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Gerdt, Vladimir Petrovich

Author ID: gerdt.vladimir-p Recent zbMATH articles by "Gerdt, Vladimir Petrovich"
Published as: Gerdt, V. P.; Gerdt, Vladimir P.; Gerdt, Vladimir; Gerdt, V.
Further Spellings: Гердт Владимир Петрович
Homepage: http://compalg.jinr.ru/CAGroup/Gerdt/
External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND
all top 5

Co-Authors

12 single-authored
19 Blinkov, Yuri A.
19 Gusev, Alexander A.
19 Vinitsky, Sergue I.
11 Chuluunbaatar, Ochbadrakh
11 Khvedelidze, Arsen Morisovich
10 Rostovtsev, Vitaly A.
10 Vorozhtsov, Evgenii V.
9 Koepf, Wolfram A.
9 Lyakhov, Dmitry A.
9 Robertz, Daniel
9 Zharkov, A. Yu.
8 Góźdź, Andrzej
8 Michels, Dominik Ludewig
8 Yanovich, Denis A.
7 Derbov, Vladimir L.
6 Kornyak, Vladimir V.
6 Weber, Andreas Günter
5 Mayr, Ernst W.
5 Pȩdrak, Aleksandra
5 Seiler, Werner M.
4 Hashemi, Amir
4 Lange-Hegermann, Markus
4 Prokopenya, Alexander N.
4 Samoylov, Valentin N.
4 Zinin, Mikhail V.
3 Bächler, Thomas
3 Chuluunbaatar, Galmandakh
3 Deveikis, Algirdas
3 Kaschiev, Michael S.
3 Kaschiev, Michail
3 La Scala, Roberto
3 Mladenov, Dimitar M.
3 Shabat, Alekseĭ Borisovich
3 Svinolupov, S. I.
3 Tupikova, Tatyana
2 Amodio, Pierluigi
2 Blinkov, Yuriĭ Anatol’evich
2 Bradford, Russell J.
2 Burdík, Čestmír
2 Davenport, James Harold
2 England, Matthew
2 Errami, Hassan
2 Fedorova, R. N.
2 Govorun, N. N.
2 Grigor’ev, Dmitriĭ Yur’evich
2 Hoyt, Charles Tapley
2 Košta, Marek
2 Kostov, Nikolay A.
2 M.-Alizadeh, Benyamin
2 Palii, Yu. G.
2 Radulescu, Ovidiu
2 Serov, Vladislav V.
2 Shirikov, V. P.
2 Sobottka, Gerrit A.
2 Sturm, Thomas
2 Uwano, Yoshio
2 Znojil, Miloslav
1 Abrashkevich, A. G.
1 Berth, Matthias
1 Carra’Ferro, Giuseppa
1 Dmitriev, Mikhail G.
1 Dobrowolski, Arkadiusz
1 Fuchssteiner, Benno
1 Gerdt, P. V.
1 Gogilidze, Soso A.
1 Hai, Lili
1 Horan, Robin
1 Hossain, Zahid
1 Khutornoj, N. V.
1 Khutornoy, N. V.
1 Kostova, Z. T.
1 Kotkova, E. A.
1 Kragler, Robert
1 Krassovitskiy, P. M.
1 Lassner, Wolfgang
1 Lavelle, Martin
1 Le Hai, Luong
1 Malykh, Mikhail Dmitrievich
1 Marinov, K. B.
1 McMullan, David
1 Mozzhilkin, Vladimir V.
1 Nesterova, M. V.
1 Oevel, Walter
1 Palii, Yuri
1 Pankratov, Il’ya Alekseevich
1 Plesken, Wilhelm
1 Pogosyan, George S.
1 Riedel-Kruse, Ingmar H.
1 Robuk, V. N.
1 Samoilov, V. N.
1 Sevastianov, Leonid A.
1 Severyanov, Vasily M.
1 Shvachka, Anatoly B.
1 Ştefănesu, D.
1 Szulerecka, A.
1 Tupikova, T. V.
1 Tyupikova, T. V.
1 Yevlakov, S.
1 Ying, Yu
1 Zhang, Xiaojing

Publications by Year

Citations contained in zbMATH Open

92 Publications have been cited 515 times in 251 Documents Cited by Year
Involutive bases of polynomial ideals. Zbl 1017.13500
Gerdt, Vladimir P.; Blinkov, Yuri A.
76
1998
Minimal involutive bases. Zbl 1017.13501
Gerdt, Vladimir P.; Blinkov, Yuri A.
33
1998
Involutive algorithms for computing Gröbner bases. Zbl 1104.13012
Gerdt, Vladimir P.
31
2005
Algorithmic Thomas decomposition of algebraic and differential systems. Zbl 1315.35013
Bächler, Thomas; Gerdt, Vladimir; Lange-Hegermann, Markus; Robertz, Daniel
29
2012
Completion of linear differential systems to involution. Zbl 1072.12500
Gerdt, Vladimir P.
17
1999
Gröbner bases and generation of difference schemes for partial differential equations. Zbl 1094.68125
Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.
14
2006
Construction of Janet bases. II: Polynomial bases. Zbl 1015.13013
Gerdt, Vladimir P.; Blinkov, Yuri A.; Yanovich, Denis A.
13
2001
A case study on the parametric occurrence of multiple steady states. Zbl 1444.92034
Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas
12
2017
On decomposition of algebraic PDE systems into simple subsystems. Zbl 1154.68111
Gerdt, Vladimir P.
10
2008
Gröbner bases and involutive methods for algebraic and differential equations. Zbl 0904.13014
Gerdt, V. P.
9
1997
On the relation between Pommaret and Janet bases. Zbl 0981.13017
Gerdt, Vladimir P.
