4.3 Critical points

The same computation which computes the Milnor resp. the Tjurina number, but with ordering dp instead of ds (i.e. in K[x1,...,xn] instead of Loc_(x)K[x1,...,xn]) gives:

We start with the ring r1 from section Section 4.1 Milnor and Tjurina and its elements.

The following will be realized below:

ring r1 = 32003,(x,y,z),ds;
int a,b,c,t=11,5,3,0;
poly f = x^a+y^b+z^(3*c)+x^(c+2)*y^(c-1)+x^(c-1)*y^(c-1)*z3+
         x^(c-2)*y^c*(y^2+t*x)^2;
timer=1;
ring r2 = 32003,(x,y,z),dp;
poly f=imap(r1,f);
ideal j=jacob(f);
vdim(std(j));
==> 536
vdim(std(j+f));
==> 195
timer=0;  // reset timer