Translate library/math.po rst: 87-102, 239-374

library/math.po

@@ -7,8 +7,8 @@ msgid ""
 msgstr ""
 "Project-Id-Version: Python 3.13\n"
 "Report-Msgid-Bugs-To: \n"
-"POT-Creation-Date: 2024-09-23 07:52+0800\n"
-"PO-Revision-Date: 2024-04-26 15:15+0800\n"
+"POT-Creation-Date: 2024-03-14 00:03+0000\n"
+"PO-Revision-Date: 2024-10-21 23:50+0800\n"
 "Last-Translator: Adrian Liaw <adrianliaw2000@gmail.com>\n"
 "Language-Team: Chinese - TAIWAN (https://github.com/python/python-docs-zh-"
 "tw)\n"
@@ -17,7 +17,7 @@ msgstr ""
 "Content-Type: text/plain; charset=UTF-8\n"
 "Content-Transfer-Encoding: 8bit\n"
 "Plural-Forms: nplurals=1; plural=0;\n"
-"X-Generator: Poedit 3.4.2\n"
+"X-Generator: Poedit 3.5\n"
 
 #: ../../library/math.rst:2
 msgid ":mod:`!math` --- Mathematical functions"
@@ -114,7 +114,6 @@ 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
-#, fuzzy
 msgid "Floats with integral values (like ``5.0``) are no longer accepted."
 msgstr "允許傳入其值為整數的浮點數（如：``5.0``）已被棄用。"
 
@@ -135,6 +134,8 @@ msgid ""
 "``float`` format. This operation often provides better accuracy than the "
 "direct expression ``(x * y) + z``."
 msgstr ""
+"融合乘加運算。回傳 ``(x * y) + z``，用近似於無限精度及範圍的方式計算，而後一"
+"次轉換為浮點數格式。此操作通常能提供比運算式 ``(x * y) + z`` 更高的精度。"
 
 #: ../../library/math.rst:92
 msgid ""
@@ -144,6 +145,9 @@ msgid ""
 "``fma(inf, 0, nan)``. In these cases, ``math.fma`` returns a NaN, and does "
 "not raise any exception."
 msgstr ""
+"此函式遵循 IEEE-754 標準中規範的融合乘加（fusedMultiplyAdd）運算。該標準保留"
+"一種由實作環境決定的案例，即 ``fma(0, inf, nan)`` 和 ``fma(inf, 0, nan)`` 的"
+"結果；在此案例中，``math.fma`` 回傳 ``NaN`` 且不會引發例外。"
 
 #: ../../library/math.rst:103
 msgid ""
@@ -347,35 +351,35 @@ msgstr "回傳 ``x * (2**i)``。此函式本質上為 :func:`frexp` 的反函式
 msgid ""
 "Return the fractional and integer parts of *x*.  Both results carry the sign "
 "of *x* and are floats."
-msgstr ""
+msgstr "回傳 *x* 的小數及整數部分，兩者皆為與 *x* 同號的浮點數。"
 
 #: ../../library/math.rst:245
 msgid "Return the floating-point value *steps* steps after *x* towards *y*."
-msgstr ""
+msgstr "回傳 *x* 向 *y* *steps* 步的浮點數值。"
 
 #: ../../library/math.rst:247
 msgid "If *x* is equal to *y*, return *y*, unless *steps* is zero."
-msgstr ""
+msgstr "除非 *steps* 為零，否則當 *x* 與 *y* 相等時回傳 *y*。"
 
 #: ../../library/math.rst:249
 msgid "Examples:"
 msgstr "範例："
 
 #: ../../library/math.rst:251
 msgid "``math.nextafter(x, math.inf)`` goes up: towards positive infinity."
-msgstr ""
+msgstr "``math.nextafter(x, math.inf)`` 增加：往正無限。"
 
 #: ../../library/math.rst:252
 msgid "``math.nextafter(x, -math.inf)`` goes down: towards minus infinity."
-msgstr ""
+msgstr "``math.nextafter(x, -math.inf)`` 減少：往負無限。"
 
 #: ../../library/math.rst:253
 msgid "``math.nextafter(x, 0.0)`` goes towards zero."
-msgstr ""
+msgstr "``math.nextafter(x, 0.0)`` 靠近零。"
 
 #: ../../library/math.rst:254
 msgid "``math.nextafter(x, math.copysign(math.inf, x))`` goes away from zero."
-msgstr ""
+msgstr "``math.nextafter(x, math.copysign(math.inf, x))`` 遠離零。"
 
