@@ -8,7 +8,7 @@ msgstr ""
88"Project-Id-Version :Python 3.12\n "
99"Report-Msgid-Bugs-To :\n "
1010"POT-Creation-Date :2023-07-17 17:39+0800\n "
11- "PO-Revision-Date :2024-01-03 17:00 +0800\n "
11+ "PO-Revision-Date :2024-02-05 16:30 +0800\n "
1212"Last-Translator :Adrian Liaw <adrianliaw2000@gmail.com>\n "
1313"Language-Team :Chinese - TAIWAN (https://github.com/python/python-docs-zh- "
1414"tw)\n "
@@ -53,66 +53,79 @@ msgstr "此模組提供下列函式。除非特意註明，否則回傳值皆為
5353
5454#: ../../library/math.rst:30
5555msgid "Number-theoretic and representation functions"
56- msgstr ""
56+ msgstr "數論與表現函式 "
5757
5858#: ../../library/math.rst:34
5959msgid ""
6060"Return the ceiling of *x*, the smallest integer greater than or equal to "
6161"*x*. If *x* is not a float, delegates to :meth:`x.__ceil__ <object."
6262"__ceil__>`, which should return an :class:`~numbers.Integral` value."
6363msgstr ""
64+ "回傳 *x* 經上取整的值，即大於或等於 *x* 的最小整數。若 *x* 並非浮點數，此函式"
65+ "將委派給 :meth:`x.__ceil__ <object.__ceil__>`，並回傳 :class:`~numbers."
66+ "Integral` 型別的值。"
6467
6568#: ../../library/math.rst:41
6669msgid ""
6770"Return the number of ways to choose *k* items from *n* items without "
6871"repetition and without order."
69- msgstr ""
72+ msgstr "回傳從 *n* 個物品中不重複且不考慮排序地取出 *k* 個物品的方法數。 "
7073
7174#: ../../library/math.rst:44
7275msgid ""
7376"Evaluates to ``n! / (k! * (n - k)!)`` when ``k <= n`` and evaluates to zero "
7477"when ``k > n``."
75- msgstr ""
78+ msgstr "當 ``k <= n`` 時其值為 ``n! / (k! * (n - k)!)``，否則其值為 ``0``。 "
7679
7780#: ../../library/math.rst:47
7881msgid ""
7982"Also called the binomial coefficient because it is equivalent to the "
8083"coefficient of k-th term in polynomial expansion of ``(1 + x)ⁿ``."
8184msgstr ""
85+ "因為此值等同於 ``(1 + x)ⁿ`` 進行多項式展開後第 k 項的係數，所以又稱為二項式係"
86+ "數。"
8287
8388#: ../../library/math.rst:51 ../../library/math.rst:258
8489msgid ""
8590"Raises :exc:`TypeError` if either of the arguments are not integers. Raises :"
8691"exc:`ValueError` if either of the arguments are negative."
8792msgstr ""
93+ "當任一參數非整數型別時會引發 :exc:`TypeError`。當任一參數為負數時會引發 :exc:"
94+ "`ValueError`。"
8895
8996#: ../../library/math.rst:59
9097msgid ""
9198"Return a float with the magnitude (absolute value) of *x* but the sign of "
9299"*y*. On platforms that support signed zeros, ``copysign(1.0, -0.0)`` "
93100"returns *-1.0*."
94101msgstr ""
102+ "回傳與 *x* 相同長度（絕對值）且與 *y* 同號的浮點數。在支援帶符號零的平臺上，"
103+ "``copysign(1.0, -0.0)`` 回傳 *-1.0*。"
95104
96105#: ../../library/math.rst:66
97106msgid "Return the absolute value of *x*."
98- msgstr ""
107+ msgstr "回傳 *x* 的絕對值。 "
99108
100109#: ../../library/math.rst:71
101110msgid ""
102111"Return *n* factorial as an integer. Raises :exc:`ValueError` if *n* is not "
103112"integral or is negative."
104113msgstr ""
114+ "以整數回傳 *n* 的階乘。若 *n* 非整數型別或其值為負會引發 :exc:`ValueError`。"
105115
106116#: ../../library/math.rst:74
107117msgid "Accepting floats with integral values (like ``5.0``) is deprecated."
108- msgstr ""
118+ msgstr "允許傳入其值為整數的浮點數（如：``5.0``）已被棄用。 "
109119
110120#: ../../library/math.rst:80
111121msgid ""
112122"Return the floor of *x*, the largest integer less than or equal to *x*. If "
113123"*x* is not a float, delegates to :meth:`x.__floor__ <object.__floor__>`, "
114124"which should return an :class:`~numbers.Integral` value."
115125msgstr ""
126+ "回傳 *x* 經下取整的值，即小於或等於 *x* 的最大整數。若 *x* 並非浮點數，此函式"
127+ "將委派給 :meth:`x.__floor__ <object.__floor__>`，並回傳 :class:`~numbers."
128+ "Integral` 型別的值。"
116129
117130#: ../../library/math.rst:87
118131msgid ""
@@ -129,6 +142,14 @@ msgid ""
129142"generally preferred when working with floats, while Python's ``x % y`` is "
130143"preferred when working with integers."
131144msgstr ""
145+ "回傳 C 函式庫所定義的 ``fmod(x, y)`` 函式值。請注意此函式與 Python 運算式 "
146+ "``x % y`` 可能會回傳不同結果。C 標準要求 ``fmod(x, y)`` 的回傳值完全等同（數"
147+ "學定義上，即無限精度）於 ``x - n*y``，*n* 為可使回傳值與 *x* 同號且長度小於 "
148+ "``abs(y)`` 的整數。Python 運算式 ``x % y`` 的回傳值則與 *y* 同號，且可能無法"
149+ "精確地計算浮點數引數。例如：``fmod(-1e-100, 1e100)`` 的值為 ``-1e-100``，但 "
150+ "Python 運算式 ``-1e-100 % 1e100`` 的結果為 ``1e100-1e-100``，此值無法準確地表"
151+ "示成浮點數，並會四捨五入為出乎意料的 ``1e100``。因此，處理浮點數時通常會選擇"
152+ "函式 :func:`fmod`，而處理整數時會選擇 Python 運算式 ``x % y``。"
132153
133154#: ../../library/math.rst:102
134155msgid ""