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#, fuzzy

msgid ""

msgstr ""

"Project-Id-Version: Python 3.9\n"

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"Language-Team: Portuguese (Brazil) (https://app.transifex.com/python-doc/"

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"Language: pt_BR\n"

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"Plural-Forms: nplurals=3; plural=(n == 0 || n == 1) ? 0 : n != 0 && n % "

"1000000 == 0 ? 1 : 2;\n"

#: ../../library/cmath.rst:2

msgid ":mod:`cmath` --- Mathematical functions for complex numbers"

msgstr ":mod:`cmath` --- Funções matemáticas para números complexos"

#: ../../library/cmath.rst:9

msgid ""

"This module provides access to mathematical functions for complex numbers. "

"The functions in this module accept integers, floating-point numbers or "

"complex numbers as arguments. They will also accept any Python object that "

"has either a :meth:`__complex__` or a :meth:`__float__` method: these "

"methods are used to convert the object to a complex or floating-point "

"number, respectively, and the function is then applied to the result of the "

"conversion."

msgstr ""

#: ../../library/cmath.rst:18

msgid ""

"On platforms with hardware and system-level support for signed zeros, "

"functions involving branch cuts are continuous on *both* sides of the branch "

"cut: the sign of the zero distinguishes one side of the branch cut from the "

"other. On platforms that do not support signed zeros the continuity is as "

"specified below."

msgstr ""

#: ../../library/cmath.rst:26

msgid "Conversions to and from polar coordinates"

msgstr "Conversões de e para coordenadas polares"

#: ../../library/cmath.rst:28

msgid ""

"A Python complex number ``z`` is stored internally using *rectangular* or "

"*Cartesian* coordinates. It is completely determined by its *real part* ``z."

"real`` and its *imaginary part* ``z.imag``. In other words::"

msgstr ""

#: ../../library/cmath.rst:35

msgid ""

"*Polar coordinates* give an alternative way to represent a complex number. "

"In polar coordinates, a complex number *z* is defined by the modulus *r* and "

"the phase angle *phi*. The modulus *r* is the distance from *z* to the "

"origin, while the phase *phi* is the counterclockwise angle, measured in "

"radians, from the positive x-axis to the line segment that joins the origin "

"to *z*."

msgstr ""

"*Coordenadas polares* fornecem uma forma alternativa de representar um "

"número complexo. Em coordenadas polares, um número complexo *z* é definido "

"pelo módulo *r* e pelo ângulo de fase *phi*. O módulo *r* é a distância de "

"*z* à origem, enquanto a fase *phi* é o ângulo anti-horário, medido em "

"radianos, do eixo x positivo ao segmento de reta que une a origem a *z*."

#: ../../library/cmath.rst:42

msgid ""

"The following functions can be used to convert from the native rectangular "

"coordinates to polar coordinates and back."

msgstr ""

"As funções a seguir podem ser usadas para converter coordenadas retangulares "

"nativas em coordenadas polares e vice-versa."

#: ../../library/cmath.rst:47

msgid ""

"Return the phase of *x* (also known as the *argument* of *x*), as a float. "

"``phase(x)`` is equivalent to ``math.atan2(x.imag, x.real)``. The result "

"lies in the range [-\\ *π*, *π*], and the branch cut for this operation lies "

"along the negative real axis, continuous from above. On systems with "

"support for signed zeros (which includes most systems in current use), this "

"means that the sign of the result is the same as the sign of ``x.imag``, "

"even when ``x.imag`` is zero::"

msgstr ""

#: ../../library/cmath.rst:64

msgid ""

"The modulus (absolute value) of a complex number *x* can be computed using "

"the built-in :func:`abs` function. There is no separate :mod:`cmath` module "

"function for this operation."

msgstr ""

"O módulo (valor absoluto) de um número complexo *x* pode ser calculado "

"usando a função embutida :func:`abs`. Não há função do módulo :mod:`cmath` "

"separada para esta operação."

#: ../../library/cmath.rst:71

msgid ""

"Return the representation of *x* in polar coordinates. Returns a pair ``(r, "

"phi)`` where *r* is the modulus of *x* and phi is the phase of *x*. "

"``polar(x)`` is equivalent to ``(abs(x), phase(x))``."

msgstr ""

"Retorna a representação de *x* em coordenadas polares. Retorna um par ``(r, "

"phi)`` onde *r* é o módulo de *x* e phi é a fase de *x*. ``polar(x)`` é "

"equivalente a ``(abs(x), phase(x))``."

