Difference between revisions of "ApCoCoA-1:CharP.GBasisModSquares"
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<title>CharP.GBasisModSquares</title> | <title>CharP.GBasisModSquares</title> | ||
<short_description>Computing a Groebner Basis of a given ideal intersected with <tt>x^2-x</tt> for all indeterminates <tt>x</tt>.</short_description> | <short_description>Computing a Groebner Basis of a given ideal intersected with <tt>x^2-x</tt> for all indeterminates <tt>x</tt>.</short_description> | ||
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This function returns the reduced Groebner basis for the given ideal intersected with the ideal generated by <tt>x^2-x</tt> for all indeterminates. If <tt>x^2-x</tt> for all indeterminates is in the ideal (e.g. the set of zeros is a subset of <tt>{0,1}^n</tt>) this method should produce the Groebner Basis much faster! | This function returns the reduced Groebner basis for the given ideal intersected with the ideal generated by <tt>x^2-x</tt> for all indeterminates. If <tt>x^2-x</tt> for all indeterminates is in the ideal (e.g. the set of zeros is a subset of <tt>{0,1}^n</tt>) this method should produce the Groebner Basis much faster! | ||
| − | Please be aware, that this is much more efficient if the term ordering is <tt>Lex</tt>, <tt>DegLex</tt> or <tt>DegRevLex</tt>. Otherwise, first a DegRevLex Groebner Basis is computed and then transformed with the <ref>FGLM.FGLM</ref>-algorithm. | + | Please be aware, that this is much more efficient if the term ordering is <tt>Lex</tt>, <tt>DegLex</tt> or <tt>DegRevLex</tt>. Otherwise, first a DegRevLex Groebner Basis is computed and then transformed with the <ref>ApCoCoA-1:FGLM.FGLM|FGLM.FGLM</ref>-algorithm. |
<itemize> | <itemize> | ||
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<seealso> | <seealso> | ||
| − | <see>FGLM.FGLM</see> | + | <see>ApCoCoA-1:FGLM.FGLM|FGLM.FGLM</see> |
| − | <see>GBasis</see> | + | <see>ApCoCoA-1:GBasis|GBasis</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | <see>Introduction to Groebner Basis in CoCoA</see> | + | <see>ApCoCoA-1:Introduction to Groebner Basis in CoCoA|Introduction to Groebner Basis in CoCoA</see> |
| − | <see>Representation of finite fields</see> | + | <see>ApCoCoA-1:Representation of finite fields|Representation of finite fields</see> |
</seealso> | </seealso> | ||
Latest revision as of 09:55, 7 October 2020
| This article is about a function from ApCoCoA-1. |
CharP.GBasisModSquares
Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x.
Syntax
CharP.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.FGLM-algorithm.
@param Ideal An Ideal.
@return The reduced Groebner Basis of the given ideal.
Example
Use R::=QQ[x,y,z]; I:=Ideal(x-y^2,x^2+xy,y^3); GBasis(I); [x^2 + xy, -y^2 + x, -xy] ------------------------------- Use Z::=ZZ[x,y,z]; -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong ------------------------------- I:=Ideal(x-y^2,x^2+xy,y^3); CharP.GBasisModSquares(I); -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [y, x] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields
