highcorner ( ideal_expression
highcorner ( module_expression
- poly, resp. vector
- 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.
- Let the ideal I be given by a standard basis. Then
highcorner(I) returns 0 if and only if
Otherwise it returns the smallest monomial m not in I which has the following
the variables of the basering):
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 .