// define a new ring option(prot); ring r1 = 32003,(x,y,z),ds; r1; // define the polynomial 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; f; // calculate its Jacobi ideal ... ideal i=jacob(f); i; // ... and the standard basis of the Jacobi ideal ideal j=std(i); // calculate the Milnor number ... "The Milnor number of f(11,5,3) for t=0 is", vdim(j); // ... and the Tjurina number j=i+f; j=std(j); "The Tjurina number of f(11,5,3) for t=0 is", vdim(j); // repeat everything for t=1 t=1; 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; ideal i1=jacob(f); ideal j1=std(i1); "The Milnor number of f(11,5,3) for t=1 is", vdim(j1); "The Tjurina number of f(11,5,3) for t=1 is", vdim(std(j1+f));