9
2000
Involutive divisions of monomials. Zbl 0972.68193
Gerdt, V. P.; Blinkov, Yu. A.
9
1998
Fast search for the Janet divisor. Zbl 1024.13009
Gerdt, V. P.; Yanovich, D. A.; Blinkov, Yu. A.
9
2001
Construction of Janet bases. I: Monomial bases. Zbl 1015.13012
Gerdt, Vladimir P.; Blinkov, Yuri A.; Yanovich, Denis A.
9
2001
Computer algebra application for classification of integrable non-linear evolution equations. Zbl 0577.35099
Gerdt, V. P.; Shvachka, A. B.; Zharkov, A. Yu.
9
1985
Identifying the parametric occurrence of multiple steady states for some biological networks. Zbl 1442.92056
Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas
9
2020
Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels. Zbl 1439.81022
Sharma, Kapil K.; Gerdt, Vladimir P.
9
2020
Involutive method for computing Gröbner bases over \(\mathbb F_2\). Zbl 1185.68868
Gerdt, V. P.; Zinin, M. V.
8
2008
On the ring of local polynomial invariants for a pair of entangled qubits. Zbl 1288.81012
Gerdt, V.; Khvedelidze, A.; Palii, Yu.
7
2010
Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals. Zbl 1327.12003
Gerdt, Vladimir; La Scala, Roberto
7
2015
Janet-like monomial division. Zbl 1169.68660
Gerdt, Vladimir P.; Blinkov, Yuri A.
7
2005
Janet-like Gröbner bases. Zbl 1169.68661
Gerdt, Vladimir P.; Blinkov, Yuri A.
7
2005
Computation of difference Gröbner bases. Zbl 1318.68203
Gerdt, Vladimir P.; Robertz, Daniel
6
2012
Consistency of finite difference approximations for linear PDE systems and its algorithmic verification. Zbl 1321.65161
Gerdt, Vladimir P.; Robertz, Daniel
6
2010
On consistency of finite difference approximations to the Navier-Stokes equations. Zbl 1412.65063
Amodio, Pierluigi; Blinkov, Yuri; Gerdt, Vladimir; La Scala, Roberto
6
2013
Construction of finitely presented Lie algebras and superalgebras. Zbl 0876.17002
Gerdt, Vladimir P.; Kornyak, Vladimir V.
6
1996
Involutive division techniques: some generalizations and optimizations. Zbl 0989.13019
Gerdt, V. P.
6
1999
Involutive division generated by an antigraded monomial ordering. Zbl 1344.68299
Gerdt, Vladimir P.; Blinkov, Yuri A.
6
2011
Involution and difference schemes for the Navier-Stokes equations. Zbl 1260.76008
Gerdt, Vladimir P.; Blinkov, Yuri A.
6
2009
Thomas decomposition of algebraic and differential systems. Zbl 1202.68488
Bächler, Thomas; Gerdt, Vladimir; Lange-Hegermann, Markus; Robertz, Daniel
6
2010
Effectiveness of involutive criteria in computation of polynomial Janet bases. Zbl 1103.68987
Gerdt, V. P.; Yanovich, D. A.
5
2006
On an algorithmic optimization in computation of involutive bases. Zbl 1037.68063
Gerdt, V. P.
5
2002
Isomorphism verification for complex and real Lie algebras by Gröbner basis technique. Zbl 0796.17001
Gerdt, V. P.; Lassner, W.
5
1993
\(\mathrm{SU}(6)\) Casimir invariants and \(\mathrm{SU}(2) \otimes \mathrm{SU}(3)\) scalars for a mixed qubit-qutrit state. Zbl 1402.81170
Gerdt, V.; Mladenov, D.; Paliĭ, Yu.; Khvedelidze, A.
4
2011
Computer algebra, symmetry analysis and integrability of nonlinear evolution equations. Zbl 0941.37049
Gerdt, Vladimir P.
4
1993
Program for constructing a complete system of relations, basis elements, and commutator table for finitely presented Lie algebras and superalgebras. Zbl 0972.68192
Gerdt, V. P.; Kornyak, V. V.
4
1997
Symbolic-numerical algorithms for solving elliptic boundary-value problems using multivariate simplex Lagrange elements. Zbl 1453.65406
Gusev, A. A.; Gerdt, V. P.; Chuluunbaatar, O.; Chuluunbaatar, G.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.; Krassovitskiy, P. M.
4
2018
Involutive bases algorithm incorporating F\(_5\) criterion. Zbl 1435.68391
Gerdt, Vladimir P.; Hashemi, Amir; M.-Alizadeh, Benyamin
3
2013
Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations. Zbl 1426.76449
Amodio, Pierluigi; Blinkov, Yuri; Gerdt, Vladimir; La Scala, Roberto
3
2017
Specialized computer algebra system GINV. Zbl 1185.68867
Blinkov, Yu. A.; Gerdt, V. P.
3
2008
A Mathematica package for simulation of quantum computation. Zbl 1202.81022
Gerdt, Vladimir P.; Kragler, Robert; Prokopenya, Alexander N.
3
2009
Computer algebra in the theory of ordinary differential equations of Halphen type. Zbl 0685.68036
Gerdt, V. P.; Kostov, N. A.
3
1989
Symbolic-numeric algorithm for computing orthonormal basis of \(\operatorname{O}(5)\times\operatorname{SU}(1,1)\) group. Zbl 07635831
Deveikis, Algirdas; Gusev, Alexander A.; Gerdt, Vladimir P.; Vinitsky, Sergue I.; Góźdź, Andrzej; Pȩdrak, Aleksandra; Burdik, Čestmir; Pogosyan, George S.
