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5.1.44 highcorner
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Syntax:
highcorner ( ideal_expression )
highcorner ( module_expression )
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Type:
poly, resp. vector
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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.
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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
the variables of the basering):
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if
then
does not divide m (e.g., m=1 if the ordering is global)
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given any set of generators
of I, let be obtained from
by deleting the terms divisible by for all i with .
Then
generate I.
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Example:
| ring r=0,(x,y),ds;
ideal i=x3,x2y,y3;
highcorner(std(i));
→ xy2
highcorner(std(ideal(1)));
→ 0
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See
dim;
std;
vdim.
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