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;The design and implementation of a framework supporting bidirectional relations for mathematical equations in Java

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Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/83987

Title:	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;The design and implementation of a framework supporting bidirectional relations for mathematical equations in Java
Authors:	廖信惠;Liao, Sin-Huei
Contributors:	資訊工程學系
Keywords:	數學公式抽象化;自動更新;數學公式關聯系統;雙向計算
Date:	2020-07-24
Issue Date:	2020-09-02 17:50:49 (UTC+8)
Publisher:	國立中央大學
Abstract:	在許多數理應用領域之中，時常會使用數學符號對應特定事物去組成公式，以表達特定的計算關係。並且，公式中變數間所對應的關係並不會更動。再加上使用公式計算的時候，其結果可能會被接著帶入其他公式，進而去計算另外的變數數值。而這種兩公式之間擁有一對互相影響的變數的情況，是本篇論文要探討的使用情境，因此，本篇提出 System of Equations（SoEs）架構。 SoEs 架構會抽象化數學公式中變數間的關係，再把實際數值計算與更動交由 Relation 結構去管理，以提供使用者去包裝成一個公式間存在變數關聯，但公式與數值之間卻不綁定的情況。 Relation 結構中，擁有多種使用者在目標情境下，可能會需要的行為函式，讓使用者對公式之間的運算能更為簡單地以一組 SoEs 架構進行更新與操作。並且在不需要知道細部更新如何在公式間傳遞的情況下，讓 SoEs 架構代替使用者對變數數值自動地進行雙向更新，以及公式之間更新的傳遞。評估之後，該架構的確能在抽象性上，以行數較少、較容易替換公式與變數型態等特性，去證明 SoEs 架構能有效降低使用者建構公式間關聯情境的成本。並且在結尾提出該架構在未來可能的發展。;In many mathematical fields, symbols are usually used to represent specific physical quantities. Equations are composed by symbols, and the relation between symbols will not be changed. We consider a scenario that two equations have a relation in between. It would make a variable computed by one equation could then be recomputed by a different equation to get the final result. We propose the structure of System of Equations (SoEs) which contains two Equations and a pair of related variables. SoEs abstracts the relation between each variable in equation and makes the actual values be managed by a Relation structure. It also provides several methods that user might need. After user updates a variable, SoEs would automatically propagate the changes in the scenario. Without knowing the detail of the actual behavior, user could use SoEs to maintain the balance of every relation. We showed that SoEs structure is easy for user to construct scenarios by an evaluation on abstraction of our work and reduced lines of code.
Appears in Collections:	[Graduate Institute of Computer Science and Information Engineering] Electronic Thesis & Dissertation

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