Research On Web-based Input And Accessibility Of Mathematical Expressions

The Internet and World Wide Web have become ubiquitous in modern life. At same time Web-based applications continue to grow in popularity all round the world. Mathematics as the language of science underpins almost all applications of science, education and engineering. The role of mathematics in e-Science and e-Education is potentially profound. Mathematics is also at the heart of representing and reasoning about scientific and engineering data and knowledge. The accessibility of mathematics information refers to the inclusive practice of making mathematics usable by people of all abilities and disabilities. An innovative research on online input mathematical formal and the accessibility of mathematical formula is addressed here. The thesis introduces an implementation method of a Web-based interactive editing tool for mathematical formulas, provides a new lineal language for standard mathematical expression, gives a universal conversion model for different mathematical expression formats, and also presents arithmetic for the computation of presentation complexity of a mathematics formula. The followings are the main research contents and productions:(1) Browser-based mathematical formula editing for the WebThe thesis presents an implementation method of Web-based visual editing and command-line editing. MathEdit, an open-source mathematical formula editor, is introduced in the thesis. Implemented in standard XHTML and JavaScript, MathEdit is an interactive tool for creating and editing mathematical expressions on the Web. Three editing styles are supported:visual user interface with point-click input, visual user interface with drag-drop input, and command-line environment with character-string input. A well-defined API enables interactions between the editor and its hosting Web page. Preference settings and customizations allow MathEdit to fit in different application environments. Supporting both display and computational aspects of mathematical expressions, MathEdit provides a convenient user interface for mathematics computation, function plotting, and mathematics-related document typeset. The design, implementation, and application of MathEdit are presented together with a comparison with several other mathematical expression editors.(2) Mathematics Standard Infix Language The mathematical expression linear syntaxes of Maple, Maxima, Mathematica, MS Office, and ASCIIMathML are compared in the thesis. Based on review of these mainstream linear syntaxes, a mathematics standard infix language (MSIL) is created. Users can use MSIL to enter mathematical expression through ASCII keyboard. Like MathML, MSIL is a universal and system-independent mathematical expression description language. Compared with current linear syntax of computer algebra system and other mathematical formula description language on computer, MSIL is more flexible and has higher input efficiency. It is more accordant with traditional representation of a mathematical expression based on paper and pen.(3) Format conversion approach for mathematical expressions.The thesis analyzes the syntax features of most common representation language for mathematical expressions. Based on the analysis result, a universal architecture for mathematical expression format conversion is given in the thesis. The translation from MathML Presentation to MathML Content has three essential issues which need to be solved. The thesis introduces a type-based solution to translating amphibious mathematical expressions. The conversion processes of MSIL to MathML Content and MathML Presentation, MathML Content to MSIL, MathML Content to Chinese Braille, and MathML Content to MathML Presentation are illustrated in details in the thesis. The rough bidirectional conversion methods between MathML Presentation and LaTeX, MathML Content and OpenMath are also introduced. These conversion programs have applied in both MathEdit and the mathematical expression format translating Web service.(4) The complexity of mathematical expression and its application in intelligent decomposition of mathematical expression.The complexity of a mathematical expression is a measure which can be used to compare the expression with other mathematical expressions and judge which one is simpler. The thesis analyzes three effect factors for the complexity of a mathematical expression:representational length, computational time, and intelligibility. Mainly the thesis introduces a binary-based calculation method for presentation complexity. Furthermore the application of presentation complexity of mathematical expressions in decomposition of mathematical expressions is also addressed. The decomposition method is helpful to learn mathematics for visual impaired person.