Compact Computer Algebra

I presented about the implementation of AsirPad, a computer algebra system with a handwriting interface on Linux PDA Zaurus, at the first workshop on Compact Computer Algebra in 2008. In order to implement a computer algebra system on compact devices, not only a CAS engine but GUI, a communication mechanism with the CAS engine and an internal form for mathematical expressions are needed. I used Risa/Asir, a handwriting interface by Qt, OpenXM protocol and Infty XML respectively for AsirPad. This implementation method is suitable for UNIX-based full CASs.

Most of CASs provide a programming language. We can extend functions in the system using it. I added a function that can check whether a chemical/ionic equation with coefficients and indices has a contradiction or not to AsirPad.

The mainstream of the current mobile devices is shifting to smartphones such as iPhone and Android, or slate computers such as iPad. At present, some computer algebra systems for these platforms are developed using the above method by me or other groups. For example, Risa/Asir on iPad, Yacas on Android/iPhone, etc. In the talk I would like to explain the current state of these computer algebra systems on compact devices.

TBA

TBA

The application of computer technology in education has become increasingly important as we move into the information age. In particular, a computer aided assessment (CAA) system can be very useful for teachers and students. The paper introduces a Web-based intelligent mathematics assessment system, MathPASS, developed jointly at Lanzhou University (LZU) and Kent State University (KSU). MathPASS is a drill-and-practice system which has been applied in remedial mathematics courses at KSU. In the Spring 2010 semester, users of MathPASS include 5900 students and 100 teachers.

MathPASS can generate random mathematical test questions based on pre-determined question prototypes, let users enter their answers in either a WYSIWYG or a character-string input environment, and check user answers with the help of a computer algebra system (CAS).

More than 400 question prototypes have been created in MathPASS by the combined efforts of mathematics teachers and mathematics education experts at KSU. A question prototype is a mathematical question template for a specific question pattern containing random parameters satisfying well-defined mathematical conditions. The different question instances of one question prototype are generated on-the-fly for each test, quiz, or homework. A guiding principle in the design of question prototypes is to split a test topic into a range of separate cases constituting significantly different experiences for a learner whose development in that topic is still at an early stage.

MathPASS employs MathEdit, a Web-based mathematical expression editor, to let users enter answers. With MathEdit, students can enter their answers via WYSIWYG editing or command-line editing mode in MathPASS. In WYSIWYG editing mode, students can create and edit mathematical expressions with a convenient and intuitive graphical user interface (GUI). In command-line editing mode, students can enter mathematical expressions with character-string input.

As a part of MathPASS, LZU and KSU are jointly designing and developing a mathematics answer checking protocol (MACP). MACP is an access protocol for communication between MACP service and its client. MACP service is a Web service for checking answers and grading questions to mathematics of middle-school and college. The MACP service aims to grade user answers through verifying the equivalence of expressions and checking expression forms of the answers. The implementation of MACP is based on Representational State Transfer (REST). A MACP service uses a server-side computer algebra system to verify equivalence of expressions and compute standard answers. The service may also judge whether a student answer is in a simplest or a required form.

[full paper (PDF 325KB) ]

The demonstration will address MathEdit, a Web-based visual interactive editor for mathematical expressions. Developed by Lanzhou University and Kent State University cooperatively, MathEdit aims to provide a solution and environment of on-line creating and editing mathematical expression for Web applications such as Web-based education system, scientic computing system, and math-relevant communication system. Abundant mathematical templates and customizable graphical user interface are oered in MathEdit for users to enter various mathematical expressions intuitively. Visual navigation allows users to jump to and select apropos sub-expression by mouse clicking as well as by key pressing. MathEdit provides two editing modes: WYSIWYG editing mode and character-string editing mode. The output format of MathEdit includes MathML Content, MathML Presentation, OpenMath, LaTex, Inx, Braille, image (PNG, GIF and BMP) and PDF. Portable API can be used for programmers to embed MathEdit easily into their Web-based application systems. Implemented in JavaScript, MathEdit is a totally Web-based system, which can run both on IE and Firefox browser. MathEdit is available on http://mathedit.lzu.edu.cn.

The following lists the main contents of the demonstration:

1. The Basic Operations of MathEdit: how to enter mathematical expression via WYSIWYG mode and character-string mode; how to get the output of MathML Content, MathML Presentation, OpenMath, LaTex, Braille, Image (png, gif) and PDF.
2. MathEdit API: how to embed MathEdit into a Web page with pop-up window mode and in-page mode.
3. Usage Instances: demonstrate some usage instances of MathEdit.

Staring with a question what defines a CAS as a compact system and what makes it different from a CAS in its classical understanding, we try come up with a list of basic properties as well as nice-to-have features for such kind of "small" systems. We argue, that the items to be included in this list should be driven more by the targeted application subset, rather than by performance capacities of the hosting devices and environments. Let us make a wish-list for potential "clients" for such light-weight Computer Algebra systems and depart from there. To start, we name a few:

• Pen and Voice-based interface support
• Support for math expression rendering tools
  • Equation line- and page-breaking
  • Expression summarizing / feature visualization
• Support for math-search engines
• Support for search & replace feature in math editors
• Expression equivalence testing for math education software
• Embedded software to generate custom numerical evaluators in real time