  | ### 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: Output: with and the properties , for all , in the case of a global ordering (polynomial ring) and `option(redSB);`: does not divide m for all monomials m of , in the case of a local ordering (localization of polynomial ring) and `option(redSB);`: if for any ,then . Here, denotes the leading term of and . `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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