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([[19,  0, 21,  1],
    [ 8,  7, 29, 18],
    [ 5, 28, 22, 20],
    [22, 15, 16, 12]], order=31)

In [4]: b = GF.Random(4); b
Out[4]: GF([27, 20,  0,  8], order=31)

In [5]: x = np.linalg.solve(A, b); x
Out[5]: GF([ 0,  7, 14, 12], order=31)

In [6]: A @ x
Out[6]: GF([27, 20,  0,  8], 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([[15, 28,  7, 29],
    [ 7,  8, 17,  5],
    [26, 11, 17, 20],
    [14, 14,  5,  8]], order=31)

In [10]: B = GF.Random((4,2)); B
Out[10]: 
GF([[10,  3],
    [ 7,  7],
    [23,  5],
    [ 6,  2]], order=31)

In [11]: X = np.linalg.solve(A, B); X
Out[11]: 
GF([[13,  4],
    [25, 14],
    [13,  0],
    [23, 23]], order=31)

In [12]: A @ X
Out[12]: 
GF([[10,  3],
    [ 7,  7],
    [23,  5],
    [ 6,  2]], order=31)