Singular

D.4.20.12 radical

Usage:

radical(I[, l]); I ideal, l list (optional)
Optional parameters in list l (can be entered in any order):
0, "fullRad" -> full radical is computed (default)
1, "equiRad" -> equiRadical is computed
"KL" -> Krick/Logar algorithm is used
"SL" -> modifications by Laplagne are used (default)
"facstd" -> uses facstd to first decompose the ideal (default for non homogeneous ideals)
"noFacstd" -> does not use facstd (default for homogeneous ideals)

Return:

ideal, the radical of I (or the equiradical if required in the input parameters)

Note:

A combination of the algorithms of Krick/Logar (with modifications by Laplagne) and Kemper is used. Works also in positive characteristic (Kempers algorithm).

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 = radical(i);
pr;
==> pr[1]=z2-y
==> pr[2]=y2z+z3+2z2+2