
def   _lowerCAmelCase				(   UpperCamelCase__:     list[int]							,					UpperCamelCase__:     list[int]						) ->   tuple[float, float]:





	"""simple docstring"""







	if not len(UpperCamelCase__						) == len(UpperCamelCase__						) == 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
	A					,			A					,			A								=				equationa
	A					,			A					,			A								=				equationa

	# Calculate the determinants of the matrices
	A								=				aa * ba - aa * ba
	A								=				ca * ba - ca * ba
	A								=				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:
			A								=				determinant_x / determinant
			A								=				determinant_y / determinant
			# Non-Trivial Solution (Consistent system)
			return (x, y)







import timeit

import numpy as np

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





def   _lowerCAmelCase				(   UpperCamelCase__:     Any						) ->   Tuple:





	"""simple docstring"""







	def wrapper(*UpperCamelCase__:     Union[str, Any]							,					**UpperCamelCase__:     List[str]						):
		A								=				timeit.default_timer()
		A								=				func(*UpperCamelCase__							,					**UpperCamelCase__						)
		A								=				timeit.default_timer() - starttime
		return delta

	A								=				func.__name__

	return wrapper





def   _lowerCAmelCase				(   UpperCamelCase__:     dict							,					UpperCamelCase__:     List[str]=1_00							,					UpperCamelCase__:     int=None						) ->   Any:





	"""simple docstring"""







	A								=				[]
	A								=				seq_shapes or {}
	for i in range(UpperCamelCase__						):
		A								=				{}
		for col_id, (k, v) in enumerate(features.items()						):
			if isinstance(UpperCamelCase__							,					_ArrayXD						):
				A								=				np.random.rand(*v.shape						).astype(v.dtype						)
			elif isinstance(UpperCamelCase__							,					datasets.Value						):
				if v.dtype == "string":
					A								=				"""The small grey turtle was surprisingly fast when challenged."""
				else:
					A								=				np.random.randint(10							,					size=1						).astype(v.dtype						).item()
			elif isinstance(UpperCamelCase__							,					datasets.Sequence						):
				while isinstance(UpperCamelCase__							,					datasets.Sequence						):
					A								=				v.feature
				A								=				seq_shapes[k]
				A								=				np.random.rand(*UpperCamelCase__						).astype(v.dtype						)
			A								=				data

		dummy_data.append((i, example)						)

	return dummy_data





def   _lowerCAmelCase				(   UpperCamelCase__:     int							,					UpperCamelCase__:     Union[str, Any]							,					UpperCamelCase__:     List[str]=1_00							,					UpperCamelCase__:     str=None						) ->   Optional[int]:





	"""simple docstring"""







	A								=				generate_examples(UpperCamelCase__							,					num_examples=UpperCamelCase__							,					seq_shapes=UpperCamelCase__						)

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

		A					,			A								=				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}.'						)

	A								=				datasets.Dataset.from_file(filename=UpperCamelCase__							,					info=datasets.DatasetInfo(features=UpperCamelCase__						)						)

	return dataset



