@@ -158,12 +158,17 @@ msgid ""
158158"zero, returns ``(0.0, 0)``, otherwise ``0.5 <= abs(m) < 1``. This is used "
159159"to\" pick apart\" the internal representation of a float in a portable way."
160160msgstr ""
161+ "以 ``(m, e)`` 對的格式回傳 *x* 的尾數 *m* 及指數 *e*。*m* 是浮點數而 *e* 是整"
162+ "數，且兩者精確地使 ``x == m * 2**e``。若 *x* 為零回傳 ``(0.0, 0)``，否則令 "
163+ "``0.5 <= abs(m) < 1``。此函式用於以可攜的方式「分割」浮點數內部表示法。"
161164
162165#: ../../library/math.rst:110
163166msgid ""
164167"Return an accurate floating point sum of values in the iterable. Avoids "
165168"loss of precision by tracking multiple intermediate partial sums."
166169msgstr ""
170+ "回傳可疊代物件（iterable）中所有值的精確浮點數和。透過追蹤過程中多個部分和以"
171+ "避免精確度損失。"
167172
168173#: ../../library/math.rst:113
169174msgid ""
@@ -173,13 +178,18 @@ msgid ""
173178"occasionally double-round an intermediate sum causing it to be off in its "
174179"least significant bit."
175180msgstr ""
181+ "此演算法準確性奠基於保證 IEEE-754 浮點標準及典型奇進偶捨模式。於有些非 "
182+ "Windows 平台建置時，底層 C 函式庫使用延伸精度加法運算，而可能導致對過程中同一"
183+ "部分和重複捨入，並使其最低有效位不如預期。"
176184
177185#: ../../library/math.rst:119
178186msgid ""
179187"For further discussion and two alternative approaches, see the `ASPN "
180188"cookbook recipes for accurate floating point summation <https://code."
181189"activestate.com/recipes/393090/>`_\\ ."
182190msgstr ""
191+ "更深入的討論及兩種替代做法請參閱 `ASPN cookbook recipes 精準的浮點數總和 "
192+ "<https://code.activestate.com/recipes/393090/>`_。"
183193
184194#: ../../library/math.rst:126
185195msgid ""
@@ -189,24 +199,27 @@ msgid ""
189199"zero, then the returned value is ``0``. ``gcd()`` without arguments returns "
190200"``0``."
191201msgstr ""
202+ "回傳指定引數的最大公因數。若存在任一非零引數，回傳值為所有引數共有因數中最大"
203+ "的正整數。若所有引數皆為零，則回傳值為 ``0``。``gcd()`` 若未傳入任何引數也將"
204+ "回傳 ``0``。"
192205
193206#: ../../library/math.rst:134
194207msgid ""
195208"Added support for an arbitrary number of arguments. Formerly, only two "
196209"arguments were supported."
197- msgstr ""
210+ msgstr "新增支援任意數量的引數。先前僅支援兩個引數。 "
198211
199212#: ../../library/math.rst:141
200213msgid ""
201214"Return ``True`` if the values *a* and *b* are close to each other and "
202215"``False`` otherwise."
203- msgstr ""
216+ msgstr "若 *a* 及 *b* 兩值足夠接近便回傳 ``True``，否則回傳 ``False``。 "
204217
205218#: ../../library/math.rst:144
206219msgid ""
207220"Whether or not two values are considered close is determined according to "
208221"given absolute and relative tolerances."
209- msgstr ""
222+ msgstr "兩數是否足夠接近取決於給定的絕對及相對容差。 "
210223
211224#: ../../library/math.rst:147
212225msgid ""
@@ -216,18 +229,24 @@ msgid ""
216229"tolerance is ``1e-09``, which assures that the two values are the same "
217230"within about 9 decimal digits. *rel_tol* must be greater than zero."
218231msgstr ""
232+ "*rel_tol* 為相對容差 ── *a* 與 *b* 兩數差的最大容許值，與 *a* 及 *b* 兩數的絕"
233+ "對值中較大者相關。例如欲設置 5% 的誤差，則傳入 ``rel_tol=0.05``。其預設值為 "
234+ "``1e-09``，該值可確保兩數於大約 9 個十進數位內相同。*rel_tol* 須大於 ``0``。"
219235
220236#: ../../library/math.rst:153
221237msgid ""
222238"*abs_tol* is the minimum absolute tolerance -- useful for comparisons near "
223239"zero. *abs_tol* must be at least zero."
