Let us start with a plane -singularity given by in , which can easily be done by hand.

We get , as test ideal and as a non-zerodivisor of . Now

Let us compute the nonnormal locus of two transversal cusps in the
plane, using the procedure ` nnlocus` from ` normal.lib` in SINGULAR.

ring S = 0,(x,y),dp; ideal I = (x2-y3)*(x3-y2); ideal NN = nnlocus(I);The radical of the singular locus is computed as

==> J[1]=xy2-y J[2]=x2y-x J[3]=y4-x J[4]=x4-yis chosen as a non-zerodivisor in and is

==> _[1]=xy2-y _[2]=y4-x2y _[3]=x3y-y3 _[4]=x4-yTyping

==> NN[1]=y3-x2 NN[2]=xy2-y NN[3]=x2y-x NN[4]=x3-y2