Singular

D.4.10.8 flatteningStrat

Usage:

flatteningStrat(M); M module

Return:

list of ideals.
The list entries L[1],...,L[r] describe the flattening stratification of M'=coker(M): setting L[0]=0, L[r+1]=1, the flattening stratification is given by the open sets Spec(A/V(L[i-1])) \ V(L[i]), i=1,...,r+1 (A = basering).

Note:

for more information see the book 'A Singular Introduction to Commutative Algebra' (by Greuel/Pfister, Springer 2002).

LIB "homolog.lib";
ring A = 0,x(0..4),dp;
// presentation matrix:
matrix M[2][4] = x(0),x(1),x(2),x(3),x(1),x(2),x(3),x(4);
list L = flatteningStrat(M);
L;
==> [1]:
==>    _[1]=x(3)^2-x(2)*x(4)
==>    _[2]=x(2)*x(3)-x(1)*x(4)
==>    _[3]=x(1)*x(3)-x(0)*x(4)
==>    _[4]=x(2)^2-x(0)*x(4)
==>    _[5]=x(1)*x(2)-x(0)*x(3)
==>    _[6]=x(1)^2-x(0)*x(2)
==> [2]:
==>    _[1]=x(4)
==>    _[2]=x(3)
==>    _[3]=x(2)
==>    _[4]=x(1)
==>    _[5]=x(0)