python-docs-pl/library/math.po at 3.9 · python/python-docs-pl

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# SOME DESCRIPTIVE TITLE.
# Copyright (C) 2001-2021, Python Software Foundation
# This file is distributed under the same license as the Python package.
# FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
# Translators:
# Michał Biliński <m.bilinskimichal@gmail.com>, 2021
"Project-Id-Version: Python 3.9\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2021-01-01 05:02+0000\n"
"PO-Revision-Date: 2017-02-16 23:18+0000\n"
"Last-Translator: Michał Biliński <m.bilinskimichal@gmail.com>, 2021\n"
"Language-Team: Polish (https://www.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:`math` --- Mathematical functions"
"This module provides access to the mathematical functions defined by the C "
"standard."
"These functions cannot be used with complex numbers; use the functions of "
"the same name from the :mod:`cmath` module if you require support for "
"complex numbers.  The distinction between functions which support complex "
"numbers and those which don't is made since most users do not want to learn "
"quite as much mathematics as required to understand complex numbers.  "
"Receiving an exception instead of a complex result allows earlier detection "
"of the unexpected complex number used as a parameter, so that the programmer "
"can determine how and why it was generated in the first place."
"The following functions are provided by this module.  Except when explicitly "
"noted otherwise, all return values are floats."
msgid "Number-theoretic and representation functions"
"Return the ceiling of *x*, the smallest integer greater than or equal to "
"*x*. If *x* is not a float, delegates to ``x.__ceil__()``, which should "
"return an :class:`~numbers.Integral` value."
"Return the number of ways to choose *k* items from *n* items without "
"repetition and without order."
"Evaluates to ``n! / (k! * (n - k)!)`` when ``k <= n`` and evaluates to zero "
"when ``k > n``."
"Also called the binomial coefficient because it is equivalent to the "
"coefficient of k-th term in polynomial expansion of the expression ``(1 + x) "
"Raises :exc:`TypeError` if either of the arguments are not integers. Raises :"
"exc:`ValueError` if either of the arguments are negative."
"Return a float with the magnitude (absolute value) of *x* but the sign of "
"*y*.  On platforms that support signed zeros, ``copysign(1.0, -0.0)`` "
"returns *-1.0*."
msgid "Return the absolute value of *x*."
"Return *x* factorial as an integer.  Raises :exc:`ValueError` if *x* is not "
"integral or is negative."
msgid "Accepting floats with integral values (like ``5.0``) is deprecated."
"Return the floor of *x*, the largest integer less than or equal to *x*. If "
"*x* is not a float, delegates to ``x.__floor__()``, which should return an :"
"class:`~numbers.Integral` value."
"Return ``fmod(x, y)``, as defined by the platform C library. Note that the "
"Python expression ``x % y`` may not return the same result.  The intent of "
"the C standard is that ``fmod(x, y)`` be exactly (mathematically; to "
"infinite precision) equal to ``x - n*y`` for some integer *n* such that the "
"result has the same sign as *x* and magnitude less than ``abs(y)``.  "
"Python's ``x % y`` returns a result with the sign of *y* instead, and may "
"not be exactly computable for float arguments. For example, ``fmod(-1e-100, "
"1e100)`` is ``-1e-100``, but the result of Python's ``-1e-100 % 1e100`` is "
"``1e100-1e-100``, which cannot be represented exactly as a float, and rounds "
"to the surprising ``1e100``.  For this reason, function :func:`fmod` is "
"generally preferred when working with floats, while Python's ``x % y`` is "
"preferred when working with integers."
"Return the mantissa and exponent of *x* as the pair ``(m, e)``.  *m* is a "
"float and *e* is an integer such that ``x == m * 2**e`` exactly. If *x* is "
"zero, returns ``(0.0, 0)``, otherwise ``0.5 <= abs(m) < 1``.  This is used "
"to \"pick apart\" the internal representation of a float in a portable way."
"Return an accurate floating point sum of values in the iterable.  Avoids "
"loss of precision by tracking multiple intermediate partial sums::"
"The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the "
"typical case where the rounding mode is half-even.  On some non-Windows "
"builds, the underlying C library uses extended precision addition and may "
"occasionally double-round an intermediate sum causing it to be off in its "
"least significant bit."
"For further discussion and two alternative approaches, see the `ASPN "
"cookbook recipes for accurate floating point summation <https://code."
"activestate.com/recipes/393090/>`_\\."
"Return the greatest common divisor of the specified integer arguments. If "
"any of the arguments is nonzero, then the returned value is the largest "
"positive integer that is a divisor of all arguments.  If all arguments are "
"zero, then the returned value is ``0``.  ``gcd()`` without arguments returns "
"Added support for an arbitrary number of arguments. Formerly, only two "
"arguments were supported."
"Return ``True`` if the values *a* and *b* are close to each other and "
"``False`` otherwise."
"Zwraca 1``True`` jeżeli wartości *a* i *b* są zbliżone do siebie i  "
"2``False`` w innym 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"
"Return ``True`` if *x* is neither an infinity nor a NaN, and ``False`` "
"otherwise.  (Note that ``0.0`` *is* considered finite.)"
"Return ``True`` if *x* is a positive or negative infinity, and ``False`` "
"otherwise."
"Return ``True`` if *x* is a NaN (not a number), and ``False`` otherwise."
"Return the integer square root of the nonnegative integer *n*. This is the "
"floor of the exact square root of *n*, or equivalently the greatest integer "
"*a* such that *a*\\ ² |nbsp| ≤ |nbsp| *n*."
"For some applications, it may be more convenient to have the least integer "
"*a* such that *n* |nbsp| ≤ |nbsp| *a*\\ ², or in other words the ceiling of "
"the exact square root of *n*. For positive *n*, this can be computed using "
"``a = 1 + isqrt(n - 1)``."
"Return the least common multiple of the specified integer arguments. If all "
"arguments are nonzero, then the returned value is the smallest positive "
"integer that is a multiple of all arguments.  If any of the arguments is "
"zero, then the returned value is ``0``.  ``lcm()`` without arguments returns "
"Return ``x * (2**i)``.  This is essentially the inverse of function :func:"
"Return the fractional and integer parts of *x*.  Both results carry the sign "
"of *x* and are floats."
msgid "Return the next floating-point value after *x* towards *y*."
msgid "If *x* is equal to *y*, return *y*."
msgid "Examples:"
msgid "``math.nextafter(x, math.inf)`` goes up: towards positive infinity."
msgid "``math.nextafter(x, -math.inf)`` goes down: towards minus infinity."
msgid "``math.nextafter(x, 0.0)`` goes towards zero."
msgid "``math.nextafter(x, math.copysign(math.inf, x))`` goes away from zero."
msgid "See also :func:`math.ulp`."
"Return the number of ways to choose *k* items from *n* items without "
"repetition and with order."
"Evaluates to ``n! / (n - k)!`` when ``k <= n`` and evaluates to zero when "
"``k > n``."
"If *k* is not specified or is None, then *k* defaults to *n* and the "
"function returns ``n!``."
"Calculate the product of all the elements in the input *iterable*. The "
"default *start* value for the product is ``1``."
"When the iterable is empty, return the start value.  This function is "
"intended specifically for use with numeric values and may reject non-numeric "
"Return the IEEE 754-style remainder of *x* with respect to *y*.  For finite "
"*x* and finite nonzero *y*, this is the difference ``x - n*y``, where ``n`` "
"is the closest integer to the exact value of the quotient ``x / y``.  If "
"``x / y`` is exactly halfway between two consecutive integers, the nearest "
"*even* integer is used for ``n``.  The remainder ``r = remainder(x, y)`` "
"thus always satisfies ``abs(r) <= 0.5 * abs(y)``."
"Special cases follow IEEE 754: in particular, ``remainder(x, math.inf)`` is "
"*x* for any finite *x*, and ``remainder(x, 0)`` and ``remainder(math.inf, "
"x)`` raise :exc:`ValueError` for any non-NaN *x*. If the result of the "
"remainder operation is zero, that zero will have the same sign as *x*."
"On platforms using IEEE 754 binary floating-point, the result of this "
"operation is always exactly representable: no rounding error is introduced."
"Return the :class:`~numbers.Real` value *x* truncated to an :class:`~numbers."
