forked from AFPy/python-docs-fr
476 lines
20 KiB
Plaintext
476 lines
20 KiB
Plaintext
# Copyright (C) 2001-2018, Python Software Foundation
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# For licence information, see README file.
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#
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msgid ""
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msgstr ""
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"Project-Id-Version: Python 3\n"
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"Report-Msgid-Bugs-To: \n"
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"POT-Creation-Date: 2023-04-14 13:19+0200\n"
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"PO-Revision-Date: 2019-05-28 20:19+0200\n"
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"Last-Translator: Jules Lasne <jules.lasne@gmail.com>\n"
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"Language-Team: FRENCH <traductions@lists.afpy.org>\n"
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"Language: fr\n"
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"MIME-Version: 1.0\n"
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"Content-Type: text/plain; charset=UTF-8\n"
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"Content-Transfer-Encoding: 8bit\n"
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"X-Generator: Poedit 2.2.3\n"
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#: library/cmath.rst:2
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msgid ":mod:`cmath` --- Mathematical functions for complex numbers"
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msgstr "Fonctions mathématiques pour nombres complexes — :mod:`cmath`"
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#: library/cmath.rst:9
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msgid ""
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"This module provides access to mathematical functions for complex numbers. "
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"The functions in this module accept integers, floating-point numbers or "
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"complex numbers as arguments. They will also accept any Python object that "
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"has either a :meth:`__complex__` or a :meth:`__float__` method: these "
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"methods are used to convert the object to a complex or floating-point "
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"number, respectively, and the function is then applied to the result of the "
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"conversion."
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msgstr ""
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"Ce module fournit l'accès aux fonctions mathématiques pour les nombres "
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"complexes. Les fonctions de ce module acceptent les entiers, les nombres "
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"flottants ou les nombres complexes comme arguments. Elles acceptent "
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"également tout objet Python ayant une méthode :meth:`__complex__` "
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"(respectivement :meth:`__float__`) : cette méthode est utilisée pour "
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"convertir l’objet en nombre complexe (respectivement un nombre flottant) et "
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"la fonction est ensuite appliquée sur le résultat de la conversion."
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#: library/cmath.rst:18
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msgid ""
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"For functions involving branch cuts, we have the problem of deciding how to "
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"define those functions on the cut itself. Following Kahan's \"Branch cuts "
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"for complex elementary functions\" paper, as well as Annex G of C99 and "
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"later C standards, we use the sign of zero to distinguish one side of the "
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"branch cut from the other: for a branch cut along (a portion of) the real "
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"axis we look at the sign of the imaginary part, while for a branch cut along "
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"the imaginary axis we look at the sign of the real part."
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msgstr ""
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#: library/cmath.rst:26
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msgid ""
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"For example, the :func:`cmath.sqrt` function has a branch cut along the "
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"negative real axis. An argument of ``complex(-2.0, -0.0)`` is treated as "
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"though it lies *below* the branch cut, and so gives a result on the negative "
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"imaginary axis::"
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msgstr ""
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#: library/cmath.rst:34
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msgid ""
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"But an argument of ``complex(-2.0, 0.0)`` is treated as though it lies above "
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"the branch cut::"
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msgstr ""
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#: library/cmath.rst:42
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msgid "Conversions to and from polar coordinates"
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msgstr "Conversion vers et à partir de coordonnées polaires"
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#: library/cmath.rst:44
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msgid ""
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"A Python complex number ``z`` is stored internally using *rectangular* or "
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"*Cartesian* coordinates. It is completely determined by its *real part* ``z."
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"real`` and its *imaginary part* ``z.imag``. In other words::"
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msgstr ""
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"Un nombre complexe Python ``z`` est stocké de manière interne en coordonnées "
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"*cartésiennes*. Il est entièrement défini par sa *partie réelle* ``z.real`` "
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"et sa *partie complexe* ``z.imag``. En d'autres termes ::"
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#: library/cmath.rst:51
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msgid ""
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"*Polar coordinates* give an alternative way to represent a complex number. "
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"In polar coordinates, a complex number *z* is defined by the modulus *r* and "
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"the phase angle *phi*. The modulus *r* is the distance from *z* to the "
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"origin, while the phase *phi* is the counterclockwise angle, measured in "
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"radians, from the positive x-axis to the line segment that joins the origin "
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"to *z*."
