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

From ApCoCoAWiki
(Initial version.)
 
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<command>
 
<command>
     <title>charP.BBasisMutantStrategyF2</title>
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     <title>CharP.BBasisMutantStrategyF2</title>
 
     <short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description>
 
     <short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description>
 
<syntax>
 
<syntax>
charP.BBasisMutantStrategyF2(I:IDEAL):LIST of POLY
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CharP.BBasisMutantStrategyF2(I:IDEAL):LIST of POLY
 
</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.
 
<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/>
 
<par/>
Let <em>I</em> be a zero-dimensional ideal over a polynomial ring with coefficient ring F2. 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/>
 +
Please note that this function is a completely ApCoCoALib driven version of the function <ref>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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     ];
 
     ];
  
-- Then we compute a Border Basis with
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-- Then we compute a border basis with
charP.BBasisMutantStrategyF2(Ideal(F));
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CharP.BBasisMutantStrategyF2(Ideal(F));
  
 +
-- Result is
 
[x[4] + 1, x[3], x[2] + 1, x[1]]
 
[x[4] + 1, x[3], x[2] + 1, x[1]]
 
 
</example>
 
</example>
  
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     <see>Introduction to Groebner Basis in CoCoA</see>
 
     <see>Introduction to Groebner Basis in CoCoA</see>
 
     <see>CharP.IMNLASolve</see>
 
     <see>CharP.IMNLASolve</see>
     <see>CharP.IMBBasisF2</see>
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     <see>CharP.IMBBasisF2</see>
 +
    <see>CharP.MBBasisF2</see>
 
   </seealso>
 
   </seealso>
  

Revision as of 17:31, 11 November 2011

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