News and Events
The next meeting of the Seminar on Computer Algebra, CMC faculty of MSU & CCAS will be on Wednesday, November 20, at 16:20, room 713 of CMC faculty.
The 19th International Conference on Applications of Computer Algebra (ACA 2013, Malaga, Spain) will take place on July 2-6, 2013.
"Computer Algebra, Quantum Computing and Quantum Information Processing"
International Conference MATHEMATICAL MODELING AND COMPUTATIONAL PHYSICS, 2013 (MMCP 2013) will be held at the LIT of the JINR on July 8 - July 12, 2013 in Dubna .
February 1, 2007
The LIT Seminar was held on February 1, 2007 to mark the 60th anniversary of the Head of our Group, Professor Vladimir Gerdt. He presented talk "Computer algebra, integrability, involutivity and all that".
About the Group
Group of Algebraic and Quantum Computations is a part of the Laboratory of Information Technologies (LIT)
of the Joint Institute for Nuclear Research (JINR). The main research and activity directions of the Group are:
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 with open source software oriented to symbolic and algebraic computation.
3. Information support of research in JINR based on the use of computer algebra; and of educational programs in JINR relied on computer algebra software. Maintenance of the specialized Web server http://compalg.jinr.ru .
4. Elaboration and analysis of mathematical models for quantum computations and quantum informatics.
Basic algorithms and software developed in the Group
The most universal algorithmic method for investigating and solving systems of polynomial algebraic, differential and difference equations is the method of Groebner bases . In the last 10 years new highly efficient involutive algorithms for computation of Groebner bases have been designed  and implemented in the GINV software . An algorithmic extension of the involutive algorithm to systems of nonlinear partial differential equations has been done in . An algorithmic approach to analyze discrete systems was developed in . In paper  a Mathematica program was created to simulate quantum computation. Symbolic-numeric algorithms for simulation of low dimensional nanostructures in external fields have been developed .
- http://www.risc.jku.at/Groebner-Bases-Bibliography/ .
- V.P.Gerdt. Involutive Algorithms for Computing Gröbner Bases. In: “Computational Commutative and Non-Commutative Algebraic Geometry”. NATO Science Series, IOS Press, 2005, pp. 199—225. arXiv:math.AC/0501111.
- V.P.Gerdt and Yu.A.Blinkov. Specialized Computer Algebra System GINV. Programming and Computer Software, Vol. 34, No. 2, 2008, 112—123.
- T.Bächler, V.Gerdt, M.Lange-Hegermann and D.Robertz. Algorithmic Thomas Decomposition of Algebraic and Differential Systems. Journal of Symbolic Computation, 47(10), 1233-1266, 2012. arXiv:math.AC/1108.0817 .
- V.V. Kornyak. Structural and Symmetry Analysis of Discrete Dynamical Systems. In “Cellular Automata”, Nova Science Publishers, Inc., 2010, pp.119—163.
- V.P. Gerdt and A.N.Prokopenya. The Circuit Model of Quantum Computation and its Simulation with Mathematica. Lecture Notes in Computer Science Vol. 7175, Springer, Heidelberg, 2012, pp.43—55.
- A.A.Gusev, O.Chuluunbaatar, V.P.Gerdt, V.A.Rostovtsev, S.I.Vinitsky, V.L.Derbov and V.V. Serov. Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models. Lecture Notes in Computer Science Vol. 6264, Springer-Verlag, Berlin, 2010, pp.106—122. arXiv:cond-mat.mes-hall/1004.4202.
Some other recent references
- V.P.Gerdt and Yu.A.Blinkov. Involutive Division Generated by an Antigraded Monomial Ordering. Lecture Notes in Computer Science, Vol. 6885, Springer-Verlag, Berlin, 2011, pp.158—74.
- V.Gerdt, A.Khvedelidze, D.Mladenov and Yu.Palii. SU(6) Casimir Invariants and SU(2)xSU(3) Scalars for a Mixed Qubit-Qutrit States. Journal of Mathematical Sciences, Vol. 179, No. 6, 2011, 690—701. arXiv:quant-ph/1106.4905 .
- V.Gerdt and D.Robertz. Computation of Difference Gröbner Bases. Computer Science Journal of Moldova, 20(2), 2012, 203—226. arXiv:cs.SC/1206.3463 .
- V.P.Gerdt and A.Hashemi. Comprehensive Involutive Systems. Lecture Notes in Computer Science, Vol. 7442, Springer-Verlag, Berlin, 2012, pp.98—116.
- V.Gerdt, A.Gusev, S.Vinitsky, O.Chuluunbaatar, L. Le Hai and V. Rostovtsev. Symbolic-Numerical Algorithm for Calculations of High|m| Rydberg States and Decay Rates. Lecture Notes in Computer Science, Vol. 7442, Springer-Verlag, Berlin, 2012, pp.155—171.
Please, see also Events
- The XIV Spanish Meeting on Computer Algebra and Applications (EACA 2014)
June 18-20 2014, Barcelona, Spain.