3
2020
Some algorithms for calculating unitary matrices for quantum circuits. Zbl 1214.68471
Gerdt, V. P.; Prokopenya, A. N.
3
2010
Milestone developments in quantum information and no-go theorems. Zbl 1513.81016
Sharma, K. K.; Gerdt, V. P.; Gerdt, P. V.
3
2020
Algorithmic verification of linearizability for ordinary differential equations. Zbl 1454.34064
Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.
3
2017
Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems. Zbl 1467.35020
Gerdt, Vladimir P.; Robertz, Daniel
3
2019
Lagrangian constraints and differential Thomas decomposition. Zbl 1334.70050
Gerdt, Vladimir P.; Robertz, Daniel
2
2016
Simulation of quantum error correction by means of QuantumCircuit package. Zbl 1301.68279
Gerdt, V. P.; Prokopenya, A. N.
2
2013
On the Hamiltonian reduction of geodesic motion on \(\mathrm{SU}(3)\) to \(\mathrm{SU}(3)/\mathrm{SU}(2)\). Zbl 1112.37040
Gerdt, V.; Horan, R.; Khvedelidze, A.; Lavelle, M.; McMullan, D.; Palii, Yu.
2
2006
A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem. Zbl 1137.65428
Vinitsky, S. I.; Gerdt, V. P.; Gusev, A. A.; Kaschiev, M. S.; Rostovtsev, V. A.; Samoilov, V. N.; Tyupikova, T. V.; Chuluunbaatar, O.
2
2007
Computer algebra tools for higher symmetry analysis of nonlinear evolution equations. (With discussion). Zbl 0793.68083
Gerdt, V. P.
2
1992
Simulation of quantum error correction with Mathematica. Zbl 1411.68207
Gerdt, Vladimir P.; Prokopenya, Alexander N.
2
2013
On selection of nonmultiplicative prolongations in computation of Janet bases. Zbl 1147.68878
Gerdt, V. P.; Blinkov, Yu. A.
2
2007
A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in magnetic field. Zbl 1141.68695
Gusev, Alexander; Gerdt, Vladimir; Kaschiev, Michail; Rostovtsev, Vitaly; Samoylov, Valentin; Tupikova, Tatyana; Vinitsky, Sergue
2
2006
A strongly consistent finite difference scheme for steady Stokes flow and its modified equations. Zbl 1453.76122
Blinkov, Yury A.; Gerdt, Vladimir P.; Lyakhov, Dmitry A.; Michels, Dominik L.
2
2018
Algebraic construction of a strongly consistent, permutationally symmetric and conservative difference scheme for 3D steady Stokes flow. Zbl 1416.76196
Zhang, Xiaojing; Gerdt, Vladimir P.; Blinkov, Yury A.
2
2019
Symbolic-numerical algorithms for solving the parametric self-adjoint 2D elliptic boundary-value problem using high-accuracy finite element method. Zbl 1455.65213
Gusev, A. A.; Gerdt, V. P.; Chuluunbaatar, O.; Chuluunbaatar, G.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.
2
2017
Symbolic-numerical algorithms to solve the quantum tunneling problem for a coupled pair of ions. Zbl 1308.81007
Gusev, A. A.; Vinitsky, S. I.; Chuluunbaatar, O.; Gerdt, V. P.; Rostovtsev, V. A.
2
2011
Discretization of quasilinear evolution equations by computer algebra methods. Zbl 1458.35367
Blinkov, Yu. A.; Gerdt, V. P.; Marinov, K. B.
2
2017
Constrained Hamiltonian systems and Gröbner bases. Zbl 1072.37511
Gerdt, Vladimir P.; Gogilidze, Soso A.
2
1999
Improved Kolchin-Ritt algorithm. Zbl 1065.68114
Carrà Ferro, G.; Gerdt, V. P.
2
2003
Quantum information scrambling and entanglement in bipartite quantum states. Zbl 1509.81177
Sharma, Kapil K.; Gerdt, Vladimir P.
2
2021
The Maple package TDDS for computing Thomas decompositions of systems of nonlinear PDEs. Zbl 07682604
Gerdt, Vladimir P.; Lange-Hegermann, Markus; Robertz, Daniel
2
2019
POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. Zbl 1196.65175
Chuluunbaatar, O.; Gusev, A. A.; Gerdt, V. P.; Rostovtsev, V. A.; Vinitsky, S. I.; Abrashkevich, A. G.; Kaschiev, M. S.; Serov, V. V.
2
2008
Describing the orbit space of the global unitary actions for mixed qudit states. Zbl 1307.81013
Gerdt, V. P.; Khvedelidze, A. M.; Palii, Yu. G.
1
2014
Symbolic algorithm for generating irreducible bases of point groups in the space of \(\mathrm{SO(3)}\) group. Zbl 1434.20034
Gusev, A. A.; Gerdt, V. P.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.; Pędrak, A.
1
2015
On the partial analytical solution of the Kirchhoff equation. Zbl 1434.35002
Michels, Dominik L.; Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Sobottka, Gerrit A.; Weber, Andreas G.
1
2015
Algebraically simple involutive differential systems and the Cauchy problem. Zbl 1288.12002
Gerdt, V. P.
1
2010
Lie symmetry analysis for Cosserat rods. Zbl 1417.74014
Michels, Dominik L.; Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Sobottka, Gerrit A.; Weber, Andreas G.
1
2014
An algorithm for analysis of the structure of finitely presented Lie algebras. Zbl 0929.17001
Gerdt, Vladimir P.; Kornyak, Vladimir V.
1
1997
Lie algebras and superalgebras defined by a finite number of relations: computer analysis. Zbl 0967.17002
Gerdt, V. P.; Kornyak, V. V.
