Difference between revisions of "ApCoCoA-1:CharP.BBasisMutantStrategyF2"

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Let <em>I</em> be a zero-dimensional ideal over a polynomial ring with coefficient ring F_2. This function computes a border basis of the zero-dimensional radical ideal generated by <em>I</em> and the field polynomials. Furthermore, it uses the Mutant Strategy for stable span computations.
 
Let <em>I</em> be a zero-dimensional ideal over a polynomial ring with coefficient ring F_2. This function computes a border basis of the zero-dimensional radical ideal generated by <em>I</em> and the field polynomials. Furthermore, it uses the Mutant Strategy for stable span computations.
 
<par/>
 
<par/>
Please note that this function is a completely ApCoCoALib driven version of the function <ref>CharP.MBBasisF2</ref>.
+
Please note that this function is a completely ApCoCoALib driven version of the function <ref>ApCoCoA-1:CharP.MBBasisF2|CharP.MBBasisF2</ref>.
 
<itemize>
 
<itemize>
 
<item>@param <em>I</em> A zero-dimensional ideal.</item>
 
<item>@param <em>I</em> A zero-dimensional ideal.</item>
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     </description>
 
     </description>
 
     <seealso>
 
     <seealso>
       <see>CharP.MXLSolve</see>
+
       <see>ApCoCoA-1:CharP.MXLSolve|CharP.MXLSolve</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>CharP.IMNLASolve</see>
+
     <see>ApCoCoA-1:CharP.IMNLASolve|CharP.IMNLASolve</see>
     <see>CharP.IMBBasisF2</see>
+
     <see>ApCoCoA-1:CharP.IMBBasisF2|CharP.IMBBasisF2</see>
     <see>CharP.MBBasisF2</see>
+
     <see>ApCoCoA-1:CharP.MBBasisF2|CharP.MBBasisF2</see>
 
   </seealso>
 
   </seealso>
  

Revision as of 08:06, 7 October 2020

CharP.BBasisMutantStrategyF2

Computes a Border Basis of a given ideal over F_2.

Syntax

CharP.BBasisMutantStrategyF2(I:IDEAL):LIST of POLY

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.

Let I be a zero-dimensional ideal over a polynomial ring with coefficient ring F_2. This function computes a border basis of the zero-dimensional radical ideal generated by I and the field polynomials. Furthermore, it uses the Mutant Strategy for stable span computations.

Please note that this function is a completely ApCoCoALib driven version of the function CharP.MBBasisF2.

  • @param I A zero-dimensional ideal.

  • @return A border basis of the zero-dimensional radical ideal generated by the Ideal I and the field polynomials.

Example

Use Z/(2)[x[1..4]];
F:=[
    x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1, 
    x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1, 
    x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1, 
    x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1
    ];

-- Then we compute a border basis with
CharP.BBasisMutantStrategyF2(Ideal(F));

-- Result is
[x[4] + 1, x[3], x[2] + 1, x[1]]


See also

CharP.MXLSolve

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

CharP.IMNLASolve

CharP.IMBBasisF2

CharP.MBBasisF2