np.linalg.solve

np.linalg.solve(x)

Solves the system of linear equations.

References

• https://numpy.org/doc/stable/reference/generated/numpy.linalg.solve.html

Examples

In [1]: GF = galois.GF(31)

# Ensure A is full rank and invertible
In [2]: while True:
   ...:     A = GF.Random((4,4))
   ...:     if np.linalg.matrix_rank(A) == 4:
   ...:         break
   ...: 

In [3]: A
Out[3]: 
GF([[24, 20, 25, 17],
    [21, 15, 17,  9],
    [ 6, 11, 11, 29],
    [19,  6, 27, 15]], order=31)

In [4]: b = GF.Random(4); b
Out[4]: GF([12, 11, 27, 12], order=31)

In [5]: x = np.linalg.solve(A, b); x
Out[5]: GF([10, 12, 16,  0], order=31)

In [6]: A @ x
Out[6]: GF([12, 11, 27, 12], order=31)

In [7]: GF = galois.GF(31)

# Ensure A is full rank and invertible
In [8]: while True:
   ...:     A = GF.Random((4,4))
   ...:     if np.linalg.matrix_rank(A) == 4:
   ...:         break
   ...: 

In [9]: A
Out[9]: 
GF([[29,  5, 20, 20],
    [ 7,  9, 16, 27],
    [26,  2, 10, 20],
    [20, 16, 26, 12]], order=31)

In [10]: B = GF.Random((4,2)); B
Out[10]: 
GF([[24, 24],
    [19, 16],
    [ 7, 27],
    [13, 10]], order=31)

In [11]: X = np.linalg.solve(A, B); X
Out[11]: 
GF([[26,  2],
    [23, 25],
    [18,  4],
    [25,  2]], order=31)

In [12]: A @ X
Out[12]: 
GF([[24, 24],
    [19, 16],
    [ 7, 27],
    [13, 10]], order=31)