D.6.4.2 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)
<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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