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

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(New page: <command> <title>CharP.LASolve</title> <short_description>Computes the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description> <syntax...)
 
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<command>
 
    <title>CharP.LASolve</title>
 
    <short_description>Computes the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description>
 
<syntax>
 
CharP.LASolve(F:LIST):LIST
 
</syntax>
 
    <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 computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses LA-Algorithm to find the unique zero. The LA-Algorithm generates a sequence of linear systems to solve the given system. The LA-Algorithm can find the unique zero only. If the given polynomial system has more than one zero's in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. To solve linear system naive Gaußian elimination is used.
 
 
 
 
<itemize>
 
<item>@param <em>F:</em> List of polynomials of given system.</item>
 
<item>@return The unique solution of the given system in <tt>F_2^n</tt>. </item>
 
</itemize>
 
 
<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 the solution with
 
CharP.LASolve(F);
 
 
[0, 1, 0, 1]
 
 
</example>
 
 
 
<example>
 
Use Z/(2)[x[1..4]];
 
F:=[
 
    x[2]x[3] + x[1]x[4] + x[2]x[4] + x[3]x[4] + x[1] + x[2] + x[3] + x[4],
 
    x[2]x[3] + x[2]x[4] + x[3]x[4] + x[2] + x[3] + x[4], 
 
    x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2], 
 
    x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2]
 
  ];
 
 
-- Solution is not unique i.e. [0, 1, 1, 1], [0, 0, 0, 0], and [1, 1, 1, 1] are solutions
 
 
-- Then we compute the solution with
 
CharP.NLASolve(F,Sparse);
 
 
x[4] = NA
 
Please Check the uniqueness of solution.
 
The Given system of polynomials does not
 
seem to have a unique solution or it has
 
no solution over the finite field F2.
 
 
 
</example>
 
 
 
    </description>
 
    <seealso>
 
      <see>CharP.MXLSolve</see>
 
    <see>Introduction to CoCoAServer</see>
 
    <see>Introduction to Groebner Basis in CoCoA</see>
 
    <see>CharP.GBasisF2</see>
 
    <see>CharP.XLSolve</see>
 
    <see>CharP.IMXLSolve</see>
 
    <see>CharP.IMNLASolve</see>
 
    <see>CharP.MNLASolve</see>
 
  </seealso>
 
 
    <types>
 
      <type>apcocoaserver</type>
 
      <type>poly_system</type>
 
    </types>
 
 
    <key>charP.nlasolve</key>
 
    <key>nlasolve</key>
 
    <key>finite field</key>
 
    <wiki-category>Package_charP</wiki-category>
 
  </command>
 

Latest revision as of 15:39, 4 June 2012