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=xy2-y J=x2y-x J=y4-x J=x4-yis chosen as a non-zerodivisor in and is
==> _=xy2-y _=y4-x2y _=x3y-y3 _=x4-yTyping NN; we get as result the following ideal defining the non-normal locus (equal to , but with different generators):
==> NN=y3-x2 NN=xy2-y NN=x2y-x NN=x3-y2