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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 $L(g_i) \vert L(g_j)$ 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=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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            User manual for Singular version 2-0-4, October 2002, generated by texinfo.