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# SOME DESCRIPTIVE TITLE.
# Copyright (C) 1990-2020, Python Software Foundation
# This file is distributed under the same license as the Python package.
#
# Translators:
msgid ""
msgstr ""
"Project-Id-Version: Python 2.7\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2020-02-09 18:46+0900\n"
"PO-Revision-Date: 2018-01-20 20:59+0000\n"
"Last-Translator: tomo\n"
"Language-Team: Portuguese (Brazil) (http://www.transifex.com/python-doc/"
"python-27/language/pt_BR/)\n"
"Language: pt_BR\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
"Plural-Forms: nplurals=2; plural=(n > 1);\n"
#: ../../library/cmath.rst:2
msgid ":mod:`cmath` --- Mathematical functions for complex numbers"
msgstr ":mod:`cmath` --- Funções matemáticas para números complexos"
#: ../../library/cmath.rst:8
msgid ""
"This module is always available. It 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 ""
#: ../../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 ""
#: ../../library/cmath.rst:42
msgid ""
"The following functions can be used to convert from the native rectangular "
"coordinates to polar coordinates and back."
msgstr ""
#: ../../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:66
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 ""
#: ../../library/cmath.rst:73
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 ""
#: ../../library/cmath.rst:83
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:90
msgid "Power and logarithmic functions"
msgstr "Funções de potência e logarítmicas"
#: ../../library/cmath.rst:94
msgid "Return the exponential value ``e**x``."
msgstr ""
#: ../../library/cmath.rst:99
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:103
msgid "*base* argument added."
msgstr ""
#: ../../library/cmath.rst:109
msgid ""
"Return the base-10 logarithm of *x*. This has the same branch cut as :func:"
"`log`."
msgstr ""
#: ../../library/cmath.rst:115
msgid ""
"Return the square root of *x*. This has the same branch cut as :func:`log`."
msgstr ""
#: ../../library/cmath.rst:119
msgid "Trigonometric functions"
msgstr "Funções trigonométricas"
#: ../../library/cmath.rst:123
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:130
msgid ""
"Return the arc sine of *x*. This has the same branch cuts as :func:`acos`."
msgstr ""
#: ../../library/cmath.rst:135
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:140
msgid "direction of continuity of upper cut reversed"
msgstr ""
#: ../../library/cmath.rst:146
msgid "Return the cosine of *x*."
msgstr ""
#: ../../library/cmath.rst:151
msgid "Return the sine of *x*."
msgstr "Devolve o seno de *x*."
#: ../../library/cmath.rst:156
msgid "Return the tangent of *x*."
msgstr ""
#: ../../library/cmath.rst:160
msgid "Hyperbolic functions"
msgstr "Funções hiperbólicas"
#: ../../library/cmath.rst:164
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:170
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:175
msgid "branch cuts moved to match those recommended by the C99 standard"
msgstr ""
#: ../../library/cmath.rst:181
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:186
msgid "direction of continuity of right cut reversed"
msgstr ""
#: ../../library/cmath.rst:192
msgid "Return the hyperbolic cosine of *x*."
msgstr "Retorna o cosseno hiperbólico de *x*."
#: ../../library/cmath.rst:197
msgid "Return the hyperbolic sine of *x*."
msgstr "Retorna o seno hiperbólico de *x*."
#: ../../library/cmath.rst:202
msgid "Return the hyperbolic tangent of *x*."
msgstr "Retorna a tangente hiperbólica de *x*."
#: ../../library/cmath.rst:206
msgid "Classification functions"
msgstr ""
#: ../../library/cmath.rst:210
msgid ""
"Return ``True`` if the real or the imaginary part of x is positive or "
"negative infinity."
msgstr ""
#: ../../library/cmath.rst:218
msgid ""
"Return ``True`` if the real or imaginary part of x is not a number (NaN)."
msgstr ""
#: ../../library/cmath.rst:224
msgid "Constants"
msgstr "Constantes"
#: ../../library/cmath.rst:229
msgid "The mathematical constant *π*, as a float."
msgstr ""
#: ../../library/cmath.rst:234
msgid "The mathematical constant *e*, as a float."
msgstr ""
#: ../../library/cmath.rst:238
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 ""
#: ../../library/cmath.rst:246
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 ""
#: ../../library/cmath.rst:256
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 ""