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Dear Simon,
>
> But I think either the result is wrong or Singular has a bug:
>> ideal J = I + x1^2 ;
>> matrix(std(quotient(J,x3))) == matrix(std(J));
> 0
On my computer this line gives 1, and I am quite sure that this is correct.
- --snip--
[EMAIL PROTECTED]:~$ /usr/local/sage/local/bin/Singular
SINGULAR / Development
A Computer Algebra System for Polynomial Computations / version 3-0-4
0<
by: G.-M. Greuel, G. Pfister, H. Schoenemann \ Nov 2007
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
> ring R = 0,(x1,x2,x3,x4,x5),dp;
> ideal I = x1*x4^2-x2*x5^2,
. x1^3*x3^3-x2^4*x4^2,
. x2*x4^8-x3^3*x5^6;
> matrix(std(quotient(I,x3))) == matrix(std(quotient(I,x3)));
1
> ideal J = I + x1^2;
> matrix(std(quotient(J,x3))) == matrix(std(quotient(J,x3)));
1
> quit
. ;
Auf Wiedersehen.
- --snap--
>
> Indeed, the quotient is bigger than J:
>> NF(std(quotient(J,x3)),std(J));
> _[1]=0
> _[2]=0
> _[3]=0
> _[4]=0
> _[5]=0
> _[6]=0
> _[7]=0
> _[8]=0
> _[9]=x1*x3^2*x5^8
> _[10]=x2*x3^2*x5^10
> _[11]=x3^5*x5^16
>> NF(std(J),std(quotient(J,x3)));
> _[1]=0
> _[2]=0
> _[3]=0
> _[4]=0
> _[5]=0
> _[6]=0
> _[7]=0
> _[8]=0
> _[9]=0
> _[10]=0
> _[11]=0
>
> One note on the situation in Sage.
>
> There is a slightly simpler definition of R:
> sage: R.<x1,x2,x3,x4,x5> = QQ[]
>
> For comparing the quotient, I don't know if by default it returns the
> reduced Gröbner basis. If not, then it has to be done explicitly
> before comparison. However, it wouldn't help here, because the ideals
> are different (according to Singular, at least).
>
> Cheers,
> Simon
>
>
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