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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);
intvec wr=1,3,5;
intvec ws=2,4;
int step=2;
prepMat(M,wr,ws,step);
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