|
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 i≠j
-
in the case of a global ordering (polynomial ring):
L(gi)
does not divide m for all monomials m of
{g1,…,gi−1,gi+1,…,gs}
-
in the case of a local or mixed ordering (localization of polynomial ring):
if
L(gi)|L(gj) for any
i≠j,
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.
|