Singular Manual: depth

| #### D.4.11.4 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 ideal generated by the variables in the basering (the maximal ideal, if the ring is local) - if called with 2 arguments: the depth of M'=coker(M) w.r.t. the ideal I. Note: Not checked: if I*M'==M', depth is infinity. 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
    M=[1];
    depth(M);  // depth(0)
    ==> 3
    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

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