#### D.7.5.2 stratify

Procedure from library `stratify.lib` (see stratify_lib).

Usage:
  stratify(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:
  list of lists, each entry of the big list corresponds to one locally closed set and has the following entries:
  1) intvec giving the corresponding rs-vector
  2) ideal determining the closed set
  3) list d of polynomials determining the open set D(d[1]) empty list if there is more than one open set
  4-n) lists of polynomials determining open sets which all lead to the same rs-vector

Note:
  * ring ordering should be global, i.e. the ring should be a polynomial ring
  * 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
  * 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
  * the entries of wr and ws as well as step should be positive integers
  * the filtrations have to be known, no sanity checks concerning the filtrations are performed !!!

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);
    intvec wr=1,3,5;
    intvec ws=2,4;
    int step=2;
    stratify(M,wr,ws,step);
    ==> [1]:
    ==>    [1]:
    ==>       0,0,0,0
    ==>    [2]:
    ==>       _[1]=t(2)
    ==>       _[2]=t(1)
    ==>    [3]:
    ==>       [1]:
    ==>          1
    ==> [2]:
    ==>    [1]:
    ==>       0,1,0,1
    ==>    [2]:
    ==>       _[1]=t(1)
    ==>    [3]:
    ==>       [1]:
    ==>          t(2)
    ==>       [2]:
    ==>          t(2)
    ==> [3]:
    ==>    [1]:
    ==>       1,2,1,2
    ==>    [2]:
    ==>       _[1]=0
    ==>    [3]:
    ==>       [1]:
    ==>          t(1)
    ==>       [2]:
    ==>          t(1)

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