Singular

You want to compute the critical values of a [b]polynomial mapping[/b]
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.

[code]
> 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;
> eliminate(i,xyz);
_[1]=64t3+176t2-24t-665
[/code]

This polynomial is irreducible over Q.
There are three isolated singularities each with Milnor number 1
[code]
> ring rdp =0,(x,y,z),dp;
> poly f = 3*x^2-3*x*y^2+y^3-3*y+3*z^2;
> vdim(std(jacob(f)));
3
[/code]

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

[code]
> setring r;
> primdecSY(i);
[1]:
[1]:
_[1]=64t3+176t2-24t-665
_[2]=z
_[3]=575y-16t2+248t+80
_[4]=1150x-144t2-68t+145
[/code]

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