D.6.4.1 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)