python · mattwang44 · Feb 6, 2024 · Jan 1, 2024 · Jan 3, 2024 · Jan 12, 2024
diff --git a/library/math.po b/library/math.po
@@ -8,7 +8,7 @@ msgstr ""
 "Project-Id-Version: Python 3.12\n"
 "Report-Msgid-Bugs-To: \n"
 "POT-Creation-Date: 2023-07-17 17:39+0800\n"
-"PO-Revision-Date: 2024-01-03 17:00+0800\n"
+"PO-Revision-Date: 2024-02-05 16:30+0800\n"
 "Last-Translator: Adrian Liaw <adrianliaw2000@gmail.com>\n"
 "Language-Team: Chinese - TAIWAN (https://github.com/python/python-docs-zh-"
 "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
 
 #: ../../library/math.rst:30
 msgid "Number-theoretic and representation functions"
-msgstr ""
+msgstr "數論與表現函式"
 
 #: ../../library/math.rst:34
 msgid ""
 "Return the ceiling of *x*, the smallest integer greater than or equal to "
 "*x*. If *x* is not a float, delegates to :meth:`x.__ceil__ <object."
 "__ceil__>`, which should return an :class:`~numbers.Integral` value."
 msgstr ""
+"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"
+"將委派給 :meth:`x.__ceil__ <object.__ceil__>`，並回傳 :class:`~numbers."
+"Integral` 型別的值。"
 
 #: ../../library/math.rst:41
 msgid ""
 "Return the number of ways to choose *k* items from *n* items without "
 "repetition and without order."
-msgstr ""
+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。"
 
 #: ../../library/math.rst:44
 msgid ""
 "Evaluates to ``n! / (k! * (n - k)!)`` when ``k <= n`` and evaluates to zero "
 "when ``k > n``."
-msgstr ""
+msgstr "當 ``k <= n`` 時其值為 ``n! / (k! * (n - k)!)``，否則其值為 ``0``。"
 
 #: ../../library/math.rst:47
 msgid ""
 "Also called the binomial coefficient because it is equivalent to the "
 "coefficient of k-th term in polynomial expansion of ``(1 + x)ⁿ``."
 msgstr ""
+"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"
+"數。"
 
 #: ../../library/math.rst:51 ../../library/math.rst:258
 msgid ""
 "Raises :exc:`TypeError` if either of the arguments are not integers. Raises :"
 "exc:`ValueError` if either of the arguments are negative."
 msgstr ""
+"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:"
+"`ValueError`。"
 
 #: ../../library/math.rst:59
 msgid ""
 "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*."
 msgstr ""
+"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，"
+"``copysign(1.0, -0.0)`` 回傳 *-1.0*。"
 
 #: ../../library/math.rst:66
 msgid "Return the absolute value of *x*."
-msgstr ""
+msgstr "回傳 *x* 的絕對值。"
 
 #: ../../library/math.rst:71
 msgid ""
 "Return *n* factorial as an integer.  Raises :exc:`ValueError` if *n* is not "
 "integral or is negative."
 msgstr ""
+"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`。"
 
 #: ../../library/math.rst:74
 msgid "Accepting floats with integral values (like ``5.0``) is deprecated."
-msgstr ""
+msgstr "允許傳入其值為整數的浮點數（如：``5.0``）已被棄用。"
 
 #: ../../library/math.rst:80
 msgid ""
 "Return the floor of *x*, the largest integer less than or equal to *x*.  If "
 "*x* is not a float, delegates to :meth:`x.__floor__ <object.__floor__>`, "
 "which should return an :class:`~numbers.Integral` value."
 msgstr ""
+"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"
+"將委派給 :meth:`x.__floor__ <object.__floor__>`，並回傳 :class:`~numbers."
+"Integral` 型別的值。"
 
 #: ../../library/math.rst:87
 msgid ""
@@ -129,6 +142,14 @@ msgid ""
 "generally preferred when working with floats, while Python's ``x % y`` is "
 "preferred when working with integers."
 msgstr ""
+"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 "
+"``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"
+"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 "
+"``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"
+"精確地計算浮點數引數。例如：``fmod(-1e-100, 1e100)`` 的值為 ``-1e-100``，但 "
+"Python 運算式 ``-1e-100 % 1e100`` 的結果為 ``1e100-1e-100``，此值無法準確地表"
+"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"
+"函式 :func:`fmod`，而處理整數時會選擇 Python 運算式 ``x % y``。"
 
 #: ../../library/math.rst:102
 msgid ""