 #: ../../library/math.rst:256
 msgid "See also :func:`math.ulp`."
@@ -389,32 +393,36 @@ msgstr "新增 *steps* 引數。"
 msgid ""
 "Return the number of ways to choose *k* items from *n* items without "
 "repetition and with order."
-msgstr ""
+msgstr "回傳從 *n* 個物品中不重複且考慮排序地取出 *k* 個物品的方法數。"
 
 #: ../../library/math.rst:268
 msgid ""
 "Evaluates to ``n! / (n - k)!`` when ``k <= n`` and evaluates to zero when "
 "``k > n``."
-msgstr ""
+msgstr "當 ``k <= n`` 時其值為 ``n! / (n - k)!``，否則其值為 ``0``。"
 
 #: ../../library/math.rst:271
 msgid ""
 "If *k* is not specified or is ``None``, then *k* defaults to *n* and the "
 "function returns ``n!``."
 msgstr ""
+"若未給定 *k* 或其值為 ``None``，則 *k* 值預設為 *n*，且函式回傳 ``n!``。"
 
 #: ../../library/math.rst:282
 msgid ""
 "Calculate the product of all the elements in the input *iterable*. The "
 "default *start* value for the product is ``1``."
 msgstr ""
+"計算傳入的 *iterable* 中所有元素的乘積。預設的乘積起始值 *start* 為 ``1``。"
 
 #: ../../library/math.rst:285
 msgid ""
 "When the iterable is empty, return the start value.  This function is "
 "intended specifically for use with numeric values and may reject non-numeric "
 "types."
 msgstr ""
+"當 *iterable* 為空時，回傳 *start* 值。此函式特別用於計算數值，並可能拒絕處理"
+"非數字類型。"
 
 #: ../../library/math.rst:294
 msgid ""
@@ -425,6 +433,10 @@ msgid ""
 "*even* integer is used for ``n``.  The remainder ``r = remainder(x, y)`` "
 "thus always satisfies ``abs(r) <= 0.5 * abs(y)``."
 msgstr ""
+"回傳 *x* 對 *y* 根據 IEEE 754 定義的餘數。對有限數 *x* 及有限非零數 *y*，該餘"
+"數值為 ``x - n*y``，``n`` 是最接近 ``x / y`` 精確值的整數。若 ``x / y`` 剛好"
+"位於兩個連續整數的正中間，``n`` 為最接近的 *偶* 數。因此該餘數 ``r = "
+"remainder(x, y)`` 必滿足 ``abs(r) <= 0.5 * abs(y)``。"
 
 #: ../../library/math.rst:301
 msgid ""
@@ -433,34 +445,38 @@ msgid ""
 "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*."
 msgstr ""
+"特殊情況遵循 IEEE 754：特別是，對任何有限數 *x*，``remainder(x, math.inf)`` "
+"值為 *x*；對任何非 ``NaN`` 值 *x*，``remainder(x, 0)`` 及 ``remainder(math."
+"inf, x)`` 會引發 :exc:`ValueError`。若取餘數操作的結果為零，則該零值會與 *x* "
+"同號。"
 
 #: ../../library/math.rst:307
 msgid ""
 "On platforms using IEEE 754 binary floating point, the result of this "
 "operation is always exactly representable: no rounding error is introduced."
 msgstr ""
+"在遵循 IEEE 754 浮點標準的平台上，此操作的結果必能精準表示，不會出現捨入誤"
+"差。"
 
 #: ../../library/math.rst:315
 msgid "Return the sum of products of values from two iterables *p* and *q*."
-msgstr ""
+msgstr "回傳兩個可疊代物件值乘積的總和。"
 
 #: ../../library/math.rst:317
 msgid "Raises :exc:`ValueError` if the inputs do not have the same length."
-msgstr ""
+msgstr "若兩個傳入物件長度不同會引發 :exc:`ValueError`。"
 
 #: ../../library/math.rst:319 ../../library/math.rst:514
 msgid "Roughly equivalent to::"
-msgstr ""
-
-#: ../../library/math.rst:321
-msgid "sum(itertools.starmap(operator.mul, zip(p, q, strict=True)))"
-msgstr "sum(itertools.starmap(operator.mul, zip(p, q, strict=True)))"
+msgstr "約等價於：::"
 