"Integral` (usually an integer). Delegates to :meth:`x.__trunc__() <object."
"__trunc__>`."
msgid "Return the value of the least significant bit of the float *x*:"
msgid "If *x* is a NaN (not a number), return *x*."
msgid "If *x* is negative, return ``ulp(-x)``."
msgid "If *x* is a positive infinity, return *x*."
"If *x* is equal to zero, return the smallest positive *denormalized* "
"representable float (smaller than the minimum positive *normalized* float, :"
"data:`sys.float_info.min <sys.float_info>`)."
"If *x* is equal to the largest positive representable float, return the "
"value of the least significant bit of *x*, such that the first float smaller "
"than *x* is ``x - ulp(x)``."
"Otherwise (*x* is a positive finite number), return the value of the least "
"significant bit of *x*, such that the first float bigger than *x* is ``x + "
"ulp(x)``."
msgid "ULP stands for \"Unit in the Last Place\"."
"See also :func:`math.nextafter` and :data:`sys.float_info.epsilon <sys."
"float_info>`."
"Note that :func:`frexp` and :func:`modf` have a different call/return "
"pattern than their C equivalents: they take a single argument and return a "
"pair of values, rather than returning their second return value through an "
"'output parameter' (there is no such thing in Python)."
"For the :func:`ceil`, :func:`floor`, and :func:`modf` functions, note that "
"*all* floating-point numbers of sufficiently large magnitude are exact "
"integers. Python floats typically carry no more than 53 bits of precision "
"(the same as the platform C double type), in which case any float *x* with "
"``abs(x) >= 2**52`` necessarily has no fractional bits."
msgid "Power and logarithmic functions"
"Return *e* raised to the power *x*, where *e* = 2.718281... is the base of "
"natural logarithms.  This is usually more accurate than ``math.e ** x`` or "
"``pow(math.e, x)``."
"Return *e* raised to the power *x*, minus 1.  Here *e* is the base of "
"natural logarithms.  For small floats *x*, the subtraction in ``exp(x) - 1`` "
"can result in a `significant loss of precision <https://en.wikipedia.org/"
"wiki/Loss_of_significance>`_\\; the :func:`expm1` function provides a way to "
"compute this quantity to full precision::"
msgid "With one argument, return the natural logarithm of *x* (to base *e*)."
"With two arguments, return the logarithm of *x* to the given *base*, "
"calculated as ``log(x)/log(base)``."
"Return the natural logarithm of *1+x* (base *e*). The result is calculated "
"in a way which is accurate for *x* near zero."
"Return the base-2 logarithm of *x*. This is usually more accurate than "
"``log(x, 2)``."
":meth:`int.bit_length` returns the number of bits necessary to represent an "
"integer in binary, excluding the sign and leading zeros."
"Return the base-10 logarithm of *x*.  This is usually more accurate than "
"``log(x, 10)``."
"Return ``x`` raised to the power ``y``.  Exceptional cases follow Annex 'F' "
"of the C99 standard as far as possible.  In particular, ``pow(1.0, x)`` and "
"``pow(x, 0.0)`` always return ``1.0``, even when ``x`` is a zero or a NaN.  "
"If both ``x`` and ``y`` are finite, ``x`` is negative, and ``y`` is not an "
"integer then ``pow(x, y)`` is undefined, and raises :exc:`ValueError`."
"Unlike the built-in ``**`` operator, :func:`math.pow` converts both its "
"arguments to type :class:`float`.  Use ``**`` or the built-in :func:`pow` "
"function for computing exact integer powers."
msgid "Return the square root of *x*."
msgid "Trigonometric functions"
"Return the arc cosine of *x*, in radians. The result is between ``0`` and "
"Return the arc sine of *x*, in radians. The result is between ``-pi/2`` and "
"``pi/2``."
"Return the arc tangent of *x*, in radians. The result is between ``-pi/2`` "
"and ``pi/2``."
"Return ``atan(y / x)``, in radians. The result is between ``-pi`` and "
"``pi``. The vector in the plane from the origin to point ``(x, y)`` makes "
"this angle with the positive X axis. The point of :func:`atan2` is that the "
"signs of both inputs are known to it, so it can compute the correct quadrant "
"for the angle. For example, ``atan(1)`` and ``atan2(1, 1)`` are both "
"``pi/4``, but ``atan2(-1, -1)`` is ``-3*pi/4``."
msgid "Return the cosine of *x* radians."
