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  Sector of algebraic and quantum computations of SD CP

Head of sector: Prof. Dr.Sc. Gerdt  V.P.
Research and activity directions:

1.   Development of computer algebra methods, algorithms and software to solve scientific and technical problems arising in research conducted at JINR and its member states.

2.   Provision of the JINR users with information about non-commercial computer algebra systems and about open source software oriented to symbolic and algebraic computation.

3.   Information support of research in JINR based on the use of computer algebra as well as educational programs in JINR relied on computer algebra software. Maintenance of the specialized Web server http://compalg.jinr.ru.

4.   Development and study of mathematical models for quantum computation and quantum informatics.

Basic algorithmic methods:

The most universal algorithmic method for investigating and solving systems of polynomial algebraic, differential and difference equations is the method of Groebner bases [1]. In the last 10 years new highly efficient algorithms for computation of Groebner bases have been designed and implemented in C/C++, Maple and Reduce [2]. In paper [3] a Mathematica program was created to simulate quantum computation. An alternative to the Groebner bases approach to analyze discrete relations was developed in [4]. In addition, it is planned to use symbolic-numeric methods of factorizing the evolution operator for nonstationary Schroedinger's equation developed in [5] to investigate evolution of multi-qubit systems.

Some recent references:
  1. http://www.ricam.oeaw.ac.at/Groebner-Bases-Bibliography/index.php - Groebner Bases Bibliography
  2. V.P. Gerdt. http://arXiv.org/math.AC/0501111.
  3. 3. V. P. Gerdt, R.Kragler, A.N.Prokopenya. Proceedings of the DST-UNISA-JINR symposium, University of South Africa, Pretoria, 2007, pp.219-232.
  4. V.V. Kornyak. http://arXiv.org/math-ph/0504048.
  5. V.P.Gerdt, A.A. Gusev, M.S. Kaschiev, V.A. Rostovtsev, V.N. Samoylov, T.V. Tyupikova, S.I. Vinitsky, Y.Uwano. Programming and Computer Software, Vol. 32, No. 2, 2006, 58--70.
Collaboration with:

Armenia Yerevan ESU G.Yu. Kryuchkyan
Bulgaria Sophia IMI BAS .M. Spiridonova
Czech Republic Prague TU . Liska
Ukraine Kiev Inst. of Cybernetics NAS N.. Glasunov
Germany Aachen
Weingarten
Keiserslautern
Kassel
Munich
TU
UAS
Univ.
Univ.
TU
W. Plesken,  D. Robertz
. Kragler
G.-. Greuel
W.M. Seiler, 
E. Mayr
Greece Volos Univ. . kritas
Romania Bucharest Univ. D. Stefanescu
Russia Moscow

S.Peterburg
Saratov
MSU
SINP MSU
PDMI RAS
SGU
E.V. Pankratiev
V.F. Edneral
N.N. Vasiliev
Yu.A. Blinkov
England Manchester Univ. H. Khudaverdian
JINR   BLTP


DLNP
LPP
D.V. Shirkov
A.V. Chizhov
S.I. Vinitsky
N.B. Skachkov
I.D. Mandzhavidze
Staff:
  1. Prof. Dr.Sc. Gerdt  V.P. - head of sector
  2. leading researcher Dr.Sc. Kornyak  V.V.
  3. senior researcher PhD Bogolubskaya  A.A.
  4. senior researcher PhD Khvedelidze  A.M.
  5. senior researcher PhD Palii  Yu.G.
  6. senior researcher Raportirenko A.M.
  7. senior researcher Rostovtsev  V.A.
  8. senior researcher PhD Tarasov  O.V.
  9. senior researcher PhD Yanovich  D.A
  10. researcher Gusev A.A.
  11. PhD student Evlakhov S.A.

Phone.: 6-34-37
e-mail: gerdt@jinr.ru

Link to the Sector's personal web-page:
http://compalg.jinr.ru/
   Copyright © LIT, JINR , 2006
    Webmaster : @jinr.ru

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