

"""simple docstring"""




import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					A     ,       A     =   np.shape(lowercase__ )

					A     =   np.zeros((rows, 1)     ,				dtype=lowercase__ )
					for row in reversed(range(lowercase__ ) ):
										A     =   0
										for col in range(row + 1     ,				lowercase__ ):
															total += coefficients[row, col] * x[col]

										A     =   (vector[row] - total) / coefficients[row, row]

					return x
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					A     ,       A     =   np.shape(lowercase__ )
					if rows != columns:
										return np.array(()     ,				dtype=lowercase__ )

					# augmented matrix
					A     =   np.concatenate((coefficients, vector)     ,				axis=1 )
					A     =   augmented_mat.astype("float64" )

					# scale the matrix leaving it triangular
					for row in range(rows - 1 ):
										A     =   augmented_mat[row, row]
										for col in range(row + 1     ,				lowercase__ ):
															A     =   augmented_mat[col, row] / pivot
															augmented_mat[col, :] -= factor * augmented_mat[row, :]

					A     =   retroactive_resolution(
					    augmented_mat[:, 0:columns]     ,				augmented_mat[:, columns : columns + 1] )

					return x


if __name__ == "__main__":
	import doctest

	doctest.testmod()













def 						A_					(						lowercase_	,  lowercase_			)				->List[Any]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		1
 while b > 0:
  if b & 1:
   res *= a

  a *= a
  b >>= 1

 return res





def 						A_					(						lowercase_	,  lowercase_	,  lowercase_			)				->Any:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		1
 while b > 0:
  if b & 1:
   SCREAMING_SNAKE_CASE				    =		((res % c) * (a % c)) % c

  a *= a
  b >>= 1

 return res




