Handwriting Interface for MathML and Other Notations of Mathematical Expressions

Masakazu Suzuki
Kyushu University

Abstract

Recently, the use of computers and networks is widely spread. However, it is true that the user interfaces of current computer systems are not convenient to input mathematical expressions. For example, the widely used data format LaTeX requires some training to master the notations, and it is not easy to understand the meaning of the written expressions by the LaTeX source at a glance. Another problem is that there are various data formats for mathematical expressions, for example, syntax-based data formats (LaTeX, MathML, and the notations used in computer algebra system formats such as Mathematica, Maple V, etc.), image data on the web, other formats of word processors, and so on. The system that integrates these data formats including MathML, in the view of the network society, provided with an easy interface for mathematical expressions, is truly expected.

To realize easier treatment of mathematical expressions of various formats, we are developing a system to edit multiple-format mathematical expressions having a handwriting interface. Actually, the system supports the input and output interface in the notations of LaTeX and MathML. The extension to any other syntax-based notations can be easily supported by preparation of the corresponding resources and some primitive functions.¹

The system looks like a simple editor or a word processor. Opening LaTeX files or MathML files, users can read and edit the texts, including mathematical expressions presented on the display in a usual printed form, and can save them into a file in both LaTeX and MathML notations. Thus, users can easily effectuate the transformation of data formats between LaTeX and MathML.

The displayed texts and mathematical expressions can be edited freely both by using ordinary editing operations such as cut, copy, paste, and delete and by using key inputs including LaTeX commands for mathematical expressions.

Further, the mathematical expressions written on the display of the system can be evaluated, factorized, expanded, or presented by graphs, etc., by Mathematica linked to the system by the protocol MathLink ([1]). The results of the calculation are put into the clipboard of the system and can be pasted at any place in the display and edited freely.

Another distinctive feature of the system is that it provides a handwriting interface to input mathematical expressions. By clicking a button, the dialog box to input pen strokes using a mouse, a data tablet, or a pen is displayed. The mathematical expressions written by hand in this dialog box are recognized and put into the mathematical text displayed on the main board of the system at its cursor position. By this handwriting interface, the system realizes a very easy intuitive method to edit or correct mathematical expressions, requiring, for example, no special skill about LaTeX notations of mathematical expressions.

In the handwriting dialog box, as soon as a character is written, it is recognized and rewritten by neat strokes in an appropriate size and position automatically. This automatic rewriting method considerably improves the accuracy of the structure analysis of the written mathematical expressions. Another merit of this method is that, by the rewriting, the user can identify each recognition error immediately when it occurs and can correct it easily.

The following experiment, carried out using 30 writers who had gotten their hands in writing mathematical expressions but had never used our system, shows the efficiency of our handwriting interface. After less than one hour of practice using our system, each writer tried to write the following mathematical expressions (1)~(4) as fast as possible.

(1) $\displaystyle \, \lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n=e,\,$ (2) $\displaystyle \, \int_0^\infty\frac{\log x}{1+x^2}dx,\,$

(3) $\displaystyle \, \sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^2},\,$ (4) $\displaystyle \, \int_0^\infty e^{-a^2x^2}dx=\frac{\sqrt{\pi}}{2\vert a\vert}$

We counted the time from the first stroke's beginning until the whole expression was exactly written up, including the time to correct.

As the result, everyone wrote up all the expressions (1)~(4) between 1.5 minutes and 4 minutes, and the average was about 2.6 minutes. For five experts of LaTeX, who had written at least five articles of mathematics using LaTeX, we counted the times to input the same expressions in the notation of LaTeX. Then, the fastest time was about 1.5 minutes, the longest was about 3.5 minutes, and the average was 2 minutes. This shows that beginners with simple training in using our interface can smoothly input complicated expressions as well as experts in the notation of LaTeX can.

¹In fact, the output in Braille Codes is also implemented in our system in this way in order to use our system in the Braille transcription of mathematical documents ([2]).

References

[1] H. Okamura, T. Kanahori, W. Cong, R. Fukuda, F. Tamari, and M. Suzuki, "Handwriting Interface for Computer Algebra Systems," Proceedings of the Fourth Asian Technology Conference in Mathematics, Guangzhou, 291-300, 1999.

[2] R. Fukuda, N. Ohtake, and M. Suzuki, "Optical Recognition and Braille Transcription of Mathematical Documents," to appear in the Proceedings of the 7th International Conference on Computers Helping People with Special Needs (ICCHP), Karlsruhe, 2000.