Group of Algebraic and Quantum Computations

News and Events

CA Workshop Dubna-2021

The 22-nd two-day workshop on Computer Algebra will take place on May 24-25, 2021. The Workshop will be dedicated to the memory of Professor Vladimir Gerdt.

We announce with deep regret and great sadness the sudden death of Vladimir Gerdt who passed away on January 5, 2021. He was a prominent scientist, one of the leading experts in the field of algebraic and quantum computations and a reliable friend. We present our sincere condolences to the family of Vladimir Petrovich.

The next meeting of the Seminar on Computer Algebra, CMC faculty of MSU & CCAS will be on Wednesday, February 24, 2021 at 16:20 Moscow time via ZOOM.

Past events

The 3rd International Conference "Computer Algebra" was held in Moscow on June 17-21, 2019.

MMCP'2019
International Conference MATHEMATICAL MODELING AND COMPUTATIONAL PHYSICS, 2019(MMCP 2019) was held on July 1-5, 2019 in Stará Lesná, Slovakia.

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-based methods, symbolic–numeric algorithms and software to solve scientific and technical problems arising in research conducted at JINR and its member states. Development of algorithms and software packages for simulation of quantum systems and oriented to the heterogeneous platform “HybriLIT”.
Provision of the JINR users with information about non-commercial computer algebra systems and open source software oriented to symbolic and algebraic computation.
2. Elaboration and analysis of mathematical models and algorithmic aspects of quantum computing and quantum information processes. Qualitative and quantitative description of entangled qubit states.

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 [1]. In the last decade new highly efficient involutive algorithms for computation of Groebner bases have been designed [2] and implemented in the GINV software [3]. An algorithmic extension of the involutive algorithm to systems of nonlinear partial differential equations has been done in [4,5]. An algorithmic approach to analyze discrete systems was developed in [6]. In paper [7] a Mathematica program was created to simulate quantum computation. New symbolic-numerical algorithms for solving the self-adjoint elliptic boundary-value problem in a d-dimensional polyhedral fiﬁnite domain, using the high-accuracy ﬁfinite element method with new high-order fully symmetric PI-type Gaussian quadratures [9].

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.Gerdt, M.Lange-Hegermann, D.Robertz. The MAPLE package TDDS for Thomas decomposition of systems of nonlinear PDEs. Computer Physics Communications, 234, 2019, 202--215. arXiv:physics.comp-ph/1801.09942
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.
K.K.Sharma, V. P.Gerdt. Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels. International Journal of Theoretical Physics, to appear. https://link.springer.com/article/10.1007/s10773-019-04332-z
A.A. Gusev, V.P. Gerdt, O. Chuluunbaatar, G. Chuluunbaatar, S.I. Vinitsky, V.L. Derbov, A. Gozdz, P.M. Krassovitskiy, Symbolic-numerical algorithms for solving elliptic boundary-value problems using multivariate simplex Lagrange elements. Lecture Notes in Computer Science 11077, pp. 197–213 (2018). https://link.springer.com/chapter/10.1007%2F978-3-319-99639-4_14

Some other recent references

V.P.Gerdt, D.A.Lyakhov, D.Michels. On the Algorithmic Linearizability for Nonlinear Ordinary Differential Equations. Journal of Symbolic Computation, 98, 2020, 3-22. Doi.org/10.1016/j.jsc.2019.07.004.
O.V.Tarasov. Functional reduction of Feynman integrals. J.High Energ. Phys. (2019) 2019: 173. https://doi.org/10.1007/JHEP02(2019)173
A.A. Gusev, S.I. Vinitsky, O. Chuluunbaatar, A. Gozdz, A. Dobrowolski, K. Mazurek, P.M. Krassovitskiy, Finite element method for solving the collective nuclear model with tetrahedral symmetry, Acta Physica Polonica B Proceedings Supplement 12, pp. 589–594 (2019).
A.A. Gusev, S.I. Vinitsky, O. Chuluunbaatar, A. Gozdz, V.L. Derbov, and P. M. Krassovitskiy. Adiabatic representation for atomic dimers and trimers in collinear configuration. Physics of Atomic Nuclei 81, pp. 945–970. (2018).
O.V.Tarasov. Massless on-shell box integral with arbitrary powers of propagators. J. Phys., vol. A51, 2018, 27, p.275401. https://arxiv.org/abs/1709.07526
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.
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.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 .

Upcoming conferences

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