224240msgstr ""
241+ "*abs_tol* 為最小絕對容差 ── 於接近零的比較時很有用。*abs_tol* 須大於 ``0``。"
225242
226243#: ../../library/math.rst:156
227244msgid ""
228245"If no errors occur, the result will be: ``abs(a-b) <= max(rel_tol * "
229246"max(abs(a), abs(b)), abs_tol)``."
230247msgstr ""
248+ "若未發生任何錯誤，函式結果為 ``abs(a-b) <= max(rel_tol * max(abs(a), "
249+ "abs(b)), abs_tol)``。"
231250
232251#: ../../library/math.rst:159
233252msgid ""
@@ -236,34 +255,43 @@ msgid ""
236255"close to any other value, including ``NaN``. ``inf`` and ``-inf`` are only "
237256"considered close to themselves."
238257msgstr ""
258+ "定義於 IEEE 754 浮點標準中的特殊值 ``NaN``、``inf`` 和 ``-inf`` 會根據該標準"
259+ "處理。更明確地說，``NaN`` 不會與包含自身在內的任何數字足夠接近，而 ``inf`` "
260+ "及 ``-inf`` 皆只與自身接近。"
239261
240262#: ../../library/math.rst:168
241263msgid ":pep:`485` -- A function for testing approximate equality"
242- msgstr ""
264+ msgstr ":pep:`485` ── 用於測試近似相等的函式 "
243265
244266#: ../../library/math.rst:173
245267msgid ""
246268"Return ``True`` if *x* is neither an infinity nor a NaN, and ``False`` "
247269"otherwise. (Note that ``0.0`` *is* considered finite.)"
248270msgstr ""
271+ "若 *x* 不是無限值或 ``NaN`` 便回傳 ``True``，否則回傳 ``False``。（注意 "
272+ "``0.0`` 被視為有限數。）"
249273
250274#: ../../library/math.rst:181
251275msgid ""
252276"Return ``True`` if *x* is a positive or negative infinity, and ``False`` "
253277"otherwise."
254- msgstr ""
278+ msgstr "若 *x* 是正無限值或負無限值便回傳 ``True``，否則回傳 ``False``。 "
255279
256280#: ../../library/math.rst:187
257281msgid ""
258282"Return ``True`` if *x* is a NaN (not a number), and ``False`` otherwise."
259283msgstr ""
284+ "若 *x* 是 ``NaN`` ── 即非數字（not a number）── 便回傳 ``True``，否則回傳 "
285+ "``False``。"
260286
261287#: ../../library/math.rst:192
262288msgid ""
263289"Return the integer square root of the nonnegative integer *n*. This is the "
264290"floor of the exact square root of *n*, or equivalently the greatest integer "
265291"*a* such that *a*\\ ² |nbsp| ≤ |nbsp| *n*."
266292msgstr ""
293+ "回傳非負整數 *n* 的整數平方根。此值為 *n* 精確平方根經下取整的值，亦等同於滿"
294+ "足 ``a² ≤ n`` 的最大整數值 *a*。"
267295
268296#: ../../library/math.rst:196
269297msgid ""
@@ -272,6 +300,9 @@ msgid ""
272300"the exact square root of *n*. For positive *n*, this can be computed using "
273301"``a = 1 + isqrt(n - 1)``."
274302msgstr ""
303+ "於有些應用中，取得滿足 ``n ≤ a²`` 的最小整數值 *a* ── 或者說 *n* 精確平方根經"
304+ "上取整的值 ── 會更加方便。對正數 *n*，此值可使用 ``a = 1 + isqrt(n - 1)`` 計"
305+ "算。"
275306
276307#: ../../library/math.rst:206
277308msgid ""
@@ -281,12 +312,15 @@ msgid ""
281312"zero, then the returned value is ``0``. ``lcm()`` without arguments returns "
282313"``1``."
283314msgstr ""
315+ "回傳指定引數的最小公倍數。若所有引數值皆非零，回傳值為所有引數共有倍數中最小"
316+ "的正整數。若存在任一引數值為零，則回傳值為 ``0``。``lcm()`` 若未傳入任何引數"
317+ "將回傳 ``1``。"
284318
285319#: ../../library/math.rst:217
286320msgid ""
287321"Return ``x * (2**i)``. This is essentially the inverse of function :func:"
288322"`frexp`."
289- msgstr ""
323+ msgstr "回傳 ``x * (2**i)``。此函式本質上為 :func:`frexp` 的反函式。 "
290324
291325#: ../../library/math.rst:223
292326msgid ""