cmath.po

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#: ../../library/cmath.rst:2
msgid ":mod:`cmath` --- Mathematical functions for complex numbers"
msgstr ":mod:`cmath` --- 複素数のための数学関数"

#: ../../library/cmath.rst:9
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 ""
"このモジュールは常に利用可能です。提供しているのは複素数を扱う数学関数へのアクセスです。このモジュール中の関数は整数、浮動小数点数または複素数を引数にとります。また、"
" :meth:`__complex__` または :meth:`__float__` どちらかのメソッドを提供している Python "
"オブジェクトも受け付けます。これらのメソッドはそのオブジェクトを複素数または浮動小数点数に変換するのにそれぞれ使われ、呼び出された関数はそうして変換された結果を利用します。"

#: ../../library/cmath.rst:19
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 ""
"ハードウェア及びシステムレベルでの符号付きゼロのサポートがあるプラットフォームでは、分枝切断 (branch cut) の関わる関数において切断された "
"*両側* "
"の分枝で連続になります。ゼロの符号でどちらの分枝であるかを区別するのです。符号付きゼロがサポートされないプラットフォームでは連続性は以下の仕様で述べるようになります。"

#: ../../library/cmath.rst:27
msgid "Conversions to and from polar coordinates"
msgstr "極座標変換"

#: ../../library/cmath.rst:29
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 ""
"Python の複素数 ``z`` は内部的には *直交座標* もしくは *デカルト座標* "
"と呼ばれる座標を使って格納されています。この座標はその複素数の *実部* ``z.real`` と *虚部* ``z.imag`` "
"で決まります。言い換えると::"

#: ../../library/cmath.rst:36
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 ""
"*極座標* は複素数を表現する別の方法です。極座標では、複素数 *z* は半径 *r* と位相角 *phi* で定義されます。半径 *r* は *z* "
"から原点までの距離です。位相 *phi* は x 軸の正の部分から原点と *z* を結んだ線分までの角度を反時計回りにラジアンで測った値です。"

#: ../../library/cmath.rst:43
msgid ""
"The following functions can be used to convert from the native rectangular "
"coordinates to polar coordinates and back."
msgstr "次の関数はネイティブの直交座標を極座標に変換したりその逆を行うのに使えます。"

#: ../../library/cmath.rst:48
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:65
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 ""
"複素数 *x* のモジュラス (絶対値) は組み込みの :func:`abs` 関数で計算できます。この演算を行う :mod:`cmath` "
"モジュールの関数はありません。"

#: ../../library/cmath.rst:72
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 ""
"*x* の極座標表現を返します。*x* の半径 *r* と *x* の位相 *phi* の組 ``(r, phi)`` "
"を返します。``polar(x)`` は ``(abs(x), phase(x))`` に等しいです。"

#: ../../library/cmath.rst:80
msgid ""
"Return the complex number *x* with polar coordinates *r* and *phi*. "
"Equivalent to ``r * (math.cos(phi) + math.sin(phi)*1j)``."
msgstr ""
"極座標 *r*, *phi* を持つ複素数 *x* を返します。値は ``r * (math.cos(phi) + "
"math.sin(phi)*1j)`` に等しいです。"

#: ../../library/cmath.rst:85
msgid "Power and logarithmic functions"
msgstr "指数関数と対数関数"

#: ../../library/cmath.rst:89
msgid ""
"Return *e* raised to the power *x*, where *e* is the base of natural "
"logarithms."
msgstr ""

#: ../../library/cmath.rst:95
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 ""
"*base* を底とする *x* の対数を返します。もし *base* が指定されていない場合には、*x* "
"の自然対数を返します。分枝切断を一つもち、``0`` から負の実数軸に沿って ``-∞`` へと延びており、上から連続しています。"

#: ../../library/cmath.rst:102
msgid ""
"Return the base-10 logarithm of *x*. This has the same branch cut as "
":func:`log`."
msgstr "*x* の底を 10 とする対数を返します。 :func:`log` と同じ分枝切断を持ちます。"

#: ../../library/cmath.rst:108
msgid ""
"Return the square root of *x*. This has the same branch cut as :func:`log`."
msgstr "*x* の平方根を返します。 :func:`log` と同じ分枝切断を持ちます。"

#: ../../library/cmath.rst:112
msgid "Trigonometric functions"
msgstr "三角関数"

