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5.1.53 interred
Syntax:
interred ( ideal_expression )
interred ( module_expression )
Type:
- the same as the input type
Purpose:
- interreduces a set of polynomials/vectors.
input: 
output: with and the properties
-
 -
for all  -
in the case of a global ordering (polynomial ring):
does not divide m for all monomials m of
 -
in the case of a local or mixed ordering (localization of polynomial ring):
if
for any ,then

Here, denotes the leading term of and
. 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
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See
ideal;
module;
std.
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