ring s = 0,(x,y),ds;
poly f = y2-2x28y-4x21y17+4x14y33-8x7y49+x56+20y65+4x49y16;
LIB "classify.lib";
classify(f);
==> The singularity is R-equivalent to A[2260]: y2+x2261
==> Milnor number(f) = 2260
==> modality(f) = 0 ring r = 0,(x,y),dp;
poly f = fetch(s,f);
vdim(std(jacob(f)+f));
==> 2260 Hence, T_global(f) = T_local(f) (= local Milnor number for A_k-sing.). ring sh = 0,(x,y,z),dp;
poly f = fetch(s,f);
poly F = homog(f,z); // homogeneous polynomial defining C
ring r1 = 0,(y,z),dp;
map phi = sh,1,y,z;
poly g = phi(F); // F in affine chart (x=1)
vdim(std(jacob(g)+g));
==> 120
ring r2 = 0,(y,z),ds; // local ring at (1:0:0)
poly g = fetch(r1,g);
vdim(std(jacob(g)+g));
==> 120 We conclude: there is (precisely) 1 singularity of C at infinity.
(We have considered all points at infinity except (0:1:0) which is obviously not on C.) Topological type of the singularity at (1:0:0) : x⁹-y¹⁶ = 0.