CODEWITHSUNDEEP
pythonnumpylinear-algebrafinite-field
MRm
MRm

Reputation: 587

Solving a system of linear equations over the field F(2) with python

Is there a way that I can solve a system of linear equations over the field F2(i.e addition and multiplication modulo 2 - the binary field) using python? I've been trying to search for a useful package for a while but hadn't come up with anything...

Thanks,

Upvotes: 8

Views: 2233

Answers (1)

Matt Hostetter
Matt Hostetter

Reputation: 580

I created a Python package galois that extends NumPy arrays over finite fields. It also supports NumPy linear algebra routines in np.linalg.

Here is an example solving a linear system Ax = b for x in GF(2).

In [1]: import numpy as np

In [2]: import galois

In [3]: GF = galois.GF(2)

In [4]: A = GF.Random((4,4)); A
Out[4]: 
GF([[0, 1, 0, 0],
    [0, 0, 1, 1],
    [0, 0, 0, 1],
    [1, 1, 0, 0]], order=2)

In [5]: x_truth = GF([1,0,1,1]); x_truth
Out[5]: GF([1, 0, 1, 1], order=2)

In [6]: b = A @ x_truth; b
Out[6]: GF([0, 0, 1, 1], order=2)

# Solve Ax = b for x
In [7]: x = np.linalg.solve(A, b); x
Out[7]: GF([1, 0, 1, 1], order=2)

# Verify that x is x_truth
In [8]: np.array_equal(x, x_truth)
Out[8]: True

Upvotes: 2

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