Procedure from library primdec.lib (see primdec_lib).
primdec.lib
equidimMaxEHV(i); i ideal
ideal, the equidimensional component (of maximal dimension) of i.
Uses algorithm of Eisenbud, Huneke and Vasconcelos.
Example:
LIB "primdec.lib"; ring r = 0,(x,y,z),dp; ideal i=intersect(ideal(z),ideal(x,y),ideal(x2,z2),ideal(x5,y5,z5)); equidimMaxEHV(i); → _[1]=z