Build. Blocks
Comb. Appl.
HCA Proving
Arrangements
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Classify
Coding
Deformations
Equidim Part
Existence
Finite Groups
Flatness
Genus
Hilbert Series
Membership
Nonnormal Locus
Normalization
Primdec
Puiseux
Plane Curves
Saturation
Solving
Space Curves
Spectrum
Equidimensional Part
Task: Calculate the equidimensional part of a variety via Ext-groups. Based on a free resolution of R/I,
and its dual,
we get
In particular, the equidimensional part of V={xz=yz=0} is given by the ideal:
This can be computed with SINGULAR using the following commands:
ring r = 0,(x,y,z),dp;
ideal I = xz,yz;
int i = 1;
resolution L = res(I, i+1);
module Im = transpose(L[i]);
module Ker = syz(transpose(L[i+1]));
module Ext = modulo(Ker,Im);
ideal Ann = quotient(Im,Ker);
Ann;
==> Ann[1]=z

Another possibility is to use the library homolog.lib:
LIB "homolog.lib";
module m=Ext_R(1,I);
quotient(m,freemodule(nrows(m)));
==> _[1]=z

Sao Carlos, 08/02 http://www.singular.uni-kl.de