slimgb bug over the integers

[Simon King]

Apparently, Singular does not guarantee that slimgb works over the integers. Nevertheless, I think the following small example should work.

> ring R = integer, (x,y), dp;
// ** You are using coefficient rings which are not fields.
// ** Please note that only limited functionality is available
// ** for these coefficients.
// **
// ** The following commands are meant to work:
// ** - basic polynomial arithmetic
// ** - std
// ** - syz
// ** - lift
// ** - reduce
> ideal i = 4*x^2*y^2+2*x*y^3+3*x*y,2*x^2+x*y,2*y^2;
> ideal G1 = std(i); G1;
G1[1]=2y2
G1[2]=3xy
G1[3]=2x2+xy
G1[4]=xy2
G1[5]=x2y
> ideal G2 = slimgb(i); G2;
G2[1]=2y2
G2[2]=2x2+xy
G2[3]=3xy

Why do I believe that std is right and slimgb is wrong?

> NF(G2,G1);
_[1]=0
_[2]=0
_[3]=0
> NF(G1,G2);
_[1]=0
_[2]=0
_[3]=0
_[4]=xy2
_[5]=x2y

Do x*y^2 and x^2*y really belong to the ideal? Yes, they do!

> y*i[1] - 2*y^3*i[2] - x*i[3];
xy2
> -x*i[1] + 2*y*i[2] + (2*x^3+x^2*y-x)*i[3];
x2y

[hannes]

if the coefficient does not form a field, a different, at least extended algorithm has to be used - it is not only a question of the arithmetic. Therefore, calling slimgb in the case above yields (now) an error.