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([[28, 16, 20,  1],
    [21, 24, 11, 28],
    [11, 16, 23, 30],
    [24, 29,  9, 12]], order=31)

In [4]: b = GF.Random(4); b
Out[4]: GF([17, 18,  1, 27], order=31)

In [5]: x = np.linalg.solve(A, b); x
Out[5]: GF([25, 30,  3, 17], order=31)

In [6]: A @ x
Out[6]: GF([17, 18,  1, 27], 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([[17,  8,  9, 24],
    [12, 29, 11, 12],
    [21, 18,  8, 19],
    [20, 16,  3, 11]], order=31)

In [10]: B = GF.Random((4,2)); B
Out[10]: 
GF([[20, 21],
    [ 9, 10],
    [ 5,  9],
    [28,  8]], order=31)

In [11]: X = np.linalg.solve(A, B); X
Out[11]: 
GF([[30,  8],
    [10,  3],
    [12, 27],
    [26, 28]], order=31)

In [12]: A @ X
Out[12]: 
GF([[20, 21],
    [ 9, 10],
    [ 5,  9],
    [28,  8]], order=31)