Singular Manual: prepMat

| #### D.7.5.1 prepMat Procedure from library `stratify.lib` (see stratify_lib). Usage: prepMat(M,wr,ws,step); where M is a matrix, wr is an intvec of size ncols(M), ws an intvec of size nrows(M) and step is an integer Return: 2 lists of submatrices corresponding to the filtrations specified by wr and ws: the first list corresponds to the list for the filtration of AdA, i.e. the ranks of these matrices will be the r_i, the second one to the list for the filtration of L, i.e. the ranks of these matrices will be the s_i Note: * the entries of the matrix M are M_ij=delta_i(x_j), * wr is used to determine what subset of the set of all dx_i is generating AdF^l(A): if (k-1)*step <= wr[i] < k*step, then dx_i is in the set of generators of AdF^l(A) for all l>=k and the i-th column of M appears in each submatrix starting from the k-th * ws is used to determine what subset of the set of all delta_i is generating Z_l(L): if (k-1)*step <= ws[i] < k*step, then delta_i is in the set of generators of Z_l(A) for l < k and the i-th row of M appears in each submatrix up to the (k-1)th * the entries of wr and ws as well as step should be positive integers Example:
    LIB "stratify.lib";
    ring r=0,(t(1..3)),dp;
    matrix M[2][3]=0,t(1),3*t(2),0,0,t(1);
    print(M);
    ==> 0,t(1),3*t(2),
    ==> 0,0,   t(1)
    intvec wr=1,3,5;
    intvec ws=2,4;
    int step=2;
    prepMat(M,wr,ws,step);
    ==> [1]:
    ==>    [1]:
    ==>       _[1,1]=0
    ==>       _[2,1]=0
    ==>    [2]:
    ==>       _[1,1]=0
    ==>       _[1,2]=t(1)
    ==>       _[2,1]=0
    ==>       _[2,2]=0
    ==>    [3]:
    ==>       _[1,1]=0
    ==>       _[1,2]=t(1)
    ==>       _[1,3]=3*t(2)
    ==>       _[2,1]=0
    ==>       _[2,2]=0
    ==>       _[2,3]=t(1)
    ==> [2]:
    ==>    [1]:
    ==>       _[1,1]=0
    ==>       _[1,2]=t(1)
    ==>       _[1,3]=3*t(2)
    ==>       _[2,1]=0
    ==>       _[2,2]=0
    ==>       _[2,3]=t(1)
    ==>    [2]:
    ==>       _[1,1]=0
    ==>       _[1,2]=0
    ==>       _[1,3]=t(1)

User manual for Singular version 4.4.1, 2025, generated by texi2html.