1
1995
Parallel computation of Janet and Gröbner bases over rational numbers. Zbl 1119.13304
Gerdt, V. P.; Yanovich, D. A.
1
2005
Symbolic algorithm for factorization of the evolution operator of the time-dependent Schrödinger equation. Zbl 1101.65089
Vinitsky, S. I.; Gerdt, V. P.; Gusev, A. A.; Kaschiev, M. S.; Rostovtsev, V. A.; Samoylov, V. N.; Tupikova, T. V.; Uwano, Y.
1
2006
Homogeneity of integrability conditions for multi-parametric families of polynomial-nonlinear evolution equations. Zbl 1037.68543
Gerdt, V. P.
1
1996
New exact solutions for polynomial oscillators in large dimensions. Zbl 1030.81003
Znojil, Miloslav; Yanovich, Denis; Gerdt, Vladimir P.
1
2003
A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in the magnetic field: Cylindrical coordinates. Zbl 1141.68680
Chuluunbaatar, Ochbadrakh; Gusev, Alexander; Gerdt, Vladimir; Kaschiev, Michail; Rostovtsev, Vitaly; Samoylov, Valentin; Tupikova, Tatyana; Vinitsky, Sergue
1
2007
Symbolic algorithm for generating the orthonormal Bargmann-Moshinsky basis for \(\mathrm{SU}(3)\) group. Zbl 1453.65081
Deveikis, A.; Gusev, A. A.; Gerdt, V. P.; Vinitsky, S. I.; Góźdź, A.; Pȩdrak, A.
1
2018
Symbolic-numerical algorithm for generating interpolation multivariate Hermite polynomials of high-accuracy finite element method. Zbl 1455.65021
Gusev, A. A.; Gerdt, V. P.; Chuluunbaatar, O.; Chuluunbaatar, G.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.
1
2017
Role of involutive criteria in computing Boolean Gröbner bases. Zbl 1184.13078
Gerdt, V. P.; Zinin, M. V.
1
2009
Symbolic-numerical algorithms for solving parabolic quantum well problem with hydrogen-like impurity. Zbl 1239.81008
Vinitsky, S. I.; Chuluunbaatar, O.; Gerdt, V. P.; Gusev, A. A.; Rostovtsev, V. A.
1
2009
Towards an algorithmisation of the Dirac constraint formalism. Zbl 1256.70009
Gerdt, V.; Khvedelidze, A.; Palii, Yu.
1
2006
Computer classification of integrable coupled KdV-like systems. Zbl 0704.68062
Gerdt, V. P.; Zharkov, A. Yu.
1
1990
Solution of polynomial equations that arise in the classification of integrable systems of the coupled Korteweg-de Vries equation type. Zbl 0724.35097
Gerdt, V. P.; Zharkov, A. Yu.
1
1989
The construction of finitely represented Lie algebras. Zbl 0919.17001
Gerdt, V. P.; Robuk, V. N.; Sever’yanov, V. M.
1
1996
Comprehensive involutive systems. Zbl 1373.13027
Gerdt, Vladimir; Hashemi, Amir
1
2012
Lie-Bäcklund symmetries of coupled nonlinear Schrödinger equations. Zbl 0927.68122
Gerdt, V. P.; Khutornoy, N. V.; Zharkov, A. Yu.
1
1991
On the consistency analysis of finite difference approximations. Zbl 1435.65130
Michels, D. L.; Gerdt, V. P.; Blinkov, Yu. A.; Lyakhov, D. A.
1
2019
A Pommaret division algorithm for computing Gröbner bases in Boolean rings. Zbl 1487.13056
Gerdt, Vladimir P.; Zinin, Mikhail V.
1
2008
Construction of a new implicit difference scheme for 2D Boussinesq paradigm equation. Zbl 1437.65090
Blinkov, Yu. A.; Gerdt, V. P.; Pankratov, I. A.; Kotkova, E. A.
1
2019
Computer algebra application for investigating integrability of nonlinear evolution systems. Zbl 1209.68676
Gerdt, V. P.; Shabat, A. B.; Svinolupov, S. I.; Zharkov, A. Yu.
1
1989
On computation of Boolean involutive bases. Zbl 1214.68472
Gerdt, V. P.; Zinin, M. V.; Blinkov, Yu. A.
1
2010
Quantum information scrambling and entanglement in bipartite quantum states. Zbl 1509.81177
Sharma, Kapil K.; Gerdt, Vladimir P.
2
2021
Identifying the parametric occurrence of multiple steady states for some biological networks. Zbl 1442.92056
Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas
9
2020
Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels. Zbl 1439.81022
Sharma, Kapil K.; Gerdt, Vladimir P.
9
2020
Symbolic-numeric algorithm for computing orthonormal basis of \(\operatorname{O}(5)\times\operatorname{SU}(1,1)\) group. Zbl 07635831
Deveikis, Algirdas; Gusev, Alexander A.; Gerdt, Vladimir P.; Vinitsky, Sergue I.; Góźdź, Andrzej; Pȩdrak, Aleksandra; Burdik, Čestmir; Pogosyan, George S.
3
2020
Milestone developments in quantum information and no-go theorems. Zbl 1513.81016
Sharma, K. K.; Gerdt, V. P.; Gerdt, P. V.
3
2020
Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems. Zbl 1467.35020
Gerdt, Vladimir P.; Robertz, Daniel
3
2019
Algebraic construction of a strongly consistent, permutationally symmetric and conservative difference scheme for 3D steady Stokes flow. Zbl 1416.76196
Zhang, Xiaojing; Gerdt, Vladimir P.; Blinkov, Yury A.
