Com vec.py e mat.py implementados:

$ python3
Python 3.6.15 (default, May 10 2022, 13:43:14) 
[GCC Apple LLVM 13.0.0 (clang-1300.0.29.30)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> 
>>> from vec import Vec
>>> from GF2 import one
>>> D = {(x, y) for x in {0, 1} for y in {0, 1}}
>>> j = Vec(D, {(x, y): one for (x, y) in D})
>>> b_00 = j - Vec(D, {(1, 1): one})
>>> b_01 = j - Vec(D, {(1, 0): one})
>>> b_10 = j - Vec(D, {(0, 1): one})
>>> b_11 = j - Vec(D, {(0, 0): one})
>>> import matutil as mu
>>> A = mu.coldict2mat({0: b_00, 1: b_01, 2: b_10, 3: b_11})
>>> import vecutil as vu
>>> b = Vec(D, {(0,0): one, (1,0): one})
>>> from solver import solve
>>> x = solve(A, b)
>>> A * x == b
True
>>> print(A)

              0   1   2   3
          -----------------
 (0, 0)  |  one one one   0
 (0, 1)  |  one one   0 one
 (1, 0)  |  one   0 one one
 (1, 1)  |    0 one one one

>>> print(b)

 (0, 0) (0, 1) (1, 0) (1, 1)
----------------------------
    one      0    one      0
>>> print(x)

 0   1 2   3
------------
 0 one 0 one
>>> quit()
$