A.6 Parameters
==============

Let us deform the above ideal now by introducing a parameter t
and compute over the ground field Q(t).
We compute the dimension at the generic point,
i.e.,
$dim_{Q(t)}Q(t)[x,y]/j$.
(This gives the
same result as for the deformed ideal above. Hence, the above small
deformation was "generic".)

For almost all
$a \in Q$
this is the same as
$dim_Q Q[x,y]/j_0$,
where
$j_0=j|_{t=a}$.

  ring Rt = (0,t),(x,y),lp;
  Rt;
==> //   characteristic : 0
==> //   1 parameter    : t 
==> //   minpoly        : 0
==> //   number of vars : 2
==> //        block   1 : ordering lp
==> //                  : names    x y 
==> //        block   2 : ordering C
  poly f = x5+y11+xy9+x3y9;
  ideal i = jacob(f);
  ideal j = i,i[1]*i[2]+t*x5y8;  // deformed ideal, parameter t
  vdim(std(j));
==> 40
  ring R=0,(x,y),lp;
  ideal i=imap(Rt,i);
  int a=random(1,30000);
  ideal j=i,i[1]*i[2]+a*x5y8;  // deformed ideal, fixed integer a
  vdim(std(j));
==> 40

<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>.
</font>

</body>
</html>
