Difference between revisions of "ApCoCoA-1:CharP.GBasisModSquares"

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   <command>
 
   <command>
 
     <title>Char2.GBasisModSquares</title>
 
     <title>Char2.GBasisModSquares</title>
     <short_description>computing a gbasis of a given ideal, intersected with x^2-x for all indeterminates x</short_description>
+
     <short_description>computing a gbasis of a given ideal, intersected with <formula>x^2-x</formula> for all indeterminates x</short_description>
 
<syntax>
 
<syntax>
 
$char2.GBasisModSquares(Ideal):List
 
$char2.GBasisModSquares(Ideal):List
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
This function returns reduced Groebner basis for the ideal, intersected with the ideal, created by x^2-x for all indeterminates. If x^2-x for  
+
This function returns reduced Groebner basis for the ideal, intersected with the ideal, created by <formula>x^2-x</formula> for all indeterminates. If <formula>x^2-x</formula> for  
all indeterminates is in the ideal (e.g. the set of zeros is a subset of {0,1}^n) this method should produce the GBasis much faster!
+
all indeterminates is in the ideal (e.g. the set of zeros is a subset of <formula>{0,1}^n</formula>) this method should produce the GBasis much faster!
 
Please be aware, that this is much more efficient if the term ordering is Lex, DegLex or DegRevLex. Otherwise, first a DegRevLex GBasis is computed and then
 
Please be aware, that this is much more efficient if the term ordering is Lex, DegLex or DegRevLex. Otherwise, first a DegRevLex GBasis is computed and then
 
transformed with the FGLM-algorithm.  
 
transformed with the FGLM-algorithm.  

Revision as of 20:19, 2 November 2007

Char2.GBasisModSquares

computing a gbasis of a given ideal, intersected with <formula>x^2-x</formula> for all indeterminates x

Syntax

$char2.GBasisModSquares(Ideal):List

Description

This function returns reduced Groebner basis for the ideal, intersected with the ideal, created by <formula>x^2-x</formula> for all indeterminates. If <formula>x^2-x</formula> for

all indeterminates is in the ideal (e.g. the set of zeros is a subset of <formula>{0,1}^n</formula>) this method should produce the GBasis much faster!

Please be aware, that this is much more efficient if the term ordering is Lex, DegLex or DegRevLex. Otherwise, first a DegRevLex GBasis is computed and then transformed with the FGLM-algorithm.

See also

FGLM

GBasis