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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: f1,,fn
output: g1,,gs with s n and the properties

  • (f1,,fn) = (g1,,gs)
  • L(gi)L(gj) for all ij
  • in the case of a global ordering (polynomial ring):
    L(gi) does not divide m for all monomials m of {g1,,gi1,gi+1,,gs}
  • in the case of a local or mixed ordering (localization of polynomial ring):
    if L(gi)|L(gj) for any ij, then ecart(gi) > ecart(gj)
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.