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 noncommercial 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 symbolicnumeric methods of factorizing the evolution operator for nonstationary Schroedinger's equation developed in [5] to investigate evolution of multiqubit systems.

Some recent references: 
 http://www.ricam.oeaw.ac.at/GroebnerBasesBibliography/index.php  Groebner Bases Bibliography
 V.P. Gerdt. http://arXiv.org/math.AC/0501111.
 3. V. P. Gerdt, R.Kragler, A.N.Prokopenya. Proceedings of the DSTUNISAJINR symposium, University of South Africa, Pretoria, 2007, pp.219232.
 V.V. Kornyak. http://arXiv.org/mathph/0504048.
 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, 5870.

Collaboration with:

Armenia 
Yerevan 
ESU 
G.Yu. Kryuchkyan 
Bulgaria 
Sophia 
IMI BAS 
Ì.M. Spiridonova 
Czech Republic 
Prague 
TU 
Ð. Liska 
Ukraine 
Kiev 
Inst. of Cybernetics NAS 
N.Ì. Glasunov 
Germany 
Aachen
Weingarten
Keiserslautern
Kassel
Munich 
TU
UAS
Univ.
Univ.
TU 
W. Plesken, D. Robertz
Ð. Kragler
G.Ì. Greuel
W.M. Seiler,
E. Mayr 
Greece 
Volos 
Univ. 
À. Àkritas 
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: 
 Prof. Dr.Sc. Gerdt V.P.  head of sector
 leading researcher Dr.Sc. Kornyak V.V.
 senior researcher PhD Bogolubskaya A.A.
 senior researcher PhD Khvedelidze A.M.
 senior researcher PhD Palii Yu.G.
 senior researcher Raportirenko A.M.
 senior researcher
Rostovtsev V.A.
 senior researcher PhD Tarasov O.V.
 senior researcher PhD Yanovich D.A
 researcher Gusev A.A.
 PhD student Evlakhov S.A.
Phone.: 63437
email: gerdt@jinr.ru
Link to the Sector's personal webpage:
http://compalg.jinr.ru/
