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