2
2019
The Maple package TDDS for computing Thomas decompositions of systems of nonlinear PDEs. Zbl 07682604
Gerdt, Vladimir P.; Lange-Hegermann, Markus; Robertz, Daniel
2
2019
On the consistency analysis of finite difference approximations. Zbl 1435.65130
Michels, D. L.; Gerdt, V. P.; Blinkov, Yu. A.; Lyakhov, D. A.
1
2019
Construction of a new implicit difference scheme for 2D Boussinesq paradigm equation. Zbl 1437.65090
Blinkov, Yu. A.; Gerdt, V. P.; Pankratov, I. A.; Kotkova, E. A.
1
2019
Symbolic-numerical algorithms for solving elliptic boundary-value problems using multivariate simplex Lagrange elements. Zbl 1453.65406
Gusev, A. A.; Gerdt, V. P.; Chuluunbaatar, O.; Chuluunbaatar, G.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.; Krassovitskiy, P. M.
4
2018
A strongly consistent finite difference scheme for steady Stokes flow and its modified equations. Zbl 1453.76122
Blinkov, Yury A.; Gerdt, Vladimir P.; Lyakhov, Dmitry A.; Michels, Dominik L.
2
2018
Symbolic algorithm for generating the orthonormal Bargmann-Moshinsky basis for \(\mathrm{SU}(3)\) group. Zbl 1453.65081
Deveikis, A.; Gusev, A. A.; Gerdt, V. P.; Vinitsky, S. I.; Góźdź, A.; Pȩdrak, A.
1
2018
A case study on the parametric occurrence of multiple steady states. Zbl 1444.92034
Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas
12
2017
Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations. Zbl 1426.76449
Amodio, Pierluigi; Blinkov, Yuri; Gerdt, Vladimir; La Scala, Roberto
3
2017
Algorithmic verification of linearizability for ordinary differential equations. Zbl 1454.34064
Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.
3
2017
Symbolic-numerical algorithms for solving the parametric self-adjoint 2D elliptic boundary-value problem using high-accuracy finite element method. Zbl 1455.65213
Gusev, A. A.; Gerdt, V. P.; Chuluunbaatar, O.; Chuluunbaatar, G.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.
2
2017
Discretization of quasilinear evolution equations by computer algebra methods. Zbl 1458.35367
Blinkov, Yu. A.; Gerdt, V. P.; Marinov, K. B.
2
2017
Symbolic-numerical algorithm for generating interpolation multivariate Hermite polynomials of high-accuracy finite element method. Zbl 1455.65021
Gusev, A. A.; Gerdt, V. P.; Chuluunbaatar, O.; Chuluunbaatar, G.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.
1
2017
Lagrangian constraints and differential Thomas decomposition. Zbl 1334.70050
Gerdt, Vladimir P.; Robertz, Daniel
2
2016
Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals. Zbl 1327.12003
Gerdt, Vladimir; La Scala, Roberto
7
2015
Symbolic algorithm for generating irreducible bases of point groups in the space of \(\mathrm{SO(3)}\) group. Zbl 1434.20034
Gusev, A. A.; Gerdt, V. P.; Vinitsky, S. I.; Derbov, V. L.; Góźdź, A.; Pędrak, A.
1
2015
On the partial analytical solution of the Kirchhoff equation. Zbl 1434.35002
Michels, Dominik L.; Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Sobottka, Gerrit A.; Weber, Andreas G.
1
2015
Describing the orbit space of the global unitary actions for mixed qudit states. Zbl 1307.81013
Gerdt, V. P.; Khvedelidze, A. M.; Palii, Yu. G.
1
2014
Lie symmetry analysis for Cosserat rods. Zbl 1417.74014
Michels, Dominik L.; Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Sobottka, Gerrit A.; Weber, Andreas G.
1
2014
On consistency of finite difference approximations to the Navier-Stokes equations. Zbl 1412.65063
Amodio, Pierluigi; Blinkov, Yuri; Gerdt, Vladimir; La Scala, Roberto
6
2013
Involutive bases algorithm incorporating F\(_5\) criterion. Zbl 1435.68391
Gerdt, Vladimir P.; Hashemi, Amir; M.-Alizadeh, Benyamin
3
2013
Simulation of quantum error correction by means of QuantumCircuit package. Zbl 1301.68279
Gerdt, V. P.; Prokopenya, A. N.
2
2013
Simulation of quantum error correction with Mathematica. Zbl 1411.68207
Gerdt, Vladimir P.; Prokopenya, Alexander N.
2
2013
Algorithmic Thomas decomposition of algebraic and differential systems. Zbl 1315.35013
Bächler, Thomas; Gerdt, Vladimir; Lange-Hegermann, Markus; Robertz, Daniel
29
2012
Computation of difference Gröbner bases. Zbl 1318.68203
Gerdt, Vladimir P.; Robertz, Daniel
6
2012
Comprehensive involutive systems. Zbl 1373.13027
Gerdt, Vladimir; Hashemi, Amir
1
2012
Involutive division generated by an antigraded monomial ordering. Zbl 1344.68299
Gerdt, Vladimir P.; Blinkov, Yuri A.
6
2011
\(\mathrm{SU}(6)\) Casimir invariants and \(\mathrm{SU}(2) \otimes \mathrm{SU}(3)\) scalars for a mixed qubit-qutrit state. Zbl 1402.81170
Gerdt, V.; Mladenov, D.; Paliĭ, Yu.; Khvedelidze, A.
4
2011
Symbolic-numerical algorithms to solve the quantum tunneling problem for a coupled pair of ions. Zbl 1308.81007
Gusev, A. A.; Vinitsky, S. I.; Chuluunbaatar, O.; Gerdt, V. P.; Rostovtsev, V. A.
2
2011
On the ring of local polynomial invariants for a pair of entangled qubits. Zbl 1288.81012
Gerdt, V.; Khvedelidze, A.; Palii, Yu.
