LIB "primdec.lib";
ring r=0,(x,y,z),ds;
ideal i=x^4-y*z^2,x*y-z^3,y^2-x^3*z;
qhweight(i);
==>
1,2,1
The ideal is quasihomogeneous. We can pass to a global ordering, which
is necessary for primary decomposition (see
limitations of this approach). ring rr=0,(x,y,z),dp;
ideal i=imap(r,i);
primdecSY(i); // Shimoyama-Yokoyama algorithm
==>
[1]:
[1]:
_[1]=x-z
_[2]=z2-y
[2]:
_[1]=x-z
_[2]=z2-y
[2]:
[1]:
_[1]=z3-xy
_[2]=x3+x2z+xz2+xy+yz
_[3]=x2z2+x2y+xyz+yz2+y2
[2]:
_[1]=z3-xy
_[2]=x3+x2z+xz2+xy+yz
_[3]=x2z2+x2y+xyz+yz2+y2
The curve seems to have 2 branches. We check this
using invariants of the singularity.
<-- Branches of an isolated space curve singularity
--> computed via Factorizing Gröbner