TeXmacs interfaces to Maxima, MuPAD and REDUCE

GNU TEXmacs is a free wysiwyg word processor providing an excellent typesetting quality of texts and formulae. It can also be used as an interface to Computer Algebra Systems (CASs). In the present work, interfaces to three general-purpose CASs have been implemented. 1 TEXmacs GNU TEXmacs [1] is a free (GPL) word processor which • typesets texts and mathematical formulae with very high quality (like LTEX), • emphasizes the logical structure of a document rather than its appearance (like LTEX), • is easy to use and intuitive (like typical wysiwyg word processors), • can be extended by a powerful programming language (like Emacs), • can include PostScript figures (as well as other figures which can be converted to PostScript), • can export LTEX, and import LTEX and html, • supports a number of languages based on Latin and Cyrillic alphabets. It uses TEX fonts both on screen and when printing documents. Therefore, it is truly wysiwyg, with equally good quality of on-screen and printed documents (in contrast to LyX which uses X fonts on screen and calls LTEX for printing). There is a similar commercial program called Scientific Workplace (for Windows). TEXmacs can also be used as an interface to any CAS which can generate LTEX output. It renders LTEX formulae on the fly, producing CAS output with highest 1 typesetting quality (better than, e.g., Mathematica, which uses fixed-width fonts for formula output). A user can utilize editing facilities of TEXmacs: copy (a part of) a previous input into the new one, edit it and sent to the CAS, copy a result derived using the CAS into a paper, etc. In the present talk, I give some examples of using Maxima, MuPAD and REDUCE via TEXmacs. It is not my aim to describe these powerful and complex CASs; I only show examples of typesetting produced by TEXmacs. This talk has been written in TEXmacs and exported to LTEX. 2 Maxima Macsyma is one of the oldest and most mature CASs. It was developed at MIT during the end of sixties – beginning of seventies. Later, it was owned by various commercial companies. Now it seems practically dead. Fortunately, a free CAS Maxima is now under GPL. It is based upon the Macsyma code base from seventies, with a number of later enhancements. It incorporates a lot of mathematical knowledge, is stable and well tested. From its very beginning, Macsyma (and Maxima) pays much attention to mathematical correctness; for example, if the form of an integral depends on the sign of a parameter, it will ask the user about it, or use an assumption – other systems only recently incorporated similar facilities. It is an excellent platform for research projects, because it provides a solid foundation, and it cannot vanish into thin air as commercial systems (e.g., Macsyma) can do at any moment. Its text-based interface now looks somewhat oldfashioned. When combined with a nice graphical interface provided by TEXmacs, it can compete with commercial CASs like Mathematica and Maple, and even produce higher-quality output. And it is difficult for commercial vendors to beat the price :–) Here is a sample Maxima session within TEXmacs. GCL (GNU Common Lisp) Version(2.4.0) Tue May 15 15:03:11 NOVST 2001 Licensed under GNU Library General Public License Contains Enhancements by W. Schelter Maxima 5.6 Tue May 15 15:03:08 NOVST 2001 (with enhancements by W. Schelter). Licensed under the GNU Public License (see file COPYING) (C1) (x^2-y^2)/(x^2+y^2)+sin(alpha)^2; (D1) x − y y2 + x2 + sin α (C2) expand((x+y-1)^5); (D2) y + 5xy − 5y + 10xy − 20xy + 10y + 10xy − 30xy + 30xy − 10y + 5xy − 20xy + 30xy − 20xy + 5y + x − 5x + 10x − 10x + 5x− 1