77msgstr ""
88"Project-Id-Version :Python 3.13\n "
99"Report-Msgid-Bugs-To :\n "
10- "POT-Creation-Date :2024-09-23 07:52+0800 \n "
11- "PO-Revision-Date :2024-04-26 15:15 +0800\n "
10+ "POT-Creation-Date :2024-03-14 00:03+0000 \n "
11+ "PO-Revision-Date :2024-10-06 23:31 +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 "
@@ -17,7 +17,7 @@ msgstr ""
1717"Content-Type :text/plain; charset=UTF-8\n "
1818"Content-Transfer-Encoding :8bit\n "
1919"Plural-Forms :nplurals=1; plural=0;\n "
20- "X-Generator :Poedit 3.4.2 \n "
20+ "X-Generator :Poedit 3.5 \n "
2121
2222#: ../../library/math.rst:2
2323msgid ":mod:`!math` --- Mathematical functions"
@@ -347,35 +347,35 @@ msgstr "回傳 ``x * (2**i)``。此函式本質上為 :func:`frexp` 的反函式
347347msgid ""
348348"Return the fractional and integer parts of *x*. Both results carry the sign "
349349"of *x* and are floats."
350- msgstr ""
350+ msgstr "回傳 *x* 的小數及整數部分，兩者皆為與 *x* 同號的浮點數。 "
351351
352352#: ../../library/math.rst:245
353353msgid "Return the floating-point value *steps* steps after *x* towards *y*."
354- msgstr ""
354+ msgstr "回傳 *x* 向 *y* *steps* 步的浮點數值。 "
355355
356356#: ../../library/math.rst:247
357357msgid "If *x* is equal to *y*, return *y*, unless *steps* is zero."
358- msgstr ""
358+ msgstr "除非 *steps* 為零，否則當 *x* 與 *y* 相等時回傳 *y*。 "
359359
360360#: ../../library/math.rst:249
361361msgid "Examples:"
362362msgstr "範例："
363363
364364#: ../../library/math.rst:251
365365msgid "``math.nextafter(x, math.inf)`` goes up: towards positive infinity."
366- msgstr ""
366+ msgstr "``math.nextafter(x, math.inf)`` 增加：往正無限。 "
367367
368368#: ../../library/math.rst:252
369369msgid "``math.nextafter(x, -math.inf)`` goes down: towards minus infinity."
370- msgstr ""
370+ msgstr "``math.nextafter(x, -math.inf)`` 減少：往負無限。 "
371371
372372#: ../../library/math.rst:253
373373msgid "``math.nextafter(x, 0.0)`` goes towards zero."
374- msgstr ""
374+ msgstr "``math.nextafter(x, 0.0)`` 靠近零。 "
375375
376376#: ../../library/math.rst:254
377377msgid "``math.nextafter(x, math.copysign(math.inf, x))`` goes away from zero."
378- msgstr ""
378+ msgstr "``math.nextafter(x, math.copysign(math.inf, x))`` 遠離零。 "
379379
380380#: ../../library/math.rst:256
381381msgid "See also :func:`math.ulp`."
@@ -389,32 +389,36 @@ msgstr "新增 *steps* 引數。"
389389msgid ""
390390"Return the number of ways to choose *k* items from *n* items without "
391391"repetition and with order."
392- msgstr ""
392+ 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。 "
393393
394394#: ../../library/math.rst:268
395395msgid ""
396396"Evaluates to ``n! / (n - k)!`` when ``k <= n`` and evaluates to zero when "
397397"``k > n``."
398- msgstr ""
398+ msgstr "當 ``k <= n`` 時其值為 ``n! / (n - k)!``，否則其值為 ``0``。 "
399399
400400#: ../../library/math.rst:271
401401msgid ""
402402"If *k* is not specified or is ``None``, then *k* defaults to *n* and the "
403403"function returns ``n!``."
404404msgstr ""
405+ "若未給定 *k* 或其值為 ``None``，則 *k* 值預設為 *n*，且函式回傳 ``n!``。"
405406
406407#: ../../library/math.rst:282
407408msgid ""
408409"Calculate the product of all the elements in the input *iterable*. The "
409410"default *start* value for the product is ``1``."
410411msgstr ""
412+ "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``。"
411413
412414#: ../../library/math.rst:285
413415msgid ""
414416"When the iterable is empty, return the start value. This function is "
415417"intended specifically for use with numeric values and may reject non-numeric "
416418"types."
417419msgstr ""
420+ "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"
421+ "非數字類型。"
418422
419423#: ../../library/math.rst:294
420424msgid ""
@@ -425,6 +429,10 @@ msgid ""
425429"*even* integer is used for ``n``. The remainder ``r = remainder(x, y)`` "
426430"thus always satisfies ``abs(r) <= 0.5 * abs(y)``."
427431msgstr ""
432+ "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"
433+ "數值為 ``x - n*y``，``n`` 是最接近 ``x / y`` 精確值的整數。若 ``x / y`` 剛好"
434+ "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 = "
435+ "remainder(x, y)`` 必滿足 ``abs(r) <= 0.5 * abs(y)``。"
428436
429437#: ../../library/math.rst:301
430438msgid ""
@@ -433,34 +441,38 @@ msgid ""
433441"x)`` raise :exc:`ValueError` for any non-NaN *x*. If the result of the "
434442"remainder operation is zero, that zero will have the same sign as *x*."
435443msgstr ""
444+ "特殊情況遵循 IEEE 754：特別是，對任何有限數 *x*，``remainder(x, math.inf)`` "
445+ "值為 *x*；對任何非 NaN 值 *x*，``remainder(x, 0)`` 及 ``remainder(math.inf, "
446+ "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"
447+ "號。"
436448
437449#: ../../library/math.rst:307
438450msgid ""
439451"On platforms using IEEE 754 binary floating point, the result of this "
440452"operation is always exactly representable: no rounding error is introduced."
