Singular

D.7.5.1 prepMat

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

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)