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5.1.64 interred
Syntax:
interred ( ideal_expression )
interred ( module_expression )
Type:
- the same as the input type
Purpose:
- interreduces a set of polynomials/vectors.
Input: 138#138
Output: 139#139 with 140#140 and the properties
-
141#141,
-
142#142 for all 143#143,
-
in the case of a global ordering (polynomial ring) and
option(redSB); :
144#144 does not divide m for all monomials m of
145#145, -
in the case of a local ordering (localization of polynomial ring) and
option(redSB); :
if
146#146 for any 143#143,then
147#147.
Here, 148#148 denotes the leading term of 149#149 and
150#150. 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
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See
ideal;
module;
std.
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