Singular

Hi,

i want to compute the critical values of different polynoms in three variables (x,y,z). Usually the following steps work really fine:

LIB "primdec.lib";
ring r=0,(x,y,z,t),dp;
poly f = 3*x^2-3*x*y^2+y^3-3*y+3*z^2;
ideal i = jacob(f),f-t;
primdecGTZ(i);

Normally i get something, that starts with an expression like:

t=a,

so i can see the critical value is a.
In the example case from above, i get:

t^4+24*t^2-48.

how can i determine the critical values in this case? Do i have to change the ordering? Or does somebody have a better idea, how to compute the critical values?
Please help!

Greetings,
default1

You want to compute the critical values of a polynomial mapping
from C^3-> C.

The primary decomposition is not what you really need to compute.
You have just to eliminate the variables x,y,z from the ideal.



This polynomial is irreducible over Q.
There are three isolated singularities each with Milnor number 1


The coordinates (x,y,z) expressed in terms by t
can be read off from the primdec result.