441453msgstr ""
454+ "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"
455+ "差。"
442456
443457#: ../../library/math.rst:315
444458msgid "Return the sum of products of values from two iterables *p* and *q*."
445- msgstr ""
459+ msgstr "回傳兩個可疊代物件值乘積的總和。 "
446460
447461#: ../../library/math.rst:317
448462msgid "Raises :exc:`ValueError` if the inputs do not have the same length."
449- msgstr ""
463+ msgstr "若兩個傳入物件長度不同會引發 :exc:`ValueError`。 "
450464
451465#: ../../library/math.rst:319 ../../library/math.rst:514
452466msgid "Roughly equivalent to::"
453- msgstr ""
454-
455- #: ../../library/math.rst:321
456- msgid "sum(itertools.starmap(operator.mul, zip(p, q, strict=True)))"
457- msgstr "sum(itertools.starmap(operator.mul, zip(p, q, strict=True)))"
467+ msgstr "約等價於：::"
458468
459- #: ../../library/math.rst:323
469+ #: ../../library/math.rst:307
460470msgid ""
461471"For float and mixed int/float inputs, the intermediate products and sums are "
462472"computed with extended precision."
463473msgstr ""
474+ "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"
475+ "算。"
464476
465477#: ../../library/math.rst:331
466478msgid ""
@@ -470,53 +482,65 @@ msgid ""
470482"delegates to :meth:`x.__trunc__ <object.__trunc__>`, which should return an :"
471483"class:`~numbers.Integral` value."
472484msgstr ""
485+ "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，"
486+ "``trunc()`` 等價於 :func:`floor`；若 *x* 為負值，``trunc()`` 等價於 :func:"
487+ "`ceil`。若 *x* 非浮點數，此函式將委派給 :meth:`x.__trunc__ <object."
488+ "__trunc__>`，而後回傳一 :class:`~numbers.Integral` 值。"
473489
474490#: ../../library/math.rst:339
475491msgid "Return the value of the least significant bit of the float *x*:"
476- msgstr ""
492+ msgstr "回傳浮點數 *x* 的最低有效位元值： "
477493
478494#: ../../library/math.rst:341
479495msgid "If *x* is a NaN (not a number), return *x*."
480- msgstr ""
496+ msgstr "若 *x* 為 ``NaN``，回傳 *x*。 "
481497
482498#: ../../library/math.rst:342
483499msgid "If *x* is negative, return ``ulp(-x)``."
484- msgstr ""
500+ msgstr "若 *x* 為負值，回傳 ``ulp(-x)``。 "
485501
486502#: ../../library/math.rst:343
487503msgid "If *x* is a positive infinity, return *x*."
488- msgstr ""
504+ msgstr "若 *x* 為正無限值，回傳 *x*。 "
489505
490506#: ../../library/math.rst:344
491507msgid ""
492508"If *x* is equal to zero, return the smallest positive *denormalized* "
493509"representable float (smaller than the minimum positive *normalized* float, :"
494510"data:`sys.float_info.min <sys.float_info>`)."
495511msgstr ""
512+ "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"
513+ "的最小正浮點數 :data:`sys.float_info.min <sys.float_info>`）。"
496514
497515#: ../../library/math.rst:347
498516msgid ""
499517"If *x* is equal to the largest positive representable float, return the "
500518"value of the least significant bit of *x*, such that the first float smaller "
501519"than *x* is ``x - ulp(x)``."
502520msgstr ""
521+ "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)`` "
522+ "為第一個小於 *x* 的浮點數值。"
503523
504524#: ../../library/math.rst:350
505525msgid ""
506526"Otherwise (*x* is a positive finite number), return the value of the least "
507527"significant bit of *x*, such that the first float bigger than *x* is ``x + "
508528"ulp(x)``."
509529msgstr ""
530+ "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"
531+ "個大於 *x* 的浮點數值。"
510532
511533#: ../../library/math.rst:354
512534msgid "ULP stands for\" Unit in the Last Place\" ."
513- msgstr ""
535+ msgstr "ULP 即最後一位上的單位值（Unit in the Last Place）。 "
514536
515537#: ../../library/math.rst:356
516538msgid ""
517539"See also :func:`math.nextafter` and :data:`sys.float_info.epsilon <sys."
518540"float_info>`."
519541msgstr ""
542+ "另請參閱 :func:`math.nextafter` 及 :data:`sys.float_info.epsilon <sys."
543+ "float_info>`。"
520544
521545#: ../../library/math.rst:362
522546msgid ""
@@ -525,6 +549,9 @@ msgid ""
525549"pair of values, rather than returning their second return value through an "
526550"'output parameter' (there is no such thing in Python)."
527551msgstr ""
552+ "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："
553+ "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"
554+ "遞第二個回傳值（Python 沒有那種東西）。"
528555
529556#: ../../library/math.rst:367
530557msgid ""
@@ -534,6 +561,10 @@ msgid ""
534561"(the same as the platform C double type), in which case any float *x* with "
535562"``abs(x) >= 2**52`` necessarily has no fractional bits."
536563msgstr ""
564+ "使用 :func:`ceil`、:func:`floor` 及 :func:`modf` 三個函式時，請注意 *所有* 足"
565+ "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"
566+ "（與 C 語言 double 型別相同），因此當浮點數 *x* 滿足 ``abs(x) >= 2**52`` 時，"
567+ "它必然沒有小數部分。"
537568
538569#: ../../library/math.rst:375
539570msgid "Power and logarithmic functions"