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msgstr ""
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"Les *coordonnées polaires* donnent une manière alternative de représenter un "
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"nombre complexe. En coordonnées polaires, un nombre complexe *z* est défini "
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"par son module *r* et par son argument (*angle de phase*) *phi*. Le module "
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"*r* est la distance entre *z* et l'origine, alors que l'argument *phi* est "
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"l'angle (dans le sens inverse des aiguilles d'une montre, ou sens "
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"trigonométrique), mesuré en radians, à partir de l'axe X positif, et vers le "
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"segment de droite joignant *z* à l'origine."
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#: library/cmath.rst:58
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msgid ""
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"The following functions can be used to convert from the native rectangular "
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"coordinates to polar coordinates and back."
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msgstr ""
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"Les fonctions suivantes peuvent être utilisées pour convertir à partir des "
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"coordonnées rectangulaires natives vers les coordonnées polaires, et vice-"
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"versa."
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#: library/cmath.rst:63
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#, fuzzy
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msgid ""
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"Return the phase of *x* (also known as the *argument* of *x*), as a float. "
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"``phase(x)`` is equivalent to ``math.atan2(x.imag, x.real)``. The result "
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"lies in the range [-\\ *π*, *π*], and the branch cut for this operation lies "
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"along the negative real axis. The sign of the result is the same as the "
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"sign of ``x.imag``, even when ``x.imag`` is zero::"
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msgstr ""
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"Renvoie l'argument de *x*, dans un nombre flottant. ``phase(x)`` est "
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"équivalent à ``math.atan2(x.imag, x.real)``. Le résultat se situe dans "
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"l'intervalle [-\\ *π*, *π*], et la coupure par cette opération se situe sur "
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"la partie négative de l'axe des réels, continue par au-dessus. Sur les "
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"systèmes supportant les zéros signés (ce qui inclut la plupart des systèmes "
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"utilisés actuellement), cela signifie que le signe du résultat est le même "
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"que ``x.imag`` même quand ``x.imag`` vaut zéro ::"
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#: library/cmath.rst:77
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msgid ""
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"The modulus (absolute value) of a complex number *x* can be computed using "
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"the built-in :func:`abs` function. There is no separate :mod:`cmath` module "
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"function for this operation."
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msgstr ""
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"Le module (valeur absolue) d'un nombre complexe *x* peut être calculé en "
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"utilisant la primitive :func:`abs`. Il n'y a pas de fonction spéciale du "
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"module :mod:`cmath` pour cette opération."
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#: library/cmath.rst:84
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msgid ""
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"Return the representation of *x* in polar coordinates. Returns a pair ``(r, "
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"phi)`` where *r* is the modulus of *x* and phi is the phase of *x*. "
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"``polar(x)`` is equivalent to ``(abs(x), phase(x))``."
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msgstr ""
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"Renvoie la représentation de *x* en coordonnées polaires. Renvoie une paire "
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"``(r, phi)`` où *r* est le module de *x* et phi est l'argument de *x*. "
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"``polar(x)`` est équivalent à ``(abs(x), phase(x))``."
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#: library/cmath.rst:92
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msgid ""
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"Return the complex number *x* with polar coordinates *r* and *phi*. "
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"Equivalent to ``r * (math.cos(phi) + math.sin(phi)*1j)``."
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msgstr ""
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"Renvoie le nombre complexe *x* dont les coordonnées polaires sont *r* et "
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"*phi*. Équivalent à ``r * (math.cos(phi) + math.sin(phi)*1j)``."
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#: library/cmath.rst:97
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msgid "Power and logarithmic functions"
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msgstr "Fonctions logarithme et exponentielle"
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#: library/cmath.rst:101
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msgid ""
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"Return *e* raised to the power *x*, where *e* is the base of natural "
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"logarithms."
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msgstr ""
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"Renvoie *e* élevé à la puissance *x*, où *e* est la base des logarithmes "
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"naturels."
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#: library/cmath.rst:107
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#, fuzzy
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msgid ""
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"Returns the logarithm of *x* to the given *base*. If the *base* is not "
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"specified, returns the natural logarithm of *x*. There is one branch cut, "
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"from 0 along the negative real axis to -∞."
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msgstr ""
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"Renvoie le logarithme de *x* dans la *base* précisée. Si la *base* n'est pas "
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"spécifiée, le logarithme *naturel* (népérien) de *x* est renvoyé. Il y a une "
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"coupure, partant de 0 sur l'axe réel négatif et vers ``-∞``, continue par au-"
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"dessus."
