5.1.95 preimage
---------------

Syntax:
preimage ( ring_name, map_name, ideal_name )

preimage ( ring_name, ideal_expression, ideal_name )
Type:
ideal
Purpose:
returns the preimage of an ideal under a given map.


The second argument has to be a map from the basering to the given ring
(or an ideal defining such a map),
and the ideal has to be an ideal in the given ring.
Note:
To compute the kernel of a map, the preimage of zero has to be determined.
Hence there is no special command for computing the kernel of a map in
SINGULAR.
Example:
  ring r1=32003,(x,y,z,w),lp;
  ring r=32003,(x,y,z),dp;
  ideal i=x,y,z;
  ideal i1=x,y;
  ideal i0=0;
  map f=r1,i;
  setring r1;
  ideal i1=preimage(r,f,i1);
  i1;
==> i1[1]=w
==> i1[2]=y
==> i1[3]=x
  // the kernel of f
  preimage(r,f,i0);
==> _[1]=w
See
ideal;
map;
ring.
<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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