Singular Manual: highcorner

  | ### 5.1.55 highcorner `Syntax:` `highcorner (` ideal_expression `)` `highcorner (` module_expression `)` `Type:` poly, resp. vector `Purpose:` returns the smallest monomial not contained in the ideal, resp. module, generated by the initial terms of the given generators. If the generators are a standard basis, this is also the smallest monomial not contained in the ideal, resp. module. If the ideal, resp. module, is not zero-dimensional, 0 is returned. The command works also in global orderings, but is not very useful there. `Note:` Let the ideal I be given by a standard basis. Then `highcorner(I)` returns 0 if and only if `dim(I)>0` or `dim(I)=-1`. Otherwise it returns the smallest monomial m not in I which has the following properties (with the variables of the basering): if then does not divide m (hence, m=1 if the ordering is global) given any set of generators of I, let be obtained from by deleting the terms divisible by for all i with . Then generate I. `Example:`
      ring r=0,(x,y),ds;
      ideal i=x3,x2y,y3;
      highcorner(std(i));
      ==> xy2
      highcorner(std(ideal(1)));
      ==> 0
See dim; groebner; std; vdim.

User manual for Singular version 4.3.1p1, 2022, generated by texi2html.