



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


def 			UpperCamelCase(  __UpperCamelCase							:		list[list] ):





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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						A__  :  Optional[Any]								=					[
						    [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]]))










import cmath
import math






def     a(      A       :    float ,     A       :    float ,     A       :    float ,     A       :    float       )		->       complex:
					"""simple docstring"""





					a					     =   math.radians(A       )
					a					     =   math.radians(A       )

					# Convert voltage and current to rectangular form
					a					     =   cmath.rect(A ,     A       )
					a					     =   cmath.rect(A ,     A       )

					# Calculate apparent power
					return voltage_rect * current_rect


if __name__ == "__main__":
				import doctest

				doctest.testmod()