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#: library/cmath.rst:114
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msgid ""
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"Return the base-10 logarithm of *x*. This has the same branch cut as :func:"
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"`log`."
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msgstr ""
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"Renvoie le logarithme en base 10 de *x*. Elle a la même coupure que :func:"
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"`log`."
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#: library/cmath.rst:120
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msgid ""
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"Return the square root of *x*. This has the same branch cut as :func:`log`."
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msgstr ""
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"Renvoie la racine carrée de *x*. Elle a la même coupure que :func:`log`."
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#: library/cmath.rst:124
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msgid "Trigonometric functions"
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msgstr "Fonctions trigonométriques"
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#: library/cmath.rst:128
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#, fuzzy
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msgid ""
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"Return the arc cosine of *x*. There are two branch cuts: One extends right "
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"from 1 along the real axis to ∞. The other extends left from -1 along the "
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"real axis to -∞."
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msgstr ""
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"Renvoie l'arc cosinus de *x*. Il y a deux coupures : une allant de 1 sur "
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"l'axe réel vers ∞, continue par en-dessous ; l'autre allant de ``-1`` sur "
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"l'axe réel vers ``-∞``, continue par au-dessus."
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#: library/cmath.rst:135
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msgid ""
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"Return the arc sine of *x*. This has the same branch cuts as :func:`acos`."
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msgstr ""
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"Renvoie l'arc sinus de *x*. Elle a les mêmes coupures que :func:`acos`."
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#: library/cmath.rst:140
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#, fuzzy
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msgid ""
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"Return the arc tangent of *x*. There are two branch cuts: One extends from "
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"``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j`` "
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"along the imaginary axis to ``-∞j``."
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msgstr ""
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"Renvoie la tangente de *x*. l y a deux coupures : une allant de ``1j`` sur "
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"l'axe imaginaire vers ``∞j``, continue par la droite ; l'autre allant de "
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"``-1j`` sur l'axe imaginaire vers ``-∞j``, continue par la gauche."
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#: library/cmath.rst:147
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msgid "Return the cosine of *x*."
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msgstr "Renvoie le cosinus de *x*."
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#: library/cmath.rst:152
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msgid "Return the sine of *x*."
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msgstr "Renvoie le sinus de *x*."
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#: library/cmath.rst:157
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msgid "Return the tangent of *x*."
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msgstr "Renvoie la tangente de *x*."
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#: library/cmath.rst:161
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msgid "Hyperbolic functions"
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msgstr "Fonctions hyperboliques"
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#: library/cmath.rst:165
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#, fuzzy
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msgid ""
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"Return the inverse hyperbolic cosine of *x*. There is one branch cut, "
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"extending left from 1 along the real axis to -∞."
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msgstr ""
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"Renvoie l'arc cosinus hyperbolique de *x*. Il y a une coupure, allant de 1 "
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"sur l'axe réel vers ``-∞``, continue par au-dessus."
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#: library/cmath.rst:171
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#, fuzzy
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msgid ""
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"Return the inverse hyperbolic sine of *x*. There are two branch cuts: One "
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"extends from ``1j`` along the imaginary axis to ``∞j``. The other extends "
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"from ``-1j`` along the imaginary axis to ``-∞j``."
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msgstr ""
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"Renvoie l'arc sinus hyperbolique de *x*. Il y a deux coupures : une allant "
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"de ``1j`` sur l'axe imaginaire vers ``∞j``, continue par la droite ; l'autre "
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"allant de ``-1j`` sur l'axe imaginaire vers ``∞j``, continue par la gauche."
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#: library/cmath.rst:178
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#, fuzzy
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msgid ""
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"Return the inverse hyperbolic tangent of *x*. There are two branch cuts: One "
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"extends from ``1`` along the real axis to ``∞``. The other extends from "
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"``-1`` along the real axis to ``-∞``."
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msgstr ""
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"Renvoie l'arc tangente hyperbolique de *x*. Il y a deux coupures : une "
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"allant de ``1`` sur l'axe réel allant vers ``∞``, continue par en-dessous ; "
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"l'autre allant de ``-1`` sur l'axe réel vers ``-∞``, continue par au-dessus."