#: ../../library/cmath.rst:79

msgid ""

"Return the complex number *x* with polar coordinates *r* and *phi*. "

"Equivalent to ``r * (math.cos(phi) + math.sin(phi)*1j)``."

msgstr ""

#: ../../library/cmath.rst:84

msgid "Power and logarithmic functions"

msgstr "Funções de potência e logarítmicas"

#: ../../library/cmath.rst:88

msgid ""

"Return *e* raised to the power *x*, where *e* is the base of natural "

"logarithms."

msgstr ""

"Retorna *e* elevado à potência *x*, onde *e* é a base de logaritmos naturais."

#: ../../library/cmath.rst:94

msgid ""

"Returns the logarithm of *x* to the given *base*. If the *base* is not "

"specified, returns the natural logarithm of *x*. There is one branch cut, "

"from 0 along the negative real axis to -∞, continuous from above."

msgstr ""

#: ../../library/cmath.rst:101

msgid ""

"Return the base-10 logarithm of *x*. This has the same branch cut as :func:"

"`log`."

msgstr ""

"Retorna o logaritmo de *x* na base 10. Este tem o mesmo corte de ramificação "

"que :func:`log`."

#: ../../library/cmath.rst:107

msgid ""

"Return the square root of *x*. This has the same branch cut as :func:`log`."

msgstr ""

"Retorna a raiz quadrada de *x*. Este tem o mesmo corte de ramificação que :"

"func:`log`."

#: ../../library/cmath.rst:111

msgid "Trigonometric functions"

msgstr "Funções trigonométricas"

#: ../../library/cmath.rst:115

msgid ""

"Return the arc cosine of *x*. There are two branch cuts: One extends right "

"from 1 along the real axis to ∞, continuous from below. The other extends "

"left from -1 along the real axis to -∞, continuous from above."

msgstr ""

#: ../../library/cmath.rst:122

msgid ""

"Return the arc sine of *x*. This has the same branch cuts as :func:`acos`."

msgstr ""

"Retorna o arco seno de *x*. Tem os mesmos cortes de ramificação que :func:"

"`acos`."

#: ../../library/cmath.rst:127

msgid ""

"Return the arc tangent of *x*. There are two branch cuts: One extends from "

"``1j`` along the imaginary axis to ``∞j``, continuous from the right. The "

"other extends from ``-1j`` along the imaginary axis to ``-∞j``, continuous "

"from the left."

msgstr ""

#: ../../library/cmath.rst:135

msgid "Return the cosine of *x*."

msgstr "Retorna o cosseno de *x*."

#: ../../library/cmath.rst:140

msgid "Return the sine of *x*."

msgstr "Retorna o seno de *x*."

#: ../../library/cmath.rst:145

msgid "Return the tangent of *x*."

msgstr "Retorna a tangente de *x*."

#: ../../library/cmath.rst:149

msgid "Hyperbolic functions"

msgstr "Funções hiperbólicas"

#: ../../library/cmath.rst:153

msgid ""

"Return the inverse hyperbolic cosine of *x*. There is one branch cut, "

"extending left from 1 along the real axis to -∞, continuous from above."

msgstr ""

#: ../../library/cmath.rst:159

msgid ""

"Return the inverse hyperbolic sine of *x*. There are two branch cuts: One "

"extends from ``1j`` along the imaginary axis to ``∞j``, continuous from the "

"right. The other extends from ``-1j`` along the imaginary axis to ``-∞j``, "

"continuous from the left."

msgstr ""

#: ../../library/cmath.rst:167

msgid ""

"Return the inverse hyperbolic tangent of *x*. There are two branch cuts: One "

"extends from ``1`` along the real axis to ``∞``, continuous from below. The "

"other extends from ``-1`` along the real axis to ``-∞``, continuous from "

"above."

msgstr ""

#: ../../library/cmath.rst:175

msgid "Return the hyperbolic cosine of *x*."

msgstr "Retorna o cosseno hiperbólico de *x*."

