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

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     <description>
 
     <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  
 
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!
+
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 00:52, 4 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