Singular

>   ring r = 0,(x,y,z),dp;
>  ideal J = x2+xy, y2-xz, x2+z2;
>  std(J);
_[1]=y2-xz
_[2]=xy-z2
_[3]=x2+z2
_[4]=yz2+z3
_[5]=xz2+yz2
_[6]=z4
> degBound;  // default value
0
>  degBound = 3;  // computation up to degree 3
>  std(J);
_[1]=y2-xz
_[2]=xy-z2
_[3]=x2+z2
_[4]=yz2+z3
_[5]=xz2+yz2

> option(prot);    // enable prot, to see that the computation is indeed shorter
>  degBound = 2;
>  std(J);
[1023:1]2(2)sss
product criterion:1 chain criterion:0
_[1]=y2-xz
_[2]=xy-z2
_[3]=x2+z2

> degBound =0;  // reset
>  std(J);               // the std computation is longer
[1023:1]2(2)sss3ss4(3)-s-5--
product criterion:6 chain criterion:1
_[1]=y2-xz
_[2]=xy-z2
_[3]=x2+z2
_[4]=yz2+z3
_[5]=xz2+yz2
_[6]=z4