### 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 largest monomial 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 4.4.1, 2025, generated by texi2html.