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#: library/cmath.rst:185
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msgid "Return the hyperbolic cosine of *x*."
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msgstr "Renvoie le cosinus hyperbolique de *x*."
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#: library/cmath.rst:190
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msgid "Return the hyperbolic sine of *x*."
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msgstr "Renvoie le sinus hyperbolique de *x*."
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#: library/cmath.rst:195
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msgid "Return the hyperbolic tangent of *x*."
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msgstr "Renvoie la tangente hyperbolique de *x*."
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#: library/cmath.rst:199
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msgid "Classification functions"
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msgstr "Fonctions de classifications"
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#: library/cmath.rst:203
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msgid ""
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"Return ``True`` if both the real and imaginary parts of *x* are finite, and "
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"``False`` otherwise."
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msgstr ""
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"Renvoie ``True`` si la partie réelle *et* la partie imaginaire de *x* sont "
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"finies, et ``False`` sinon."
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#: library/cmath.rst:211
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msgid ""
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"Return ``True`` if either the real or the imaginary part of *x* is an "
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"infinity, and ``False`` otherwise."
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msgstr ""
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"Renvoie ``True`` si soit la partie réelle *ou* la partie imaginaire de *x* "
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"est infinie, et ``False`` sinon."
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#: library/cmath.rst:217
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msgid ""
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"Return ``True`` if either the real or the imaginary part of *x* is a NaN, "
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"and ``False`` otherwise."
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msgstr ""
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"Renvoie ``True`` si soit la partie réelle *ou* la partie imaginaire de *x* "
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"est NaN, et ``False`` sinon."
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#: library/cmath.rst:223
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msgid ""
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"Return ``True`` if the values *a* and *b* are close to each other and "
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"``False`` otherwise."
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msgstr ""
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"Renvoie ``True`` si les valeurs *a* et *b* sont proches l'une de l'autre, et "
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"``False`` sinon."
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#: library/cmath.rst:226
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msgid ""
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"Whether or not two values are considered close is determined according to "
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"given absolute and relative tolerances."
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msgstr ""
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"Déterminer si deux valeurs sont proches se fait à l'aide des tolérances "
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"absolues et relatives données en paramètres."
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#: library/cmath.rst:229
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msgid ""
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"*rel_tol* is the relative tolerance -- it is the maximum allowed difference "
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"between *a* and *b*, relative to the larger absolute value of *a* or *b*. "
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"For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default "
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"tolerance is ``1e-09``, which assures that the two values are the same "
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"within about 9 decimal digits. *rel_tol* must be greater than zero."
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msgstr ""
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"*rel_tol* est la tolérance relative -- c'est la différence maximale permise "
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"entre *a* et *b*, relativement à la plus grande valeur de *a* ou de *b*. Par "
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"exemple, pour définir une tolérance de 5%,, précisez ``rel_tol=0.05``. La "
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"tolérance par défaut est ``1e-09``, ce qui assure que deux valeurs sont les "
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"mêmes à partir de la 9\\ :sup:`e` décimale. *rel_tol* doit être supérieur à "
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"zéro."
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#: library/cmath.rst:235
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msgid ""
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"*abs_tol* is the minimum absolute tolerance -- useful for comparisons near "
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"zero. *abs_tol* must be at least zero."
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msgstr ""
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"*abs_tol* est la tolérance absolue minimale -- utile pour les comparaisons "
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"proches de zéro. *abs_tol* doit valoir au moins zéro."
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#: library/cmath.rst:238
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msgid ""
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"If no errors occur, the result will be: ``abs(a-b) <= max(rel_tol * "
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"max(abs(a), abs(b)), abs_tol)``."
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msgstr ""
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"Si aucune erreur n'est rencontrée, le résultat sera : ``abs(a-b) <= "
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"max(rel_tol * max(abs(a), abs(b)), abs_tol)``."
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#: library/cmath.rst:241
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msgid ""
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"The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be "
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"handled according to IEEE rules. Specifically, ``NaN`` is not considered "
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"close to any other value, including ``NaN``. ``inf`` and ``-inf`` are only "
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"considered close to themselves."
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msgstr ""
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"Les valeurs spécifiques suivantes : ``NaN``, ``inf``, et ``-inf`` définies "
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"dans la norme IEEE 754 seront manipulées selon les règles du standard IEEE. "
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"En particulier, ``NaN`` n'est considéré proche d'aucune autre valeur, "
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"``NaN`` inclus. ``inf`` et ``-inf`` ne sont considérés proches que d'eux-"
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"mêmes."
