f-a*d*f-b*d*f+a*b*d*f-b*e*f+a*b*e*f-d*e*f+a*d*e*f+2b*d*e*f-2a*b*d*e*f;
poly dpxA2=1-a-b+a*b;
poly dpab2=b*e-a*b*e-b*d*e+a*b*d*e+a*f-a*b*f-a*d*f+a*b*d*f-a*e*f-b*e*f+2a*b*e*f+a*d*e*f+b*d*e*f-2a*b*d*e*f;
poly dpxb3=b-a*b-b*c*e+a*b*c*e+c*f-a*c*f-b*c*f+a*b*c*f-b*e*f+a*b*e*f-c*e*f+a*c*e*f+2b*c*e*f-2a*b*c*e*f;
poly dpxA3=0;
poly dpab3=1-a*b-b*c*e+a*b*c*e-a*c*f+a*b*c*f-e*f+a*b*e*f+a*c*e*f+b*c*e*f-2a*b*c*e*f;
poly dpxb4=c-a*c-b*c*d+a*b*c*d+b*f-a*b*f-b*c*f+a*b*c*f-b*d*f+a*b*d*f-c*d*f+a*c*d*f+2b*c*d*f-2a*b*c*d*f;
poly dpxA4=0;
poly dpab4=b*c-a*b*c-b*c*d+a*b*c*d+f-a*b*f-a*c*f-b*c*f+2a*b*c*f-d*f+a*b*d*f+a*c*d*f+b*c*d*f-2a*b*c*d*f;
poly dpxb5=c*d-a*c*d-b*c*d+a*b*c*d+b*e-a*b*e-b*c*e+a*b*c*e-b*d*e+a*b*d*e-c*d*e+a*c*d*e+2b*c*d*e-2a*b*c*d*e;
poly dpxA5=0;
poly dpab5=a*c-a*b*c-a*c*d+a*b*c*d+e-a*b*e-a*c*e-b*c*e+2a*b*c*e-d*e+a*b*d*e+a*c*d*e+b*c*d*e-2a*b*c*d*e;
ideal I=pab-pa2b,dpxb0-pxA*dpab0-dpxA0*pab,dpxb1-pxA*dpab1-dpxA1*pab,dpxb2-pxA*dpab2-dpxA2*pab,dpxb3-pxA*dpab3-dpxA3*pab,dpxb4-pxA*dpab4-dpxA4*pab,dpxb5-pxA*dpab5-dpxA5*pab;
option(prot);
LIB "primdec.lib";
list l=minAssGTZ(I);
Author:  hannes [ Sat Aug 25, 2018 4:52 pm ]
Post subject:  Re: Bug in minAssGTZ with real coefficients?
main incredience of minAssGTZ are Groebner bases,
which are not useful for inexact coeffcients, and factorization,
which is not implemented for inexact coeffcients:
in short: that cannot work.
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