5.1.52 interred
---------------
Syntax:
interred ( ideal_expression )

interred ( module_expression )
Type:
the same as the input type
Purpose:
interreduces a set of polynomials/vectors.


input: $f_1,\dots,f_n$


output: $g_1,\dots,g_s$ with $s \leq n$ and the properties
* $(f_1,\dots,f_n) = (g_1,\dots,g_s)$
* $L(g_i)\neq L(g_j)$ for all $i\neq j$
* in the case of a global ordering (polynomial ring):


$L(g_i)$
 does not divide m for all monomials m of
$\{g_1,\dots,g_{i-1},g_{i+1},\dots,g_s\}$
* in the case of a local or mixed ordering (localization of polynomial ring):

 if
$L(g_i) | L(g_j)$ for any $i \neq j$,
then
$ecart(g_i) > ecart(g_j)$
Here, $L(g)$ denotes the leading term of $g$ and
$ecart(g):=deg(g)-deg(L(g))$.
Example:
  ring r=0,(x,y,z),dp;
  ideal i=x2+z,z,2z;
  interred(i);
==> _[1]=z
==> _[2]=x2
  ring R=0,(x,y,z),ds;
  ideal i=zx+y3,z+y3,z+xy;
  interred(i);
==> _[1]=z+xy
==> _[2]=xy-y3
==> _[3]=x2y-y3
See
ideal;
module;
std.
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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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