April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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第二章
而另一種定義方式稍嫌冗長，但當 upvalue 的歸屬權模糊不清的情況下，還蠻方便的。
例如：定義四元數與複數的加法時，若使用前述第一種方式定義 upvalue，此時 upvalue
應屬於四元數或複數並未清楚界定，則可使用
TagSet
及
TagSetDelayed
語法明確指定屬
於
四元數
quaternion
的 upvalue，而非複數
Complex
。[Page-029]
upvalue 的語 法 解決 了 兩個 問 題：首 先，你 不 必解 除 保護 Mathematica 的內 建指 令；
其次，設定 upvalue 可以避免 Mathematica 每次執行更改過的內建指令時（如
Plus
或
Times
指令），均優先檢查自訂定義，而導致效能變差的情況。藉由新物件的 upvalue
設定，Mathematica 只 有 在新 物 件出 現 的情 況 下才 須 考慮 其 操作 定 義，當 upvalue 與
downvalue 同時存在的情況下，upvalue 有較高的優先權，但你應盡量避免這種情況。
函數屬性
Mathematica 根據一組事先規範的函數屬性控制函數行為，使用者應熟悉這些屬性，
因 為 自 訂 函 數 要 輸 出 正 確 的 結 果 經 常 需 要 這 些 函 數 屬 性 的 配 合。
Attributes[f]
、
SetAttributes[f,attr]
與
ClearAttributes[f,attr]
指 令 分 別 對 函 數 f 的 屬 性 進 行 查
詢、設定
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