D.6.3.9 arnoldMorseSplit

Usage:

arnoldMorseSplit(f); f poly

Assume:

base ring is local, f in maxideal(2) has isolated critical point at 0

Compute:

result of Splitting Lemma applied to f

Return:

polynomial g in maxideal(3) right equivalent to f

LIB "arnoldclassify.lib";
ring r=0,(x,y,z),ds;
export r;
poly f=(x2+3y-2z)^2+xyz-(x-y3+x2*z3)^3;
poly g=arnoldMorseSplit(f);
g;
==> 3/2x2y-y3