7
2010
Consistency of finite difference approximations for linear PDE systems and its algorithmic verification. Zbl 1321.65161
Gerdt, Vladimir P.; Robertz, Daniel
6
2010
Thomas decomposition of algebraic and differential systems. Zbl 1202.68488
Bächler, Thomas; Gerdt, Vladimir; Lange-Hegermann, Markus; Robertz, Daniel
6
2010
Some algorithms for calculating unitary matrices for quantum circuits. Zbl 1214.68471
Gerdt, V. P.; Prokopenya, A. N.
3
2010
Algebraically simple involutive differential systems and the Cauchy problem. Zbl 1288.12002
Gerdt, V. P.
1
2010
On computation of Boolean involutive bases. Zbl 1214.68472
Gerdt, V. P.; Zinin, M. V.; Blinkov, Yu. A.
1
2010
Involution and difference schemes for the Navier-Stokes equations. Zbl 1260.76008
Gerdt, Vladimir P.; Blinkov, Yuri A.
6
2009
A Mathematica package for simulation of quantum computation. Zbl 1202.81022
Gerdt, Vladimir P.; Kragler, Robert; Prokopenya, Alexander N.
3
2009
Role of involutive criteria in computing Boolean Gröbner bases. Zbl 1184.13078
Gerdt, V. P.; Zinin, M. V.
1
2009
Symbolic-numerical algorithms for solving parabolic quantum well problem with hydrogen-like impurity. Zbl 1239.81008
Vinitsky, S. I.; Chuluunbaatar, O.; Gerdt, V. P.; Gusev, A. A.; Rostovtsev, V. A.
1
2009
On decomposition of algebraic PDE systems into simple subsystems. Zbl 1154.68111
Gerdt, Vladimir P.
10
2008
Involutive method for computing Gröbner bases over \(\mathbb F_2\). Zbl 1185.68868
Gerdt, V. P.; Zinin, M. V.
8
2008
Specialized computer algebra system GINV. Zbl 1185.68867
Blinkov, Yu. A.; Gerdt, V. P.
3
2008
POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. Zbl 1196.65175
Chuluunbaatar, O.; Gusev, A. A.; Gerdt, V. P.; Rostovtsev, V. A.; Vinitsky, S. I.; Abrashkevich, A. G.; Kaschiev, M. S.; Serov, V. V.
2
2008
A Pommaret division algorithm for computing Gröbner bases in Boolean rings. Zbl 1487.13056
Gerdt, Vladimir P.; Zinin, Mikhail V.
1
2008
A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem. Zbl 1137.65428
Vinitsky, S. I.; Gerdt, V. P.; Gusev, A. A.; Kaschiev, M. S.; Rostovtsev, V. A.; Samoilov, V. N.; Tyupikova, T. V.; Chuluunbaatar, O.
2
2007
On selection of nonmultiplicative prolongations in computation of Janet bases. Zbl 1147.68878
Gerdt, V. P.; Blinkov, Yu. A.
2
2007
A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in the magnetic field: Cylindrical coordinates. Zbl 1141.68680
Chuluunbaatar, Ochbadrakh; Gusev, Alexander; Gerdt, Vladimir; Kaschiev, Michail; Rostovtsev, Vitaly; Samoylov, Valentin; Tupikova, Tatyana; Vinitsky, Sergue
1
2007
Gröbner bases and generation of difference schemes for partial differential equations. Zbl 1094.68125
Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.
14
2006
Effectiveness of involutive criteria in computation of polynomial Janet bases. Zbl 1103.68987
Gerdt, V. P.; Yanovich, D. A.
5
2006
On the Hamiltonian reduction of geodesic motion on \(\mathrm{SU}(3)\) to \(\mathrm{SU}(3)/\mathrm{SU}(2)\). Zbl 1112.37040
Gerdt, V.; Horan, R.; Khvedelidze, A.; Lavelle, M.; McMullan, D.; Palii, Yu.
2
2006
A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in magnetic field. Zbl 1141.68695
Gusev, Alexander; Gerdt, Vladimir; Kaschiev, Michail; Rostovtsev, Vitaly; Samoylov, Valentin; Tupikova, Tatyana; Vinitsky, Sergue
2
2006
Symbolic algorithm for factorization of the evolution operator of the time-dependent Schrödinger equation. Zbl 1101.65089
Vinitsky, S. I.; Gerdt, V. P.; Gusev, A. A.; Kaschiev, M. S.; Rostovtsev, V. A.; Samoylov, V. N.; Tupikova, T. V.; Uwano, Y.
1
2006
Towards an algorithmisation of the Dirac constraint formalism. Zbl 1256.70009
Gerdt, V.; Khvedelidze, A.; Palii, Yu.
1
2006
Involutive algorithms for computing Gröbner bases. Zbl 1104.13012
Gerdt, Vladimir P.
31
2005
Janet-like monomial division. Zbl 1169.68660
Gerdt, Vladimir P.; Blinkov, Yuri A.
7
2005
Janet-like Gröbner bases. Zbl 1169.68661
Gerdt, Vladimir P.; Blinkov, Yuri A.
7
2005
Parallel computation of Janet and Gröbner bases over rational numbers. Zbl 1119.13304
Gerdt, V. P.; Yanovich, D. A.
1
2005
Improved Kolchin-Ritt algorithm. Zbl 1065.68114
Carrà Ferro, G.; Gerdt, V. P.
2
2003
New exact solutions for polynomial oscillators in large dimensions. Zbl 1030.81003
Znojil, Miloslav; Yanovich, Denis; Gerdt, Vladimir P.