#: ../../library/cmath.rst:116
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 ""
"*x* の逆余弦を返します。この関数には二つの分枝切断 (branch cut) があります: 一つは 1 "
"から右側に実数軸に沿って∞へと延びていて、下から連続しています。もう一つは -1 から左側に実数軸に沿って -∞へと延びていて、上から連続しています。"

#: ../../library/cmath.rst:123
msgid ""
"Return the arc sine of *x*. This has the same branch cuts as :func:`acos`."
msgstr "*x* の逆正弦を返します。 :func:`acos` と同じ分枝切断を持ちます。"

#: ../../library/cmath.rst:128
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 ""
"*x* の逆正接を返します。二つの分枝切断があります: 一つは ``1j`` から虚数軸に沿って ``∞j`` "
"へと延びており、右から連続です。もう一つは ``-1j`` から虚数軸に沿って ``-∞j`` へと延びており、左から連続です。"

#: ../../library/cmath.rst:136
msgid "Return the cosine of *x*."
msgstr "*x* の余弦を返します。"

#: ../../library/cmath.rst:141
msgid "Return the sine of *x*."
msgstr "*x* の正弦を返します。"

#: ../../library/cmath.rst:146
msgid "Return the tangent of *x*."
msgstr "*x* の正接を返します。"

#: ../../library/cmath.rst:150
msgid "Hyperbolic functions"
msgstr "双曲線関数"

#: ../../library/cmath.rst:154
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 "*x* の逆双曲線余弦を返します。分枝切断が一つあり、1 の左側に実数軸に沿って -∞へと延びていて、上から連続しています。"

#: ../../library/cmath.rst:160
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 ""
"*x* の逆双曲線正弦を返します。二つの分枝切断があります: 一つは ``1j`` から虚数軸に沿って ``∞j`` "
"へと延びており、右から連続です。もう一つは ``-1j`` から虚数軸に沿って ``-∞j`` へと延びており、左から連続です。"

#: ../../library/cmath.rst:168
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 ""
"*x* の逆双曲線正接を返します。二つの分枝切断があります: 一つは ``1`` から実数軸に沿って ``∞`` "
"へと延びており、下から連続です。もう一つは ``-1`` から実数軸に沿って ``-∞`` へと延びており、上から連続です。"

#: ../../library/cmath.rst:176
msgid "Return the hyperbolic cosine of *x*."
msgstr "*x* の双曲線余弦を返します。"

#: ../../library/cmath.rst:181
msgid "Return the hyperbolic sine of *x*."
msgstr "*x* の双曲線正弦を返します。"

#: ../../library/cmath.rst:186
msgid "Return the hyperbolic tangent of *x*."
msgstr "*x* の双曲線正接を返します。"

#: ../../library/cmath.rst:190
msgid "Classification functions"
msgstr "類別関数"

#: ../../library/cmath.rst:194
msgid ""
"Return ``True`` if both the real and imaginary parts of *x* are finite, and "
"``False`` otherwise."
msgstr "*x* の実部、虚部ともに有限であれば ``True`` を返し、それ以外の場合  ``False`` を返します。"

#: ../../library/cmath.rst:202
msgid ""
"Return ``True`` if either the real or the imaginary part of *x* is an "
"infinity, and ``False`` otherwise."
msgstr "*x* の実数部または虚数部が正または負の無限大であれば ``True`` を、そうでなければ ``False`` を返します。"

#: ../../library/cmath.rst:208
msgid ""
"Return ``True`` if either the real or the imaginary part of *x* is a NaN, "
"and ``False`` otherwise."
msgstr "*x* の実部と虚部のどちらかが NaN のとき ``True`` を返し、それ以外の場合  ``False`` を返します。"

#: ../../library/cmath.rst:214
msgid ""
"Return ``True`` if the values *a* and *b* are close to each other and "
"``False`` otherwise."
msgstr "値 *a* と *b* が互いに近い場合 ``True`` を、そうでない場合は ``False`` を返します。"

#: ../../library/cmath.rst:217
msgid ""
"Whether or not two values are considered close is determined according to "
"given absolute and relative tolerances."
msgstr "2値が近いと見なされるかどうかは与えられた絶対または相対許容差により決定されます。"

#: ../../library/cmath.rst:220
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* は相対許容差、すなわち *a* と *b* の絶対値の大きい方に対する *a* と *b* の許容される最大の差です。\n"
"例えば許容差を 5% に設定する場合 ``rel_tol=0.05`` を渡します。\n"
"デフォルトの許容差は ``1e-09`` で、2値が9桁同じことを保証します。\n"
"*rel_tol* は0より大きくなければなりません。"

