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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
See ideal; module; std.

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