1
2003
On an algorithmic optimization in computation of involutive bases. Zbl 1037.68063
Gerdt, V. P.
5
2002
Construction of Janet bases. II: Polynomial bases. Zbl 1015.13013
Gerdt, Vladimir P.; Blinkov, Yuri A.; Yanovich, Denis A.
13
2001
Fast search for the Janet divisor. Zbl 1024.13009
Gerdt, V. P.; Yanovich, D. A.; Blinkov, Yu. A.
9
2001
Construction of Janet bases. I: Monomial bases. Zbl 1015.13012
Gerdt, Vladimir P.; Blinkov, Yuri A.; Yanovich, Denis A.
9
2001
On the relation between Pommaret and Janet bases. Zbl 0981.13017
Gerdt, Vladimir P.
9
2000
Completion of linear differential systems to involution. Zbl 1072.12500
Gerdt, Vladimir P.
17
1999
Involutive division techniques: some generalizations and optimizations. Zbl 0989.13019
Gerdt, V. P.
6
1999
Constrained Hamiltonian systems and Gröbner bases. Zbl 1072.37511
Gerdt, Vladimir P.; Gogilidze, Soso A.
2
1999
Involutive bases of polynomial ideals. Zbl 1017.13500
Gerdt, Vladimir P.; Blinkov, Yuri A.
76
1998
Minimal involutive bases. Zbl 1017.13501
Gerdt, Vladimir P.; Blinkov, Yuri A.
33
1998
Involutive divisions of monomials. Zbl 0972.68193
Gerdt, V. P.; Blinkov, Yu. A.
9
1998
Gröbner bases and involutive methods for algebraic and differential equations. Zbl 0904.13014
Gerdt, V. P.
9
1997
Program for constructing a complete system of relations, basis elements, and commutator table for finitely presented Lie algebras and superalgebras. Zbl 0972.68192
Gerdt, V. P.; Kornyak, V. V.
4
1997
An algorithm for analysis of the structure of finitely presented Lie algebras. Zbl 0929.17001
Gerdt, Vladimir P.; Kornyak, Vladimir V.
1
1997
Construction of finitely presented Lie algebras and superalgebras. Zbl 0876.17002
Gerdt, Vladimir P.; Kornyak, Vladimir V.
6
1996
Homogeneity of integrability conditions for multi-parametric families of polynomial-nonlinear evolution equations. Zbl 1037.68543
Gerdt, V. P.
1
1996
The construction of finitely represented Lie algebras. Zbl 0919.17001
Gerdt, V. P.; Robuk, V. N.; Sever’yanov, V. M.
1
1996
Lie algebras and superalgebras defined by a finite number of relations: computer analysis. Zbl 0967.17002
Gerdt, V. P.; Kornyak, V. V.
1
1995
Isomorphism verification for complex and real Lie algebras by Gröbner basis technique. Zbl 0796.17001
Gerdt, V. P.; Lassner, W.
5
1993
Computer algebra, symmetry analysis and integrability of nonlinear evolution equations. Zbl 0941.37049
Gerdt, Vladimir P.
4
1993
Computer algebra tools for higher symmetry analysis of nonlinear evolution equations. (With discussion). Zbl 0793.68083
Gerdt, V. P.
2
1992
Lie-Bäcklund symmetries of coupled nonlinear Schrödinger equations. Zbl 0927.68122
Gerdt, V. P.; Khutornoy, N. V.; Zharkov, A. Yu.
1
1991
Computer classification of integrable coupled KdV-like systems. Zbl 0704.68062
Gerdt, V. P.; Zharkov, A. Yu.
1
1990
Computer algebra in the theory of ordinary differential equations of Halphen type. Zbl 0685.68036
Gerdt, V. P.; Kostov, N. A.
3
1989
Solution of polynomial equations that arise in the classification of integrable systems of the coupled Korteweg-de Vries equation type. Zbl 0724.35097
Gerdt, V. P.; Zharkov, A. Yu.
1
1989
Computer algebra application for investigating integrability of nonlinear evolution systems. Zbl 1209.68676
Gerdt, V. P.; Shabat, A. B.; Svinolupov, S. I.; Zharkov, A. Yu.
1
1989
Computer algebra application for classification of integrable non-linear evolution equations. Zbl 0577.35099
Gerdt, V. P.; Shvachka, A. B.; Zharkov, A. Yu.
9
1985
all top 5

Cited by 324 Authors

