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D.4.20.16 equidim

Procedure from library primdec.lib (see primdec_lib).

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

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, except I is unit ideal. - a[1],...,a[s-1] the lower dimensional equidimensional loci. If I is the unit ideal, a list containing the unit ideal as a[1] is returned.

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.

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));
==> [1]:
==>    _[1]=z4
==>    _[2]=y5
==>    _[3]=x5
==>    _[4]=x3z3
==>    _[5]=x4y4
==> [2]:
==>    _[1]=yz
==>    _[2]=xz
==>    _[3]=x2
==> [3]:
==>    _[1]=z