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#: library/cmath.rst:250
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msgid ":pep:`485` -- A function for testing approximate equality"
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msgstr ":pep:`485` -- Une fonction pour tester des égalités approximées"
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#: library/cmath.rst:254
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msgid "Constants"
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msgstr "Constantes"
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#: library/cmath.rst:258
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msgid "The mathematical constant *π*, as a float."
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msgstr "La constante mathématique *π*, en tant que flottant."
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#: library/cmath.rst:263
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msgid "The mathematical constant *e*, as a float."
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msgstr "La constante mathématique *e*, en tant que flottant."
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#: library/cmath.rst:268
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msgid "The mathematical constant *τ*, as a float."
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msgstr "La constante mathématique *τ*, sous forme de flottant."
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#: library/cmath.rst:275
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msgid "Floating-point positive infinity. Equivalent to ``float('inf')``."
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msgstr ""
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"Nombre à virgule flottante positif infini. Équivaut à ``float('inf')``."
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#: library/cmath.rst:282
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msgid ""
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"Complex number with zero real part and positive infinity imaginary part. "
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"Equivalent to ``complex(0.0, float('inf'))``."
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msgstr ""
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"Nombre complexe dont la partie réelle vaut zéro et la partie imaginaire un "
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"infini positif. Équivalent à ``complex(0.0, float('inf'))``."
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#: library/cmath.rst:290
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msgid ""
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"A floating-point \"not a number\" (NaN) value. Equivalent to "
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"``float('nan')``."
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msgstr ""
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"Un nombre à virgule flottante *NaN* (*Not a number*). Équivalent à "
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"``float('nan')``."
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#: library/cmath.rst:298
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msgid ""
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"Complex number with zero real part and NaN imaginary part. Equivalent to "
|
||
"``complex(0.0, float('nan'))``."
|
||
msgstr ""
|
||
"Nombre complexe dont la partie réelle vaut zéro et la partie imaginaire vaut "
|
||
"un *NaN*. Équivalent à ``complex(0.0, float('nan'))``."
|
||
|
||
#: library/cmath.rst:306
|
||
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 ""
|
||
"Notez que la sélection de fonctions est similaire, mais pas identique, à "
|
||
"celles du module :mod:`math`. La raison d'avoir deux modules est que "
|
||
"certains utilisateurs ne sont pas intéressés par les nombres complexes, et "
|
||
"peut-être ne savent même pas ce qu'ils sont. Ils préféreraient alors que "
|
||
"``math.sqrt(-1)`` lève une exception au lieu de renvoyer un nombre complexe. "
|
||
"Également, notez que les fonctions définies dans :mod:`cmath` renvoient "
|
||
"toujours un nombre complexe, même si le résultat peut être exprimé à l'aide "
|
||
"d'un nombre réel (en quel cas la partie imaginaire du complexe vaut zéro)."
|
||
|
||
#: library/cmath.rst:314
|
||
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 ""
|
||
"Une note sur les *coupures* : ce sont des courbes sur lesquelles la fonction "
|
||
"n'est pas continue. Ce sont des caractéristiques nécessaires de beaucoup de "
|
||
"fonctions complexes. Il est supposé que si vous avez besoin d'utiliser des "
|
||
"fonctions complexes, vous comprendrez ce que sont les coupures. Consultez "
|
||
"n'importe quel livre (pas trop élémentaire) sur les variables complexes pour "
|
||
"plus d'informations. Pour des informations sur les choix des coupures à des "
|
||
"fins numériques, voici une bonne référence :"
|
||
|
||
#: library/cmath.rst:324
|
||
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. In Iserles, A., and Powell, M. (eds.), The state of the "
|
||
"art in numerical analysis. Clarendon Press (1987) pp165--211."
|
||
|
||
#~ 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 ""
|
||
#~ "Sur les plate-formes avec un support système et matériel des zéros "
|
||
#~ "signés, les fonctions incluant une coupure complexe sont continues *de "
|
||
#~ "chaque* côté de la coupure : le signe du zéro distingue les deux "
|
||
#~ "extrémités de la coupure. Sur les plate-formes ne supportant pas les "
|
||
#~ "zéros signés, la continuité est spécifiée en-dessous."
|