
5.1.50 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 zerodimensional, 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;
std;
vdim.
