MathEdit: A Web-based Visual Interactive Editor for Mathematical Expressions

1. MathEdit: A Web-based Visual Interactive Editor for Mathematical Expressions Wei Su (苏伟)1, Paul S.Wang 2 and Lian Li (李廉) 1 Department of Computer Science, Lanzhou University, PRC Department of Computer Science, Kent State University, USA wsu@cs.kent.edu 2009-11

2. Outline • Background • Introduction • Input methods • Output format • Customization and MathEdit API • Content-based Editing and Presentation-based Editing • Comparison

3. 1. Background WME is a modern distributed system on the Web for mathematics education. The approach is to provide each participating school with a website that is comprehensive, well-organized, dynamic, interactive, hands-on and ready to use by teachers for mathematics teaching in the classroom.

4. Background • A totally Web-based tool for the interactive entering and editing of mathematical expressions especially for applying the Web in of mathematics, science, and technology. • The editor should be easy to use and provide an intuitive GUI for editing mathematical expressions • This editor must be easily integrated with the Web-based systems. And the entered expressions should be encoded as common formats which have interoperability with other programs. • The editor must also be flexible, customizable and extensible to address different user groups at various levels.

5. Background (cont.) 5. The editor should satisfy two distinct needs for mathematical expressions • Capturing meaning and semantics (Content)The expressions can be used to compute, prove and plot • Describing the visual appearance (Presentation)The expressions can be used to display, typeset in the applications or on the Web.

6. MathML • The Mathematical Markup Language (MathML), a W3C standard, supports both a presentation encoding and a content encoding for the different purposes.

7. 2. Introduction • MathEdit, a Web-based visual interactive mathematical expression editor, aims to provide an integrated solution of on-line entering and editing of mathematical expressions.

8. MathEdit Overview • MathEdit provides convenient and intuitive graphical user interface. • It provides MathML-Content based editing and MathML-Presentation based editing. • MathML, OpenMath, LaTex, Infix, Picture (Gif, Png), PDF could be generated by MathEdit. • It also provides well-defined API. • It can work with IE and the Mozilla-family browsers • Written in JavaScript and MathML. • Developed jointly by Lanzhou university/China and Kent State University/USA .

9. MathEdit Authoring Environment

10. The Feature of MathEdit • Totally Web-based tool • Integrate Content-based editing and Presentation-based editing • Easy to use, what you see is what you get • Various editing mode • Adaptable and customizable • Easily to include in your web application • Open source and Free

11. The architecture of MathEdit

12. Some Examples of Math expression • Demo

13. 3 Input Methods in MathEdit • Full-visual Input Style In full-visual input style the expression is edited by directly manipulating and navigating its on-screen display. • Character-string Input Style In character-string input style editing can be done via infix or some other string representations of the expression.

14. 3.1. Visual Navigation Convenient visual navigation is important and a user has two ways to visually navigate the displayed expression: • Basic Navigation • Traversal Navigation • Mouse Click

15. Basic Navigation • MathEdit keeps track of the sub-expression and displays a color background to visually identify it to the user. • The arrow keys are used to move the current sub-expression • up to the parent node • down to the first child • left/right to sibling nodes. • MathEdit also allows the user to use the mouse click to select single operand.

16. Traversal Navigation • MathEdit also supports a systematic traversal of the entire expression so the user has a way of reaching any node on the tree. By pressing the PageDown key, the current node is moved in a traversal sequence defined by DFS (depth-first search). The PageUp key, on the other hand, provides the inverse-orient traversal.

17. PageDown Key or Tab Key

18. PageUp Key or Shift+Tab

19. 3.2 Standard Infix Format • In all the character-sting input formats, infix is the most readable and efficient for entering mathematical expressions. • Infix is also most widely used in computing systems such as computer algebra systems (maple, mathematica, maxima), general-purpose programming languages, and electronic calculators. • Unlike being concerned with presentation in asciimathml and MS word, the standard infix format represents the semantic content of mathematical expressions with proper typographical display.

20. Standard Infix Format

21. Example • (sin(AL)-cos(x^2))/sqrt(x^3+1)

22. MathEdit Infix Version

23. 4. Output Format

24. Conversion • Mathematical Expression Conversion Web Service can be accessed at http://www.mathedit.org/mets/

25. 5. Web API and Customization

26. User-customizable Configurations • GUI properties such as the toolbar, the input palettes and other properties • Input methods and output formats • Editing mode such as Presentation-based editing, Content-based editing or mix editing mode • Initial mathematical expression for editing • Shortcut key for entering and editing formula • Templates and corresponding MathML • Mathematical functions

27. Web API var matheditWin2=new mathedit("matheditWin2"); matheditWin2.set("editmode","content"); matheditWin2.set("EditorSize","286,100"); matheditWin2.set("toolbarID","tnew,tundo,tredo,tcut,tcopy,tpaste"); matheditWin2.set("templateID","s1sqrt,s1root,s1sup,s1divides,s3log"); matheditWin2.display("embed2"); var mathmlpst=matheditWind2.get("mmlpresentation"); var infixm=matheditWind2.get("infix");

28. MathEdit Usage Examples

29. 6. Content-based editing Vs. Presentation-based editing • Content perform computations indicated by the formulas (semantics) • Presentation: visually display mathematical formulas

30. Content-based editing and Presentation-based editing • The two distinct needs for mathematical expressions are to visually display mathematical formulas and to perform computations indicated by the formulas. The former is the presentation aspect whereas the latter is the semantics aspect of a mathematical expression. • By customizing by MathEdit API, MathEdit supports Content-based editing and Presentation-based editing for the two purpose of entering mathematical expression mention above.

31. For MathEdit • we must improve the ability for capturing semantic meaning in content-based editing and describing more layout appearances in presentation-based editing, very different requirements indeed. • But our editor should provide a uniform user interface, coherent user interactions, and same output results in both of these modes.

32. Well-formed

33. Presentation-based editing • Presentation-based editing enables users to enter arbitrary expressions that may or may not have widely accepted mathematical meaning or may not be mathematical at all.

34. The Difference between Content-based Editing and Presentation-based Editing

35. Integrated for Content and Presentation

36. 7. Compare the other editors with MathEdit

37. MathBoard

38. MathEdit Users • More than 200 users downloaded MathEdit from April 2009 • The Users came from 32 countries,including:China , USA,UK,India,Greece,Brazil,Argentina,Germany,Romania,Finland,Canada,Nigeriam,Philippines,Colombia,Malaysia,Austrilia,Iran,Japan,Korea,… • 25 universities, including:University of Oxford,Bluesky Academy,Korea University,NTU,NAU,OSU,University of Toronto,College of Charleston • Some companies:IDEAL Group Inc.,June Inc.,TSL Jamaica Ltd,and pellissippi State Tech CC,GMA Enterprise.

39. Thank you！