Solve Binary Linear System

[Juan Grados]

I have the equation Ax=b where all matrix entries and all entrie of vector b are in GF(2). How I will be able to solve this linear system equation over GF(2) in SAGE software?

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MSc. Juan del Carmen Grados Vásquez
Laboratório Nacional de Computação Científica 
Tel: +55 24 2233-6260

(http://www.lncc.br/)
http://juaninf.blogspot.com
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[Robert Bradshaw]

sage: A = random_matrix(GF(2), 10000, 10000)
sage: A.det()
1
sage: b = random_vector(GF(2), 10000)
sage: %time x = A \ b
CPU times: user 1.61 s, sys: 0.06 s, total: 1.67 s
Wall time: 1.67 s
sage: A * x == b
True

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[Juan Grados]

Thanks, 

But if the matrix A is non-square How I will be able to solve?. I am trying but I get number of rows of self must equal degree of B

2013/4/17 Robert Bradshaw <robe...@gmail.com>

[John H Palmieri]

On Thursday, April 18, 2013 8:01:38 AM UTC-7, juaninf wrote:

Thanks, 

But if the matrix A is non-square How I will be able to solve?. I am trying but I get number of rows of self must equal degree of B

This is a math question now. If A is n x k, and if you want to solve Ax = b, then b needs to be an n-dimensional vector. It sounds like you're trying with b of the wrong dimension.

sage: A = random_matrix(GF(2), 10, 20)
sage: b = random_vector(GF(2), 10)
sage: A \ b
(1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)