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

From ApCoCoAWiki
(New page: <command> <title>CharP.LAAlgorithm</title> <short_description>Computes the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description> <sy...)
 
m (insert version info)
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
 +
{{Version|1}}
 
<command>
 
<command>
 
     <title>CharP.LAAlgorithm</title>
 
     <title>CharP.LAAlgorithm</title>
Line 56: Line 57:
 
     </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.GBasisF2</see>
+
     <see>ApCoCoA-1:CharP.GBasisF2|CharP.GBasisF2</see>
     <see>CharP.XLSolve</see>
+
     <see>ApCoCoA-1:CharP.XLSolve|CharP.XLSolve</see>
     <see>CharP.IMXLSolve</see>
+
     <see>ApCoCoA-1:CharP.IMXLSolve|CharP.IMXLSolve</see>
     <see>CharP.IMNLASolve</see>
+
     <see>ApCoCoA-1:CharP.IMNLASolve|CharP.IMNLASolve</see>
     <see>CharP.MNLASolve</see>
+
     <see>ApCoCoA-1:CharP.MNLASolve|CharP.MNLASolve</see>
 
   </seealso>
 
   </seealso>
  
Line 74: Line 75:
 
     <key>nlasolve</key>
 
     <key>nlasolve</key>
 
     <key>finite field</key>
 
     <key>finite field</key>
     <wiki-category>Package_charP</wiki-category>
+
     <wiki-category>ApCoCoA-1:Package_charP</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 09:56, 7 October 2020

This article is about a function from ApCoCoA-1.

CharP.LAAlgorithm

Computes the unique F_2-rational zero of a given polynomial system over F_2.

Syntax

CharP.LAAlgorithm(F:LIST):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 computes the unique zero in F_2^n of a polynomial system over F_2 . 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 F_2^n then this function does not find any zero. In this case the trivial solution is given. To solve linear systems naive Gaußian elimination is used.


  • @param F: List of polynomials of given system.

  • @return The unique solution of the given system in F_2^n.

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.LAAlgorithm(F);

[0, 1, 0, 1]


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.LAAlgorithm(F);

[0, 0, 0, 0]


See also

CharP.MXLSolve

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

CharP.GBasisF2

CharP.XLSolve

CharP.IMXLSolve

CharP.IMNLASolve

CharP.MNLASolve