






def    __magic_name__    (	SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE				)     ->    tuple[float, float]:

							# Check if the input is valid
							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
							_lowercase							,							_lowercase							,							_lowercase							:   Tuple 							=   equationa
							_lowercase							,							_lowercase							,							_lowercase							:   Dict 							=   equationa

							# Calculate the determinants of the matrices
							_lowercase							:   str 							=   aa * ba - aa * ba
							_lowercase							:   Any 							=   ca * ba - ca * ba
							_lowercase							:   Optional[int] 							=   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:
																					_lowercase							:   Union[str, Any] 							=   determinant_x / determinant
																					_lowercase							:   Tuple 							=   determinant_y / determinant
																					# Non-Trivial Solution (Consistent system)
																					return (x, y)






"""simple docstring"""


import timeit

import numpy as np

import datasets
from datasets.arrow_writer import ArrowWriter
from datasets.features.features import _ArrayXD






def  lowercase						(	lowerCAmelCase__						):
			def wrapper(*lowerCAmelCase__	,**lowerCAmelCase__						):
						lowerCamelCase_					=  timeit.default_timer()
						lowerCamelCase_					=  func(*lowerCAmelCase__	,**lowerCAmelCase__						)
						lowerCamelCase_					=  timeit.default_timer() - starttime
						return delta

			lowerCamelCase_					=  func.__name__

			return wrapper






def  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__=100	,lowerCAmelCase__=None						):
			lowerCamelCase_					=  []
			lowerCamelCase_					=  seq_shapes or {}
			for i in range(lowerCAmelCase__						):
						lowerCamelCase_					=  {}
						for col_id, (k, v) in enumerate(features.items()						):
									if isinstance(lowerCAmelCase__	,_ArrayXD						):
												lowerCamelCase_					=  np.random.rand(*v.shape						).astype(v.dtype						)
									elif isinstance(lowerCAmelCase__	,datasets.Value						):
												if v.dtype == "string":
															lowerCamelCase_					=  '''The small grey turtle was surprisingly fast when challenged.'''
												else:
															lowerCamelCase_					=  np.random.randint(10	,size=1						).astype(v.dtype						).item()
									elif isinstance(lowerCAmelCase__	,datasets.Sequence						):
												while isinstance(lowerCAmelCase__	,datasets.Sequence						):
															lowerCamelCase_					=  v.feature
												lowerCamelCase_					=  seq_shapes[k]
												lowerCamelCase_					=  np.random.rand(*lowerCAmelCase__						).astype(v.dtype						)
									lowerCamelCase_					=  data

						dummy_data.append((i, example)						)

			return dummy_data






def  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__	,lowerCAmelCase__=100	,lowerCAmelCase__=None						):
			lowerCamelCase_					=  generate_examples(lowerCAmelCase__	,num_examples=lowerCAmelCase__	,seq_shapes=lowerCAmelCase__						)

			with ArrowWriter(features=lowerCAmelCase__	,path=lowerCAmelCase__						) as writer:
						for key, record in dummy_data:
									lowerCamelCase_					=  features.encode_example(lowerCAmelCase__						)
									writer.write(lowerCAmelCase__						)

						lowerCamelCase_		, lowerCamelCase_					=  writer.finalize()

			if not num_final_examples == num_examples:
						raise ValueError(
						    f"Error writing the dataset, wrote {num_final_examples} examples but should have written {num_examples}."						)

			lowerCamelCase_					=  datasets.Dataset.from_file(filename=lowerCAmelCase__	,info=datasets.DatasetInfo(features=lowerCAmelCase__						)						)

			return dataset