#: ../../library/cmath.rst:226
msgid ""
"*abs_tol* is the minimum absolute tolerance -- useful for comparisons near "
"zero. *abs_tol* must be at least zero."
msgstr "*abs_tol* は最小の絶対許容差です。0に近い値を比較するのに有用です。*abs_tol* は0より大きくなければなりません。"

#: ../../library/cmath.rst:229
msgid ""
"If no errors occur, the result will be: ``abs(a-b) <= max(rel_tol * "
"max(abs(a), abs(b)), abs_tol)``."
msgstr ""
"エラーが起こらなければ結果は ``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)`` "
"です。"

#: ../../library/cmath.rst:232
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 ""
"IEEE 754 特殊値 ``NaN``、``inf``、``-inf`` は IEEE の規則に従って処理されます。\n"
"具体的には、``NaN`` は自身を含めたあらゆる値に近いとは見なされません。\n"
"``inf`` と ``-inf`` は自身とのみ近いと見なされます。"

#: ../../library/cmath.rst:241
msgid ":pep:`485` -- A function for testing approximate equality"
msgstr ":pep:`485` -- A function for testing approximate equality"

#: ../../library/cmath.rst:245
msgid "Constants"
msgstr "定数"

#: ../../library/cmath.rst:249
msgid "The mathematical constant *π*, as a float."
msgstr "定数 *π* (円周率)で、浮動小数点数です。"

#: ../../library/cmath.rst:254
msgid "The mathematical constant *e*, as a float."
msgstr "定数 *e* (自然対数の底)で、浮動小数点数です。"

#: ../../library/cmath.rst:259
msgid "The mathematical constant *τ*, as a float."
msgstr "数学定数 *τ* で、浮動小数点数です。"

#: ../../library/cmath.rst:266
msgid "Floating-point positive infinity. Equivalent to ``float('inf')``."
msgstr "浮動小数点数の正の無限大です。``float('inf')`` と等価です。"

#: ../../library/cmath.rst:273
msgid ""
"Complex number with zero real part and positive infinity imaginary part. "
"Equivalent to ``complex(0.0, float('inf'))``."
msgstr "実部がゼロ、虚部が正の無限大の複素数です。``complex(0.0, float('inf'))`` と等価です。"

#: ../../library/cmath.rst:281
msgid ""
"A floating-point \"not a number\" (NaN) value.  Equivalent to "
"``float('nan')``."
msgstr "浮動小数点数の非数 \"not a number\" (NaN) です。``float('nan')`` と等価です。"

#: ../../library/cmath.rst:289
msgid ""
"Complex number with zero real part and NaN imaginary part. Equivalent to "
"``complex(0.0, float('nan'))``."
msgstr "実部がゼロ、虚部が NaN の複素数です。``complex(0.0, float('nan'))`` と等価です。"

#: ../../library/cmath.rst:297
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 ""
":mod:`math` "
"と同じような関数が選ばれていますが、全く同じではないので注意してください。機能を二つのモジュールに分けているのは、複素数に興味がなかったり、もしかすると複素数とは何かすら知らないようなユーザがいるからです。そういった人たちはむしろ、"
" ``math.sqrt(-1)`` が複素数を返すよりも例外を送出してほしいと考えます。また、 :mod:`cmath` "
"で定義されている関数は、たとえ結果が実数で表現可能な場合 (虚数部がゼロの複素数) でも、常に複素数を返すので注意してください。"

#: ../../library/cmath.rst:305
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 ""
"分枝切断 (branch cut) に関する注釈: "
"分枝切断を持つ曲線上では、与えられた関数は連続ではなくなります。これらは多くの複素関数における必然的な特性です。複素関数を計算する必要がある場合、これらの分枝に関して理解しているものと仮定しています。悟りに至るために何らかの"
" (到底基礎的とはいえない) "
"複素数に関する書をひもといてください。数値計算を目的とした分枝切断の正しい選択方法についての情報としては、以下がよい参考文献となります:"

#: ../../library/cmath.rst:315
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 "
"nothings's sign bit.  In Iserles, A., and Powell, M. (eds.), The state of "
"the art in numerical analysis. Clarendon Press (1987) pp165--211."