Singular Manual: interred

  | ### 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.

User manual for Singular version 4.4.1, 2025, generated by texi2html.