D.4.3.3 depth

Procedure from library homolog.lib (see homolog_lib).

Usage:

depth(M,[I]); M module, I ideal

Return:

int,
- if called with 1 argument: the depth of M’=coker(M) w.r.t. the maxideal in the basering (which is then assumed to be local)
- if called with 2 arguments: the depth of M’=coker(M) w.r.t. the ideal I.

Note:

procedure makes use of KoszulHomology.

Example:

LIB "homolog.lib";
ring R=0,(x,y,z),dp;
ideal I=x2,xy,yz;
module M=0;
depth(M,I);   // depth(<x2,xy,yz>,Q[x,y,z])
→ 2
ring r=0,(x,y,z),ds;  // local ring
matrix M[2][2]=x,xy,1+yz,0;
print(M);
→ x,   xy,
→ 1+yz,0  
depth(M);     // depth(maxideal,coker(M))
→ 2
ideal I=x;
depth(M,I);   // depth(<x>,coker(M))
→ 0
I=x+z;
depth(M,I);   // depth(<x+z>,coker(M))
→ 1