
def 							UpperCAmelCase_		(							__SCREAMING_SNAKE_CASE							):
	lowercase       =    current_set.copy()
	for row_index, row in enumerate(__lowercase							):
		lowercase       =    row[0]
		for column_index, column in enumerate(__lowercase							):
			if magnitude == 0:
				lowercase       =    column
				continue
			lowercase       =    column / magnitude
    # Subtract to cancel term
	lowercase       =    current_set[0]
	lowercase       =    [first_row]
	lowercase       =    current_set[1::]
	for row in current_set:
		lowercase       =    []
		# If first term is 0, it is already in form we want, so we preserve it
		if row[0] == 0:
			final_set.append(__lowercase							)
			continue
		for column_index in range(len(__lowercase							)							):
			temp_row.append(first_row[column_index] - row[column_index]							)
		final_set.append(__lowercase							)
	# Create next recursion iteration set
	if len(final_set[0]							) != 3:
		lowercase       =    final_set[0]
		lowercase       =    []
		lowercase       =    []
		for row in final_set[1::]:
			current_first_column.append(row[0]							)
			next_iteration.append(row[1::]							)
		lowercase       =    simplify(__lowercase							)
		for i in range(len(__lowercase							)							):
			resultant[i].insert(0 ,							current_first_column[i]							)
		resultant.insert(0 ,							__lowercase							)
		lowercase       =    resultant
	return final_set






def 							UpperCAmelCase_		(							__SCREAMING_SNAKE_CASE							):



	if len(__lowercase							) == 0:
		raise IndexError('solve_simultaneous() requires n lists of length n+1'							)
	lowercase       =    len(__lowercase							) + 1
	if any(len(__lowercase							) != _length for item in equations							):
		raise IndexError('solve_simultaneous() requires n lists of length n+1'							)
	for row in equations:
		if any(not isinstance(__lowercase ,							(int, float)							) for column in row							):
			raise ValueError('solve_simultaneous() requires lists of integers'							)
	if len(__lowercase							) == 1:
		return [equations[0][-1] / equations[0][0]]
	lowercase       =    equations.copy()
	if any(0 in row for row in data_set							):
		lowercase       =    data_set.copy()
		lowercase       =    []
		for row_index, row in enumerate(__lowercase							):
			if 0 not in row:
				lowercase       =    data_set.pop(__lowercase							)
				break
		if not full_row:
			raise ValueError('solve_simultaneous() requires at least 1 full equation'							)
		data_set.insert(0 ,							__lowercase							)
	lowercase       =    data_set.copy()
	lowercase       =    simplify(__lowercase							)
	lowercase       =    simplified[::-1]
	lowercase       =    []
	for row in simplified:
		lowercase       =    row[-1]
		if not solutions:
			if row[-2] == 0:
				solutions.append(0							)
				continue
			solutions.append(current_solution / row[-2]							)
			continue
		lowercase       =    row.copy()[: len(__lowercase							) - 1 :]
		while temp_row[0] == 0:
			temp_row.pop(0							)
		if len(__lowercase							) == 0:
			solutions.append(0							)
			continue
		lowercase       =    temp_row[1::]
		lowercase       =    temp_row[::-1]
		for column_index, column in enumerate(__lowercase							):
			current_solution -= column * solutions[column_index]
		solutions.append(__lowercase							)
	lowercase       =    []
	for item in solutions:
		final.append(float(round(__lowercase ,							5							)							)							)
	return final[::-1]


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	UpperCAmelCase	      = [
	    [2, 1, 1, 1, 1, 4],
	    [1, 2, 1, 1, 1, 5],
	    [1, 1, 2, 1, 1, 6],
	    [1, 1, 1, 2, 1, 7],
	    [1, 1, 1, 1, 2, 8],
	]
	print(solve_simultaneous(eq))
	print(solve_simultaneous([[4, 2]]))








'''simple docstring'''




import math
def 	UpperCAmelCase_							(					__lowercase							:      int       )		->       bool:


     '''simple docstring'''



     return math.sqrt(__lowercase       ) * math.sqrt(__lowercase       ) == num
def 	UpperCAmelCase_							(					__lowercase							:      int       )		->       bool:


     '''simple docstring'''



     _UpperCAmelCase     							=   0
     _UpperCAmelCase     							=   n
     while left <= right:
          _UpperCAmelCase     							=   (left + right) // 2
          if mid**2 == n:
               return True
          elif mid**2 > n:
               _UpperCAmelCase     							=   mid - 1
          else:
               _UpperCAmelCase     							=   mid + 1
     return False


if __name__ == "__main__":
  import doctest

  doctest.testmod()




