D.4.7.8 radicalEHV

Procedure from library primdec.lib (see primdec_lib).

Usage:

radicalEHV(i); i ideal.

Return:

ideal, the radical of i.

Note:

Uses the algorithm of Eisenbud/Huneke/Vasconcelos, which reduces the computation to the complete intersection case, by taking, in the general case, a generic linear combination of the input.
Works only in characteristic 0 or p large.

Example:

LIB "primdec.lib";
ring  r = 0,(x,y,z),dp;
poly  p = z2+1;
poly  q = z3+2;
ideal i = p*q^2,y-z2;
ideal pr= radicalEHV(i);
pr;
→ pr[1]=z2-y
→ pr[2]=y2z+yz+2y+2
→ pr[3]=y3+y2+2yz+2z