-#: ../../library/math.rst:323
+#: ../../library/math.rst:307
 msgid ""
 "For float and mixed int/float inputs, the intermediate products and sums are "
 "computed with extended precision."
 msgstr ""
+"對浮點數或混合整數及浮點數的傳入物件，其過程中的乘積及總和皆使用延伸精度計"
+"算。"
 
 #: ../../library/math.rst:331
 msgid ""
@@ -470,53 +486,65 @@ msgid ""
 "delegates to :meth:`x.__trunc__ <object.__trunc__>`, which should return an :"
 "class:`~numbers.Integral` value."
 msgstr ""
+"回傳去除小數部分而僅餘整數部分的 *x*。此函式會向零捨入：若 *x* 為正值，"
+"``trunc()`` 等價於 :func:`floor`；若 *x* 為負值，``trunc()`` 等價於 :func:"
+"`ceil`。若 *x* 非浮點數，此函式將委派給 :meth:`x.__trunc__ <object."
+"__trunc__>`，而後回傳一 :class:`~numbers.Integral` 值。"
 
 #: ../../library/math.rst:339
 msgid "Return the value of the least significant bit of the float *x*:"
-msgstr ""
+msgstr "回傳浮點數 *x* 的最低有效位元值："
 
 #: ../../library/math.rst:341
 msgid "If *x* is a NaN (not a number), return *x*."
-msgstr ""
+msgstr "若 *x* 為 ``NaN``，回傳 *x*。"
 
 #: ../../library/math.rst:342
 msgid "If *x* is negative, return ``ulp(-x)``."
-msgstr ""
+msgstr "若 *x* 為負值，回傳 ``ulp(-x)``。"
 
 #: ../../library/math.rst:343
 msgid "If *x* is a positive infinity, return *x*."
-msgstr ""
+msgstr "若 *x* 為正無限值，回傳 *x*。"
 
 #: ../../library/math.rst:344
 msgid ""
 "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>`)."
 msgstr ""
+"若 *x* 等於零，回傳 *反正規化* 可表示的最小正浮點數（此值小於 *正規化* 可表示"
+"的最小正浮點數 :data:`sys.float_info.min <sys.float_info>`）。"
 
 #: ../../library/math.rst:347
 msgid ""
 "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)``."
 msgstr ""
+"若 *x* 等於可表示的最大正浮點數，回傳 *x* 的最低有效位元值，使 ``x-ulp(x)`` "
+"為第一個小於 *x* 的浮點數值。"
 
 #: ../../library/math.rst:350
 msgid ""
 "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)``."
 msgstr ""
+"否則（當 *x* 為正有限數），回傳 *x* 的最低有效位元值，使 ``x+ulp(x)`` 為第一"
+"個大於 *x* 的浮點數值。"
 
 #: ../../library/math.rst:354
 msgid "ULP stands for \"Unit in the Last Place\"."
-msgstr ""
+msgstr "ULP 即最後一位上的單位值（Unit in the Last Place）。"
 
 #: ../../library/math.rst:356
 msgid ""
 "See also :func:`math.nextafter` and :data:`sys.float_info.epsilon <sys."
 "float_info>`."
 msgstr ""
+"另請參閱 :func:`math.nextafter` 及 :data:`sys.float_info.epsilon <sys."
+"float_info>`。"
 
 #: ../../library/math.rst:362
 msgid ""
@@ -525,6 +553,9 @@ msgid ""
 "pair of values, rather than returning their second return value through an "
 "'output parameter' (there is no such thing in Python)."
 msgstr ""
+"請注意 :func:`frexp` 及 :func:`modf` 的呼叫/回傳模式與 C 語言中相應函式不同："
+"它們傳入一個引數並回傳一對值，而非透過一個「輸出參數（output parameter）」傳"
+"遞第二個回傳值（Python 沒有那種東西）。"
 
 #: ../../library/math.rst:367
 msgid ""
@@ -534,6 +565,10 @@ msgid ""
 "(the same as the platform C double type), in which case any float *x* with "
 "``abs(x) >= 2**52`` necessarily has no fractional bits."
 msgstr ""
+"使用 :func:`ceil`、:func:`floor` 及 :func:`modf` 三個函式時，請注意 *所有* 足"
+"夠大的浮點數都是精確的整數。Python 的浮點數型別的精確度通常不會超過 53 位元"
+"（與 C 語言 double 型別相同），因此當浮點數 *x* 滿足 ``abs(x) >= 2**52`` 時，"
+"它必然沒有小數部分。"
 
 #: ../../library/math.rst:375
 msgid "Power and logarithmic functions"