#: ../../library/cmath.rst:180

msgid "Return the hyperbolic sine of *x*."

msgstr "Retorna o seno hiperbólico de *x*."

#: ../../library/cmath.rst:185

msgid "Return the hyperbolic tangent of *x*."

msgstr "Retorna a tangente hiperbólica de *x*."

#: ../../library/cmath.rst:189

msgid "Classification functions"

msgstr "Funções de classificação"

#: ../../library/cmath.rst:193

msgid ""

"Return ``True`` if both the real and imaginary parts of *x* are finite, and "

"``False`` otherwise."

msgstr ""

"Retorna ``True`` se ambas as partes real e imaginária de *x* forem finitas, "

"e ``False`` caso contrário."

#: ../../library/cmath.rst:201

msgid ""

"Return ``True`` if either the real or the imaginary part of *x* is an "

"infinity, and ``False`` otherwise."

msgstr ""

"Retorna ``True`` se ou a parte real ou a imaginária de *x* for infinita, e "

"``False`` caso contrário."

#: ../../library/cmath.rst:207

msgid ""

"Return ``True`` if either the real or the imaginary part of *x* is a NaN, "

"and ``False`` otherwise."

msgstr ""

"Retorna ``True`` se ou a parte real ou a imaginária de *x* for NaN, e "

"``False`` caso contrário."

#: ../../library/cmath.rst:213

msgid ""

"Return ``True`` if the values *a* and *b* are close to each other and "

"``False`` otherwise."

msgstr ""

"Retorna ``True`` se os valores *a* e *b* estiverem próximos e ``False`` caso "

"contrário."

#: ../../library/cmath.rst:216

msgid ""

"Whether or not two values are considered close is determined according to "

"given absolute and relative tolerances."

msgstr ""

"Se dois valores são ou não considerados próximos, é determinado de acordo "

"com as tolerâncias absolutas e relativas fornecidas."

#: ../../library/cmath.rst:219

msgid ""

"*rel_tol* is the relative tolerance -- it is the maximum allowed difference "

"between *a* and *b*, relative to the larger absolute value of *a* or *b*. "

"For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default "

"tolerance is ``1e-09``, which assures that the two values are the same "

"within about 9 decimal digits. *rel_tol* must be greater than zero."

msgstr ""

"*rel_tol* é a tolerância relativa -- é a diferença máxima permitida entre "

"*a* e *b*, em relação ao maior valor absoluto de *a* ou *b*. Por exemplo, "

"para definir uma tolerância de 5%, passe ``rel_tol=0.05``. A tolerância "

"padrão é ``1e-09``, o que garante que os dois valores sejam iguais em cerca "

"de 9 dígitos decimais. *rel_tol* deve ser maior que zero."

#: ../../library/cmath.rst:225

msgid ""

"*abs_tol* is the minimum absolute tolerance -- useful for comparisons near "

"zero. *abs_tol* must be at least zero."

msgstr ""

"*abs_tol* é a tolerância absoluta mínima -- útil para comparações próximas a "

"zero. *abs_tol* deve ser pelo menos zero."

#: ../../library/cmath.rst:228

msgid ""

"If no errors occur, the result will be: ``abs(a-b) <= max(rel_tol * "

"max(abs(a), abs(b)), abs_tol)``."

msgstr ""

"Se nenhum erro ocorrer, o resultado será: ``abs(a-b) <= max(rel_tol * "

"max(abs(a), abs(b)), abs_tol)``."

#: ../../library/cmath.rst:231

msgid ""

"The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be "

"handled according to IEEE rules. Specifically, ``NaN`` is not considered "

"close to any other value, including ``NaN``. ``inf`` and ``-inf`` are only "

"considered close to themselves."

msgstr ""

"Os valores especiais do IEEE 754 de ``NaN``, ``inf`` e ``-inf`` serão "

"tratados de acordo com as regras do IEEE. Especificamente, ``NaN`` não é "

"considerado próximo a qualquer outro valor, incluindo ``NaN``. ``inf`` e ``-"

"inf`` são considerados apenas próximos a si mesmos."

#: ../../library/cmath.rst:240

msgid ":pep:`485` -- A function for testing approximate equality"

msgstr ":pep:`485` -- Uma função para testar igualdade aproximada"

#: ../../library/cmath.rst:244

msgid "Constants"

msgstr "Constantes"

#: ../../library/cmath.rst:248

msgid "The mathematical constant *π*, as a float."

msgstr "A constante matemática *π*, como um ponto flutuante."

