5.1.22 eliminate
----------------

Syntax:
eliminate ( ideal_expression, product_of_ring_variables)

eliminate ( module_expression, product_of_ring_variables)

eliminate ( ideal_expression, product_of_ring_variables, intvec_hilb )

eliminate ( module_expression, product_of_ring_variables, intvec_hilb )
Type:
the same as the type of the first argument
Purpose:
eliminates variables occurring as factors of the second argument from an
ideal, resp. module, by intersecting it with the subring not containing
these variables.

eliminate does not need a special ordering nor a standard basis as input.
Note:
Since elimination is expensive, for homogeneous input it might be useful
first to compute the Hilbert function of the ideal (first
argument) with a fast ordering (e.g., dp). Then make use of it to speed
up the computation: a Hilbert-driven elimination uses the intvec
provided as the third argument.
Example:
  ring r=32003,(x,y,z),dp;
  ideal i=x2,xy,y5;
  eliminate(i,x);
==> _[1]=y5
  ring R=0,(x,y,t,s,z),dp;
  ideal i=x-t,y-t2,z-t3,s-x+y3;
  eliminate(i,ts);
==> _[1]=y2-xz
==> _[2]=xy-z
==> _[3]=x2-y
  intvec v=hilb(std(i),1);
  eliminate(i,ts,v);
==> _[1]=y2-xz
==> _[2]=xy-z
==> _[3]=x2-y
See
hilb;
ideal;
module;
std.
<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>
