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([[11, 20,  8, 13],
    [20, 22, 25,  2],
    [ 7, 16,  3, 27],
    [19, 27, 10, 22]], order=31)

In [4]: b = GF.Random(4); b
Out[4]: GF([19, 23,  9,  9], order=31)

In [5]: x = np.linalg.solve(A, b); x
Out[5]: GF([ 0,  0, 18, 19], order=31)

In [6]: A @ x
Out[6]: GF([19, 23,  9,  9], 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, 10, 22,  7],
    [20, 21, 13,  0],
    [ 9, 24,  9, 22],
    [16, 29, 26, 28]], order=31)

In [10]: B = GF.Random((4,2)); B
Out[10]: 
GF([[ 8, 17],
    [27, 24],
    [17,  8],
    [14,  3]], order=31)

In [11]: X = np.linalg.solve(A, B); X
Out[11]: 
GF([[27,  2],
    [ 7, 30],
    [16, 29],
    [15, 24]], order=31)

In [12]: A @ X
Out[12]: 
GF([[ 8, 17],
    [27, 24],
    [17,  8],
    [14,  3]], order=31)