#: ../../library/cmath.rst:253

msgid "The mathematical constant *e*, as a float."

msgstr "A constante matemática *e*, como um ponto flutuante."

#: ../../library/cmath.rst:258

msgid "The mathematical constant *τ*, as a float."

msgstr "A constante matemática *τ*, como um ponto flutuante."

#: ../../library/cmath.rst:265

msgid "Floating-point positive infinity. Equivalent to ``float('inf')``."

msgstr "Infinito positivo de ponto flutuante. Equivale a ``float('inf')``."

#: ../../library/cmath.rst:272

msgid ""

"Complex number with zero real part and positive infinity imaginary part. "

"Equivalent to ``complex(0.0, float('inf'))``."

msgstr ""

"Número complexo com parte real zero e parte imaginária infinita positiva. "

"Equivale a ``complex(0.0, float('inf'))``."

#: ../../library/cmath.rst:280

msgid ""

"A floating-point \"not a number\" (NaN) value. Equivalent to "

"``float('nan')``."

msgstr ""

"Um valor de ponto flutuante \"não um número\" (NaN). Equivale a "

"``float('nan')``."

#: ../../library/cmath.rst:288

msgid ""

"Complex number with zero real part and NaN imaginary part. Equivalent to "

"``complex(0.0, float('nan'))``."

msgstr ""

"Número complexo com parte real zero e parte imaginária NaN. Equivale a "

"``complex(0.0, float('nan'))``."

#: ../../library/cmath.rst:296

msgid ""

"Note that the selection of functions is similar, but not identical, to that "

"in module :mod:`math`. The reason for having two modules is that some users "

"aren't interested in complex numbers, and perhaps don't even know what they "

"are. They would rather have ``math.sqrt(-1)`` raise an exception than "

"return a complex number. Also note that the functions defined in :mod:"

"`cmath` always return a complex number, even if the answer can be expressed "

"as a real number (in which case the complex number has an imaginary part of "

"zero)."

msgstr ""

"Observe que a seleção de funções é semelhante, mas não idêntica, àquela no "

"módulo :mod:`math`. A razão para ter dois módulos é que alguns usuários não "

"estão interessados em números complexos e talvez nem saibam o que são. Eles "

"preferem que ``math.sqrt(-1)`` gere uma exceção do que retorne um número "

"complexo. Observe também que as funções definidas em :mod:`cmath` sempre "

"retornam um número complexo, mesmo que a resposta possa ser expressa como um "

"número real (nesse caso o número complexo tem uma parte imaginária de zero)."

#: ../../library/cmath.rst:304

msgid ""

"A note on branch cuts: They are curves along which the given function fails "

"to be continuous. They are a necessary feature of many complex functions. "

"It is assumed that if you need to compute with complex functions, you will "

"understand about branch cuts. Consult almost any (not too elementary) book "

"on complex variables for enlightenment. For information of the proper "

"choice of branch cuts for numerical purposes, a good reference should be the "

"following:"

msgstr ""

"Uma nota sobre cortes de ramificação: são curvas ao longo das quais a função "

"dada não é contínua. Eles são um recurso necessário de muitas funções "

"complexas. Presume-se que se você precisar calcular com funções complexas, "

"você entenderá sobre cortes de ramificação. Consulte quase qualquer livro "

"(não muito elementar) sobre variáveis complexas para obter esclarecimento. "

"Para informações sobre a escolha adequada dos cortes de ramificação para "

"fins numéricos, uma boa referência deve ser a seguinte:"

#: ../../library/cmath.rst:314

msgid ""

"Kahan, W: Branch cuts for complex elementary functions; or, Much ado about "

"nothing's sign bit. In Iserles, A., and Powell, M. (eds.), The state of the "

"art in numerical analysis. Clarendon Press (1987) pp165--211."

msgstr ""

"Kahan, W: Branch cuts for complex elementary functions; or, Much ado about "

"nothing's sign bit. Em Iserles, A. e Powell, M. (eds.), The state of the "

"art in numerical analysis. Clarendon Press (1987) pp165--211."