5.1.44 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.
Note:
Let the ideal I be given by a standard basis. Then
highcorner(I) returns 0 iff dim(I)>0 or dim(I)=-1.
Otherwise it returns the smallest monomial m not in I which has the following
properties (with
$x_i$
the variables of the basering):
* if
$x_i>1$ then $x_i$
does not divide m (e.g., m=1 if the ordering is global)
* given any set of generators
$f_1,\dots,f_k$ of I, let $f'_i$ be obtained from
$f_i$ by deleting the terms divisible by $x_i\cdot m$ for all i with $x_i<1$.
Then $f'_1,\dots,f'_k$ 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.
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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