



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


if is_sentencepiece_available():
							from ..ta.tokenization_ta import TaTokenizer
else:
							from ...utils.dummy_sentencepiece_objects import TaTokenizer

lowercase_						=       TaTokenizer

if is_tokenizers_available():
							from ..ta.tokenization_ta_fast import TaTokenizerFast
else:
							from ...utils.dummy_tokenizers_objects import TaTokenizerFast

lowercase_						=       TaTokenizerFast

lowercase_						=       {"""configuration_mt5""": ["""MT5Config""", """MT5OnnxConfig"""]}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							lowercase_						=       [
							    """MT5EncoderModel""",
							    """MT5ForConditionalGeneration""",
							    """MT5ForQuestionAnswering""",
							    """MT5Model""",
							    """MT5PreTrainedModel""",
							    """MT5Stack""",
							]

try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							lowercase_						=       ["""TFMT5EncoderModel""", """TFMT5ForConditionalGeneration""", """TFMT5Model"""]

try:
							if not is_flax_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							lowercase_						=       ["""FlaxMT5EncoderModel""", """FlaxMT5ForConditionalGeneration""", """FlaxMT5Model"""]


if TYPE_CHECKING:
							from .configuration_mta import MTaConfig, MTaOnnxConfig

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_mta import (
														    MTaEncoderModel,
														    MTaForConditionalGeneration,
														    MTaForQuestionAnswering,
														    MTaModel,
														    MTaPreTrainedModel,
														    MTaStack,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_mta import TFMTaEncoderModel, TFMTaForConditionalGeneration, TFMTaModel

							try:
														if not is_flax_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_flax_mta import FlaxMTaEncoderModel, FlaxMTaForConditionalGeneration, FlaxMTaModel

else:
							import sys

							lowercase_						=       _LazyModule(
							    __name__,
							    globals()["""__file__"""],
							    _import_structure,
							    extra_objects={"""MT5Tokenizer""": MTaTokenizer, """MT5TokenizerFast""": MTaTokenizerFast},
							    module_spec=__spec__,
							)









from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowercase_						=       2_9979_2458

# Symbols
lowercase_			,      lowercase_			,      lowercase_			,      lowercase_						=       symbols("""ct x y z""")



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			if velocity > c:
						raise ValueError("Speed must not exceed light speed 299,792,458 [m/s]!"					)
			elif velocity < 1:
						# Usually the speed should be much higher than 1 (c order of magnitude)
						raise ValueError("Speed must be greater than or equal to 1!"					)

			return velocity / c



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_					) ** 2					)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return np.array(
			    [
			        [gamma(SCREAMING_SNAKE_CASE_					), -gamma(SCREAMING_SNAKE_CASE_					) * beta(SCREAMING_SNAKE_CASE_					), 0, 0],
			        [-gamma(SCREAMING_SNAKE_CASE_					) * beta(SCREAMING_SNAKE_CASE_					), gamma(SCREAMING_SNAKE_CASE_					), 0, 0],
			        [0, 0, 1, 0],
			        [0, 0, 0, 1],
			    ]					)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_ = None					):
			# Ensure event is not empty
			if event is None:
						lowercase__   					=			np.array([ct, x, y, z]					)  # Symbolic four vector
			else:
						event[0] *= c  # x0 is ct (speed of light * time)

			return transformation_matrix(SCREAMING_SNAKE_CASE_					) @ event


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# Example of symbolic vector:
							lowercase_						=       transform(2997_9245)
							print("""Example of four vector: """)
							print(F'ct\' = {four_vector[0]}')
							print(F'x\' = {four_vector[1]}')
							print(F'y\' = {four_vector[2]}')
							print(F'z\' = {four_vector[3]}')

							# Substitute symbols with numerical values
							lowercase_						=       {ct: c, x: 1, y: 1, z: 1}
							lowercase_						=       [four_vector[i].subs(sub_dict) for i in range(4)]

							print(F'\n{numerical_vector}')




