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

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<command> | <command> | ||

<title>Char2.GBasisModSquares</title> | <title>Char2.GBasisModSquares</title> | ||

− | <short_description> | + | <short_description>Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x.</short_description> |

<syntax> | <syntax> | ||

− | + | Char2.GBasisModSquares(Ideal:IDEAL):LIST | |

</syntax> | </syntax> | ||

<description> | <description> | ||

− | { | + | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. |

+ | <par/> | ||

+ | This function returns the reduced Groebner basis for the given ideal intersected with the ideal generated by x^2-x for all indeterminates. If x^2-x 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 Groebner Basis much faster! | ||

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

− | + | <itemize> | |

− | + | <item>@param <em>Ideal</em> An Ideal.</item> | |

− | + | <item>@return The reduced Groebner Basis of the given ideal.</item> | |

− | + | </itemize> | |

</description> | </description> | ||

+ | |||

<seealso> | <seealso> | ||

<see>FGLM</see> | <see>FGLM</see> | ||

<see>GBasis</see> | <see>GBasis</see> | ||

</seealso> | </seealso> | ||

− | <key> | + | |

+ | <key>gbasismodsquares</key> | ||

<key>char2.gbasismodsquares</key> | <key>char2.gbasismodsquares</key> | ||

<wiki-category>Package_char2</wiki-category> | <wiki-category>Package_char2</wiki-category> | ||

</command> | </command> |

## Revision as of 07:23, 23 April 2009

## Char2.GBasisModSquares

Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x.

### Syntax

Char2.GBasisModSquares(Ideal:IDEAL):LIST

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

This function returns the reduced Groebner basis for the given ideal intersected with the ideal generated by x^2-x for all indeterminates. If x^2-x 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 Groebner Basis much faster!

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

@param

*Ideal*An Ideal.@return The reduced Groebner Basis of the given ideal.

### See also