D.4.7.11 equidim

Procedure from library primdec.lib (see primdec_lib).

Usage:

equidim(i) or equidim(i,1) ; i ideal

Return:

list of equidimensional ideals a[1],...,a[s] with:
- a[s] the equidimensional locus of i, i.e. the intersection of the primary ideals of dimension of i
- a[1],...,a[s-1] the lower dimensional equidimensional loci.

Note:

An embedded component q (primary ideal) of i can be replaced in the decomposition by a primary ideal q1 with the same radical as q.
equidim(i,1) uses the algorithm of Eisenbud/Huneke/Vasconcelos.

Example:

LIB "primdec.lib";
ring  r = 32003,(x,y,z),dp;
ideal i = intersect(ideal(z),ideal(x,y),ideal(x2,z2),ideal(x5,y5,z5));
equidim(i);
→ [1]:
→    _[1]=z4
→    _[2]=y5
→    _[3]=x5
→    _[4]=x3z3
→    _[5]=x4y4
→ [2]:
→    _[1]=yz
→    _[2]=xz
→    _[3]=x2
→ [3]:
→    _[1]=z