ApCoCoA-1:CharP.XLSolve

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CharP.GBasisF2

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

Syntax

CharP.XLSolve(F:LIST):LIST

Description


This function computes the unique zero in F_2^n of a polynomial system over F_2 . It uses XL-Algorithm to find the unique zero. The XL-Algorithm is impelemented only to find a unique solution. If the given polynomial system has more than one zeros in F_2^n 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.

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.


  • @param F A system of polynomial over F_2 having a unique zero in F_2^n.

  • @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.XLSolve(F);

-- And we achieve the following information on the screen together with the solution at the end.
----------------------------------------

  The size of Matrix is:
		No. of Rows=4
		No. of Columns=11
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The variables found till now, if any are:
	[x[1], x[2], x[3], x[4]]
	The size of Matrix is:
		No. of Rows=16
		No. of Columns=15
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The variables found till now, if any are:
	[0, 1, 0, 1]
[0, 1, 0, 1]


See also

GBasis

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

CharP.GBasisF4

CharP.GBasisF8

CharP.GBasisF16

CharP.GBasisF32