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D.4.22.16 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, 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.
- 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
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