





def      A__       (    SCREAMING_SNAKE_CASE_   :      list[int]				,	SCREAMING_SNAKE_CASE_   :      list[int]						)  ->  tuple[float, float]:






   """simple docstring"""







   if not len(SCREAMING_SNAKE_CASE_						) == len(SCREAMING_SNAKE_CASE_						) == 3:
      raise ValueError('''Please enter a valid equation.'''						)
   if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
      raise ValueError('''Both a & b of two equations can\'t be zero.'''						)

   # Extract the coefficients
   _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   equationa
   _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   equationa

   # Calculate the determinants of the matrices
   _UpperCAmelCase           =   aa * ba - aa * ba
   _UpperCAmelCase           =   ca * ba - ca * ba
   _UpperCAmelCase           =   aa * ca - aa * ca

   # Check if the system of linear equations has a solution (using Cramer's rule)
   if determinant == 0:
      if determinant_x == determinant_y == 0:
         raise ValueError('''Infinite solutions. (Consistent system)'''						)
      else:
         raise ValueError('''No solution. (Inconsistent system)'''						)
   else:
      if determinant_x == determinant_y == 0:
         # Trivial solution (Inconsistent system)
         return (0.0, 0.0)
      else:
         _UpperCAmelCase           =   determinant_x / determinant
         _UpperCAmelCase           =   determinant_y / determinant
         # Non-Trivial Solution (Consistent system)
         return (x, y)






import numpy as np
def      A__       (    SCREAMING_SNAKE_CASE_   :      np.ndarray				,	SCREAMING_SNAKE_CASE_   :      float						)  ->  np.ndarray:






   """simple docstring"""







   return np.where(vector > 0				,	SCREAMING_SNAKE_CASE_				,	(alpha * (np.exp(SCREAMING_SNAKE_CASE_						) - 1))						)


if __name__ == "__main__":
   import doctest

   doctest.testmod()