python-docs-pl/library/cmath.po at 3.11 · python/python-docs-pl

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# SOME DESCRIPTIVE TITLE.
# Copyright (C) 2001-2026, Python Software Foundation
# This file is distributed under the same license as the Python package.
# FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
# Translators:
# python-doc bot, 2025
"Project-Id-Version: Python 3.11\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2026-04-09 17:33+0000\n"
"PO-Revision-Date: 2025-09-22 16:49+0000\n"
"Last-Translator: python-doc bot, 2025\n"
"Language-Team: Polish (https://app.transifex.com/python-doc/teams/5390/pl/)\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
"Language: pl\n"
"Plural-Forms: nplurals=4; plural=(n==1 ? 0 : (n%10>=2 && n%10<=4) && "
"(n%100<12 || n%100>14) ? 1 : n!=1 && (n%10>=0 && n%10<=1) || (n%10>=5 && "
"n%10<=9) || (n%100>=12 && n%100<=14) ? 2 : 3);\n"
msgid ":mod:`cmath` --- Mathematical functions for complex numbers"
msgstr ":mod:`cmath` --- Matematyczne funkcje dla liczb zespolonych"
"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:`~object.__complex__` or a :meth:`~object.__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."
"For functions involving branch cuts, we have the problem of deciding how to "
"define those functions on the cut itself. Following Kahan's \"Branch cuts "
"for complex elementary functions\" paper, as well as Annex G of C99 and "
"later C standards, we use the sign of zero to distinguish one side of the "
"branch cut from the other: for a branch cut along (a portion of) the real "
"axis we look at the sign of the imaginary part, while for a branch cut along "
"the imaginary axis we look at the sign of the real part."
"For example, the :func:`cmath.sqrt` function has a branch cut along the "
"negative real axis. An argument of ``complex(-2.0, -0.0)`` is treated as "
"though it lies *below* the branch cut, and so gives a result on the negative "
"imaginary axis::"
"But an argument of ``complex(-2.0, 0.0)`` is treated as though it lies above "
"the branch cut::"
msgid "Conversions to and from polar coordinates"
"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::"
"*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 "
"The following functions can be used to convert from the native rectangular "
"coordinates to polar coordinates and back."
"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.  The sign of the result is the same as the "
"sign of ``x.imag``, even when ``x.imag`` is zero::"
"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."
"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))``."
"Return the complex number *x* with polar coordinates *r* and *phi*. "
"Equivalent to ``r * (math.cos(phi) + math.sin(phi)*1j)``."
msgid "Power and logarithmic functions"
"Return *e* raised to the power *x*, where *e* is the base of natural "
"logarithms."
"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 -∞."
"Return the base-10 logarithm of *x*. This has the same branch cut as :func:"
"Return the square root of *x*. This has the same branch cut as :func:`log`."
msgid "Trigonometric functions"
"Return the arc cosine of *x*. There are two branch cuts: One extends right "
"from 1 along the real axis to ∞. The other extends left from -1 along the "
"real axis to -∞."
"Return the arc sine of *x*. This has the same branch cuts as :func:`acos`."
"Return the arc tangent of *x*. There are two branch cuts: One extends from "
"``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j`` "
"along the imaginary axis to ``-∞j``."
msgid "Return the cosine of *x*."
msgid "Return the sine of *x*."
msgid "Return the tangent of *x*."
msgid "Hyperbolic functions"
"Return the inverse hyperbolic cosine of *x*. There is one branch cut, "
"extending left from 1 along the real axis to -∞."
"Return the inverse hyperbolic sine of *x*. There are two branch cuts: One "
"extends from ``1j`` along the imaginary axis to ``∞j``.  The other extends "
"from ``-1j`` along the imaginary axis to ``-∞j``."
"Return the inverse hyperbolic tangent of *x*. There are two branch cuts: One "
"extends from ``1`` along the real axis to ``∞``. The other extends from "
"``-1`` along the real axis to ``-∞``."
msgid "Return the hyperbolic cosine of *x*."
msgstr "Zwraca cosinus hiperboliczny z *x*."
msgid "Return the hyperbolic sine of *x*."
msgstr "Zwraca sinus hiperboliczny z *x*."
msgid "Return the hyperbolic tangent of *x*."
msgstr "Zwraca tangens hiperboliczny z *x*."
msgid "Classification functions"
msgstr "Funkcje klasyfikujące"
"Return ``True`` if both the real and imaginary parts of *x* are finite, and "
"``False`` otherwise."
"Zwraca ``True`` jeżeli obie rzeczywista i urojona część *x* są skończone, i "
"``False`` w przeciwnym wypadku."
"Return ``True`` if either the real or the imaginary part of *x* is an "
"infinity, and ``False`` otherwise."
"Zwraca ``True`` jeżeli rzeczywista lub urojona część *x* jest skończona, i "
"``False`` w przeciwnym wypadku."
"Return ``True`` if either the real or the imaginary part of *x* is a NaN, "
"and ``False`` otherwise."
"Zwraca ``True`` jeżeli rzeczywista lub urojona część *x* jest NaN, i "
"``False`` w przeciwnym wypadku."
"Return ``True`` if the values *a* and *b* are close to each other and "
"``False`` otherwise."
"Zwraca ``True`` jeżeli wartości *a* i *b* są zbliżone do siebie i ``False`` "
"w przeciwnym wypadku."
"Whether or not two values are considered close is determined according to "
"given absolute and relative tolerances."
"To czy dwie wartości są zbliżone do siebie, zależy od dostarczonej "
"absolutnej lub relatywnej tolerancji."
"*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."
"*abs_tol* is the minimum absolute tolerance -- useful for comparisons near "
"zero. *abs_tol* must be at least zero."
"If no errors occur, the result will be: ``abs(a-b) <= max(rel_tol * "
"max(abs(a), abs(b)), abs_tol)``."
"Jeżeli nie wystąpi żaden błąd wynikiem będzie:\n"
" ``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``."
"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."
msgid ":pep:`485` -- A function for testing approximate equality"
msgid "Constants"
msgstr "Stały"
msgid "The mathematical constant *π*, as a float."
msgstr "Stałą matematyczną *π*, jako liczbę zmiennoprzecinkową"
msgid "The mathematical constant *e*, as a float."
msgstr "Stałą matematyczną *e*, jako liczbę zmiennoprzecinkową"
msgid "The mathematical constant *τ*, as a float."
msgstr "Stałą matematyczną *τ*, jako liczbę zmiennoprzecinkową"
msgid "Floating-point positive infinity. Equivalent to ``float('inf')``."
"Complex number with zero real part and positive infinity imaginary part. "
"Equivalent to ``complex(0.0, float('inf'))``."
"A floating-point \"not a number\" (NaN) value.  Equivalent to "
"``float('nan')``."
"Complex number with zero real part and NaN imaginary part. Equivalent to "
"``complex(0.0, float('nan'))``."
"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 "
"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:"
"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."
msgid "module"
msgstr "moduł"
msgid "math"
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