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5.1.59 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) and option(redSB);:
    $L(g_i)$ 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 ordering (localization of polynomial ring) and option(redSB);:
    if $L(g_i) \vert L(g_j)$ 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=zx+y3,z+y3,z+xy;
  interred(i);
==> _[1]=xz-z
==> _[2]=xy+z
==> _[3]=y3+xz
  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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