Top
Back: help
Forward: hilb
FastBack: Functions and system variables
FastForward: Control structures
Up: Functions
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

5.1.48 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 does not divide m (hence, m=1 if the ordering is global)
  • given any set of generators
Example:
 
See dim; std; vdim.

Top Back: help Forward: hilb FastBack: Functions and system variables FastForward: Control structures Up: Functions Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.