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研究生:廖信惠
研究生(外文):Sin-Huei Liao
論文名稱:在Java程式語言中以雙向結構表達數學公式間關聯之設計與實作
論文名稱(外文):The design and implementation of a framework supporting bidirectional relations for mathematical equations in Java
指導教授:莊永裕
學位類別:碩士
校院名稱:國立中央大學
系所名稱:資訊工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:73
中文關鍵詞:數學公式抽象化自動更新數學公式關聯系統雙向計算
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摘要 i
Abstract ii
目錄 iv
圖目錄 vii
表目錄 viii
一、 緒論 1
二、 研究動機 4
2.1 動機實例 .................................................................. 4
2.2 Naive 實作 ................................................................ 5
2.3 使用 Map 結構的實作.................................................. 6
2.4 使用 Map 結構實作公式間的關聯................................... 9
2.5 利用 Reactive programming 維持更新一致性 .................... 11
2.6 現行實作的問題 ......................................................... 12
三、 提案 14
3.1 Equation 結構............................................................ 14
3.1.1 Equation 結構中展現變數間的關聯........................ 15
3.1.2 Equation 結構中重新計算的機制........................... 16
3.1.3 Equation 結構所包含的基礎公式資訊..................... 18
3.2 Relation 結構 ............................................................ 18
3.2.1 管理不同公式的實際數值 .................................... 19
3.2.2 利用 Relation 結構維持公式間更新的一致性............ 20
3.3 本章節的結論 ............................................................ 21
四、 實作 22
4.1 使用 Java 實作........................................................... 22
4.2 System of Equations 架構............................................. 23
4.3 Equation 類別............................................................ 25
4.3.1 Expression 結構 ................................................ 25
4.3.2 利用 Expression 完成重新計算 ............................. 27
4.4 Relation 類別 ............................................................ 29
4.4.1 建立 Relation 物件............................................. 29
4.4.2 資料儲存的結構 ................................................ 30
4.4.3 SoEs 架構下的 Multi-directional Reactive ............... 31
4.4.4 Equation 物件的替換.......................................... 32
五、 評估與討論 33
5.1 使用情境 .................................................................. 33
5.1.1 最簡單的使用情境 ............................................. 33
5.1.2 其他使用情境的差異 .......................................... 34
5.2 比較對象 .................................................................. 35
5.2.1 Naive .............................................................. 36
5.2.2 Observer pattern ............................................... 36
5.3 抽象性 ..................................................................... 37
5.3.1 運算關係的數量評估 .......................................... 37
5.3.2 變數型態改變變動評估 ....................................... 38
5.3.3 相同數學公式應用於不同使用情境的評估 ............... 39
5.3.4 評估更動在多個候選變數下的處理方式 .................. 40
5.3.5 抽象性比較的結論 ............................................. 41
5.4 基礎公式型態的行數比較引出所有案例比較 ..................... 42
5.4.1 建立運算關係 ................................................... 42
5.4.2 完成使用情境 ................................................... 44
5.4.3 數值更新 ......................................................... 44
5.4.4 優劣討論 ......................................................... 45
5.5 case study 的實作評估 ................................................. 46
5.5.1 使用 SoEs 建立 case study 的使用情境................... 47
5.5.2 使用 Observer Pattern 建立 case study 的使用情境 . . . 49
5.5.3 對使用情境進行更新 .......................................... 50
六、 相關研究 52
6.1 Reactive Programming................................................. 52
6.1.1 SignalJ ............................................................ 52
6.1.2 Coherent.......................................................... 53
6.1.3 Propagator ....................................................... 53
6.2 Symbolic Computation................................................. 54
6.3 Constraint Satisfication ................................................ 54
七、 總結 56
參考文獻 59
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