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([[ 0, 23, 13, 28],
    [ 3, 28,  9, 29],
    [28, 27, 12, 18],
    [10, 29, 17, 18]], order=31)

In [4]: b = GF.Random(4); b
Out[4]: GF([ 5, 12, 30, 17], order=31)

In [5]: x = np.linalg.solve(A, b); x
Out[5]: GF([29, 26, 17, 13], order=31)

In [6]: A @ x
Out[6]: GF([ 5, 12, 30, 17], 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([[25,  6,  9,  0],
    [11, 22, 13, 15],
    [20,  3,  2, 18],
    [ 1, 12, 19,  4]], order=31)

In [10]: B = GF.Random((4,2)); B
Out[10]: 
GF([[21,  2],
    [ 6, 11],
    [12, 29],
    [14,  1]], order=31)

In [11]: X = np.linalg.solve(A, B); X
Out[11]: 
GF([[23,  2],
    [14, 15],
    [29, 26],
    [ 4, 25]], order=31)

In [12]: A @ X
Out[12]: 
GF([[21,  2],
    [ 6, 11],
    [12, 29],
    [14,  1]], order=31)