A.27 Fast lexicographical GB
============================

Compute Groebner basis in lexicographical ordering
by using the FGLM algorithm (stdfglm)
and Hilbert driven Groebner (stdhilb).

The command stdfglm applies only for zero-dimensional ideals and
returns a reduced Groebner basis.

For the ideal below, stdfglm is more than 100 times
and stdhilb about 10 times faster than std.

  ring r =32003,(a,b,c,d,e),lp;
  ideal i=a+b+c+d, ab+bc+cd+ae+de, abc+bcd+abe+ade+cde,
          abc+abce+abde+acde+bcde, abcde-1;
  int t=timer;
  ideal j1=stdfglm(i);
  timer-t;
==> 0
  size(j1);   // size (no. of polys) in computed GB
==> 5
  t=timer;
  ideal j2=stdhilb(i);
  timer-t;
==> 0
  size(j2);   // size (no. of polys) in computed GB
==> 158
  // usual Groebner basis computation for lex ordering
  t=timer;
  ideal j0 =std(i);
  timer-t;
==> 1
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&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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