**Report
of PSI RAS on project EmNet/NIS/II
(No INTAS-IA03, June 1, 1995 - May 31, 1997)**

Every mathematician who even try to write or read mathematical paper on PC in Russian found a lot of problems. The most exhaustive TeX Distributions for UN*X system such as NTeX for LINUX and TeTeX for almost all UN*X systems contains necessary packages for Russian LaTeX. The arising problems are individual for each distribution and not only Russian dvi files are incompatible but the proceeding of Russian LaTeX file from other system requires the preamble editing. There was no TeX Distribution with Russian support for DOS/Windows systems freely available via networking.

The Russian TeX Distribution for DOS/Windows'95 was created under particular support of Russian Foundation Base Researches (RFBR) and now it is available on

Based on the most fast, flexible and powerful EmTeX executable, it contains an unique intelligence user interface which make it easy to proceed with any TeX (LaTeX, old AMSLaTeX, new AMSLaTeX, AMSTeX, Plain, LaTeX 2e etc.) file. As soon as You will have this TeX installed, You will be able to read and print practically any file from electronic archive without even looking inside. The full Russian support is provided.

**WG 3.1 - LINUX**

Economically Effective Technology
of Regional Nets Creation for Science and High School

http://www.botik.ru/970301
(only in Russian)

The cheapist net technology has been developed to permit the regional medium size nets (200--500 computers) with a cost $ 200--300 for a link. This technology is PC's only based. It does not use such expansive equipment as Cisco and Sun hardware. The technology is LINUX based and does not use any commercial Software.

**WG 3.2 - Hardware Expertise**

We have performed evaluation of the used MIPS computer class. The machines of the class (2 RS-3000 based servers and 29 RS-2000 based workstations) were switched to 220V operation mode, every machine was tested and faulty machines identified.

We have compiled and run the dhrystone-2.1 benchmark on them to get the idea of their performance; the benckmark yielded 35460 and 24752 for servers and workstations respectively. As this is rather poor performance nowadays, and HDD on the workstations is rather small (200MB), we concluded that the workstations cannot be used as standalone workstations.

However, they have all necessary to perform in the role of X-terminals - large monitor, keyboard, mouse, software and enough processor power for the task. We have configured one of workstations in this mode and, after some days of trial exploitation, have cloned the configuration to the rest of workstations, and in this state they were shipped to other participants of the EmNet/NIS project.

**WG 4.2 - Other Symbolic
Manipulation Packages**

Docon System (S. D. Mechveliani)

From 1995 the pure functional version of the Algebraic domain constructor in the Haskell functional environment are developing. The project is in its beginning, but the recent version of the program --- sources and some documentation is ftp-available:

ftp://ftp.botik.ru/pub/local/Mechveliani - docon-0.01.tar.gz (95Kb

Aim: implement the categorial
and pure functional approach to computer algebra.

Some details:

- Algebraic category hierarchy
- Pure functionality and "lazy'' computation
- Old Domain constructor CAC was written in FLAC (REFAL family: pattern matching, functional, typeless, strict, first-order). Now many new features and questions arise concerning the strong typing, abstract data types and "laziness''
- The algorithmic library is so far very small. It is supposed to grow

**WG 4.3 - Software for
Mathematical Modeling**

Calculation of central generators
of the universal enveloping algebras and Vassiliev-Kontsevich weight systems

ftp://math.botik.ru/pub/uea

Algebra of 3-graphs

ftp://math.botik.ru/pub/a3g

The algebra of 3-graphs is a linear space spanned by all connected regular 3-valent graphs (loops and double edges allowed) endowed with cyclic order of (half) edges at every vertex, modulo two types of relations: antisymmetry and what we call Kirchhof law (aka IHX).

The product of two graphs is defined as their connected sum after cutting and pasting over an arbitrary edge.

**WG 4.4 - Computer Tools
for Mathematical Education**

Construction of study materials on mathematical courses with using of computer algebra systems

Many mathematical courses of the high school use conceptions and chapters of asymptotical analysis and optimal processes theory. High level of the exposition of the mathematical courses given with traditional methods is still actual but new informational technologies keep a reserve of increasing teaching quality and better mastering of the courses material by the students. Such a possibility is given with methods of artificial intelligence and computer algebra methods of computer computations.Applying of these methods leads to improvements, perfections of the teaching process and provides appearing of the new development horizons of the branches of mathematics connected with integration with computer algebra methods and new conceptions of approximate computations. Prof. Dmitriev M.G. and his post graduate students proposes to use the symbolic computation system REDUCE for automatization of the computations applying to one of the most popular methods of asymptotic integration of the singularly perturbed ordinary differential equations - the boundary functions method that includes the Poincare method of building of the asymptotics of the regular pertubated ordinary differential equations. From one side such an application allows to build the asymptotics in analytical form because the method of building of the asymptotic is analytical itself and further using of numerical methods interrupt a logical chain of using analytical forms, and from the other side the lack of sufficient skills in real practice for building the highest approximations leads to the weak practical usage of such a mode of accuracy increasing of approximations (due to the highest approximations). Therefore we obtain one more high accuracy method of the approximated solution of problems with a small parameter besides natural applying to the symbolic computations in asymptotic analysis.

Though there are a lot of computer algebra systems (MAPLE, MATHEMATICA, DERIVE etc.) the choice of REDUCE isn't casual.Firstly Prof. Dmitriev M.G. possesses with the licensed product and secondly REDUCE contains input operators of the asymptotic analysis and a large library of auxiliary programs in spite of the pure interface of REDUCE.

The created software on the asymptotic analysis of the singularly perturbed initial problems can be used in educational process on the course of differential equations and the theory of the optimal control.

In 1995, 1996 in Pereslavl two international workshops "New computer technologies in control systems" were organized by Dmitriev M.G. In the frames of these workshops the one of project's goal(organization of net between the specialists in optimal control theory and computer algebra systems applications) were discussed. The special project for NATO grant program was prepared in 1995.

Teaching Mathematics with
Maple and MuPAD

(S. V. Duzhin)

Since 1994, I teach mathematics (mainly linear algebra and geometry) in the University of Pereslavl. Although I prefer to teach mathematics in the normal way, I do have some experience in computer assisted mathematical education in networked environment:

Mathematics with Maple

(http://www.botik.ru/~duzhin/maple/Maple.html)
(only in English)

A review of the basic first year course of mathematics implemented
as a set of 10 Maple worksheets, complete with problems and solutions.
It was designed as a distance learning course on a university network in
University of Aizu, Japan.

Introduction to MuPAD

(http://www.botik.ru/mupad/MuPAD.koi8.html)
(only in Russian)

An experimental WAN distance learning course dedicated to mathematical
computations with the MuPAD computer algebra system. The set consists of
4 lessons that I sent by e-mail from Japan to my students at the University
of Pereslavl. An archive of selected correspondence on the subject is also
included.

**List of EmNet/NIS/II
Workshop, Meeting and Conference participants**

- 1. Workshop El-Pub-96 (Novosibirsk, April 16-18, 1996): Znamenskii S. V.
- 2. EmNet/NIS/II Meeting in Pereslavl-Zalessky (June 2-5, 1996): Abramov S. M., Dmitriev M. G., Nesterova M. V., Znamenskii S.V.
- 3. Workshop El-Pub-97 (Novosibirsk, April 24-26, 1997): Znamenskii S. V., Znamenskaya L. N.
- 4. Workshop LINUX (Helsinki, May, 1997): Pozlevich R. V.