"Return the Euclidean distance between two points *p* and *q*, each given as "
"a sequence (or iterable) of coordinates.  The two points must have the same "
"dimension."
msgid "Roughly equivalent to::"
"Return the Euclidean norm, ``sqrt(sum(x**2 for x in coordinates))``. This is "
"the length of the vector from the origin to the point given by the "
"coordinates."
"For a two dimensional point ``(x, y)``, this is equivalent to computing the "
"hypotenuse of a right triangle using the Pythagorean theorem, ``sqrt(x*x + "
"Added support for n-dimensional points. Formerly, only the two dimensional "
"case was supported."
msgid "Return the sine of *x* radians."
msgid "Return the tangent of *x* radians."
msgid "Angular conversion"
msgid "Convert angle *x* from radians to degrees."
msgid "Convert angle *x* from degrees to radians."
msgid "Hyperbolic functions"
"`Hyperbolic functions <https://en.wikipedia.org/wiki/Hyperbolic_function>`_ "
"are analogs of trigonometric functions that are based on hyperbolas instead "
"of circles."
msgid "Return the inverse hyperbolic cosine of *x*."
msgid "Return the inverse hyperbolic sine of *x*."
msgid "Return the inverse hyperbolic tangent of *x*."
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 "Special functions"
"Return the `error function <https://en.wikipedia.org/wiki/Error_function>`_ "
"The :func:`erf` function can be used to compute traditional statistical "
"functions such as the `cumulative standard normal distribution <https://en."
"wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function>`_::"
"Return the complementary error function at *x*.  The `complementary error "
"function <https://en.wikipedia.org/wiki/Error_function>`_ is defined as "
"``1.0 - erf(x)``.  It is used for large values of *x* where a subtraction "
"from one would cause a `loss of significance <https://en.wikipedia.org/wiki/"
"Loss_of_significance>`_\\."
"Return the `Gamma function <https://en.wikipedia.org/wiki/Gamma_function>`_ "
"Return the natural logarithm of the absolute value of the Gamma function at "
msgid "Constants"
msgstr "Stały"
msgid "The mathematical constant *π* = 3.141592..., to available precision."
msgid "The mathematical constant *e* = 2.718281..., to available precision."
"The mathematical constant *τ* = 6.283185..., to available precision. Tau is "
"a circle constant equal to 2\\ *π*, the ratio of a circle's circumference to "
"its radius. To learn more about Tau, check out Vi Hart's video `Pi is "
"(still) Wrong <https://www.youtube.com/watch?v=jG7vhMMXagQ>`_, and start "
"celebrating `Tau day <https://tauday.com/>`_ by eating twice as much pie!"
"A floating-point positive infinity.  (For negative infinity, use ``-math."
"inf``.)  Equivalent to the output of ``float('inf')``."
"A floating-point \"not a number\" (NaN) value.  Equivalent to the output of "
"``float('nan')``."
"The :mod:`math` module consists mostly of thin wrappers around the platform "
"C math library functions.  Behavior in exceptional cases follows Annex F of "
"the C99 standard where appropriate.  The current implementation will raise :"
"exc:`ValueError` for invalid operations like ``sqrt(-1.0)`` or ``log(0.0)`` "
"(where C99 Annex F recommends signaling invalid operation or divide-by-"
"zero), and :exc:`OverflowError` for results that overflow (for example, "
"``exp(1000.0)``).  A NaN will not be returned from any of the functions "
"above unless one or more of the input arguments was a NaN; in that case, "
"most functions will return a NaN, but (again following C99 Annex F) there "
"are some exceptions to this rule, for example ``pow(float('nan'), 0.0)`` or "
"``hypot(float('nan'), float('inf'))``."
"Note that Python makes no effort to distinguish signaling NaNs from quiet "
"NaNs, and behavior for signaling NaNs remains unspecified. Typical behavior "
"is to treat all NaNs as though they were quiet."
msgid "Module :mod:`cmath`"
msgid "Complex number versions of many of these functions."
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