Dear Thomas,
On Dec 2, 10:11 pm, Thomas Kahle <[EMAIL PROTECTED]> wrote:
<snip>
> std(quotient(I,x3))
> std(I)
>
> *** Here I compare the output manually since I dont know hot to compare
> ideals in singular ****
As much as I know, by default Singular's std computes the *reduced*
Gröbner basis. So, at least the list of generators is the same. And
then you can compare it by typecast to a matrix:
> matrix(std(quotient(I,x3))) == matrix(std(I));
1
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
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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