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([[ 4, 10,  8,  9],
    [11,  4,  7, 25],
    [12, 20, 16, 27],
    [14,  7, 25,  4]], order=31)

In [4]: b = GF.Random(4); b
Out[4]: GF([ 3, 15, 16, 30], order=31)

In [5]: x = np.linalg.solve(A, b); x
Out[5]: GF([10, 27,  8,  7], order=31)

In [6]: A @ x
Out[6]: GF([ 3, 15, 16, 30], 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([[16, 17,  4, 27],
    [24, 24, 25, 15],
    [20, 16,  5, 25],
    [14, 13, 16,  3]], order=31)

In [10]: B = GF.Random((4,2)); B
Out[10]: 
GF([[15, 10],
    [26,  7],
    [14, 16],
    [ 8,  8]], order=31)

In [11]: X = np.linalg.solve(A, B); X
Out[11]: 
GF([[23, 11],
    [ 1, 13],
    [ 0,  2],
    [15, 29]], order=31)

In [12]: A @ X
Out[12]: 
GF([[15, 10],
    [26,  7],
    [14, 16],
    [ 8,  8]], order=31)