39 Gerdt, Vladimir Petrovich
23 Seiler, Werner M.
14 Hashemi, Amir
12 Robertz, Daniel
10 Gusev, Alexander A.
10 Vinitsky, Sergue I.
9 Blinkov, Yuri A.
8 Ceria, Michela
8 Lange-Hegermann, Markus
7 Chuluunbaatar, Ochbadrakh
7 England, Matthew
7 Khvedelidze, Arsen Morisovich
6 La Scala, Roberto
6 Mora, Teo
6 Mou, Chenqi
6 Yanovich, Denis A.
5 Gao, Xiaoshan
5 Góźdź, Andrzej
5 Sturm, Thomas
5 Wang, Dongming
4 Bokut, Leonid A.
4 Davenport, James Harold
4 Derbov, Vladimir L.
4 Roggero, Margherita
4 Zinin, Mikhail V.
3 Albert, Mario
3 Bertone, Cristina
3 Blinkov, Yuriĭ Anatol’evich
3 Chen, Yufu
3 Cioffi, Francesca
3 Deveikis, Algirdas
3 Ivanov, Sergeĭ V.
3 Lyakhov, Dmitry A.
3 Michels, Dominik Ludewig
3 Mogilevich, Lev I.
3 Orth, Matthias
3 Ovchinnikov, Alexey Igorevich
3 Pȩdrak, Aleksandra
3 Plesken, Wilhelm
3 Prokopenya, Alexander N.
3 Rostovtsev, Vitaly A.
3 Sadeghimanesh, AmirHosein
3 Seiß, Matthias
3 Semenov, Artem S.
3 Sinha, Suprabhat
3 Weber, Andreas Günter
2 Bächler, Thomas
2 Binaei, Bentolhoda
2 Boulier, François
2 Bradford, Russell J.
2 Chuluunbaatar, Galmandakh
2 Darmofal, David L.
2 Dong, Rina
2 Enolskiĭ, Viktor Zelikovich
2 Feliu, Elisenda
2 Florescu, Dorian
2 Frontin, Cory V.
2 Grigor’ev, Dmitriĭ Yur’evich
2 He, Yang-Hui Evariste
2 Hernando, Antonio
2 Hess, Peter Otto
2 Huang, S.-L. Tracy
2 Huang, Zhenyu
2 Iohara, Kenji
2 Iosif, Alexandru
2 Kostov, Nikolay A.
2 Lai, Jiahua
2 Lemaire, François
2 Li, Zhibin
2 Malbos, Philippe
2 Mehta, Dhagash
2 Mikhalëv, Aleksandr Aleksandrovich
2 Moreno Maza, Marc
2 Niu, Wei
2 Palii, Yu. G.
2 Pankrat’ev, Evgeniĭ Vasil’evich
2 Parnian, Hossein
2 Pogudin, Gleb A.
2 Pommaret, Jean-Francois
2 Radulescu, Ovidiu
2 Rahkooy, Hamid
2 Roanes-Lozano, Eugenio
2 Rosenkranz, Markus
2 Sendra, Juan Rafael
2 Slater, Paul B.
2 Teelen, Kristof
2 Tiwari, Sharwan Kumar
2 Veelaert, Peter
2 Visconti, Andrea
2 Williams, David M.
2 Zhang, Shanqing
2 Zhang, Xiaojing
2 Zharkov, A. Yu.
2 Zhi, Lihong
1 Abbasi, M. R.
1 Ábrahám, Erika
1 Adler, Vsevolod Eduardovich
1 Aktaş, Metin
1 Alexandrov, Dmitriy E.
1 Alonso, Mariemi E.
...and 224 more Authors
all top 5

Cited in 66 Serials

46 Journal of Symbolic Computation
25 Programming and Computer Software
18 Mathematics in Computer Science
13 Journal of Mathematical Sciences (New York)
9 Applicable Algebra in Engineering, Communication and Computing
8 Quantum Information Processing
5 Journal of Systems Science and Complexity
4 Computers & Mathematics with Applications
4 International Journal of Theoretical Physics
4 Journal of Algebra
4 Advances in Applied Mathematics
4 Acta Applicandae Mathematicae
3 Theoretical and Mathematical Physics
3 Mathematics of Computation
3 Applied Mathematics and Computation
3 Journal of Pure and Applied Algebra
3 Foundations of Computational Mathematics
2 Communications in Algebra
2 Journal of Mathematical Analysis and Applications
2 Physica A
2 Bulletin of Mathematical Biology
2 Mathematics and Computers in Simulation
2 Mathematical and Computer Modelling
2 International Journal of Algebra and Computation
2 Linear Algebra and its Applications
2 Annals of Mathematics and Artificial Intelligence
2 Journal of High Energy Physics
2 Journal of Algebra and its Applications
2 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika
2 Russian Journal of Nonlinear Dynamics
1 Archive for History of Exact Sciences
1 Journal of Computational Physics
1 Journal of Mathematical Physics
1 Mathematical Biosciences
1 Mathematical Notes
1 Mathematische Semesterberichte
1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1 Advances in Mathematics
1 Canadian Journal of Mathematics
1 Collectanea Mathematica
1 Journal of Computational and Applied Mathematics
1 Journal of Differential Equations
1 Kybernetika
1 Theoretical Computer Science
1 Bulletin of the Iranian Mathematical Society
1 Physica D
1 Applied Numerical Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Science in China. Series A
1 Multidimensional Systems and Signal Processing
1 Pattern Recognition
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 St. Petersburg Mathematical Journal
1 Finite Fields and their Applications
1 Journal of Mathematical Chemistry
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 International Journal of Nonlinear Sciences and Numerical Simulation
1 Computational Methods in Applied Mathematics
1 Acta Mathematica Scientia. Series B. (English Edition)
1 SIAM Journal on Applied Dynamical Systems
1 Journal of Physics A: Mathematical and Theoretical
1 Symmetry
1 Bulletin of Mathematical Sciences
1 Mathematics
1 Journal of Logical and Algebraic Methods in Programming
1 International Journal of Applied and Computational Mathematics
all top 5

Cited in 42 Fields

124 Computer science (68-XX)
118 Commutative algebra (13-XX)
44 Partial differential equations (35-XX)
33 Numerical analysis (65-XX)
33 Quantum theory (81-XX)
28 Field theory and polynomials (12-XX)
23 Ordinary differential equations (34-XX)
16 Algebraic geometry (14-XX)
13 Nonassociative rings and algebras (17-XX)
12 Associative rings and algebras (16-XX)
11 Systems theory; control (93-XX)
10 Biology and other natural sciences (92-XX)
9 Fluid mechanics (76-XX)
7 Topological groups, Lie groups (22-XX)
6 Mechanics of particles and systems (70-XX)
5 Group theory and generalizations (20-XX)
5 Information and communication theory, circuits (94-XX)
4 Combinatorics (05-XX)
4 Dynamical systems and ergodic theory (37-XX)
4 Global analysis, analysis on manifolds (58-XX)
4 Mechanics of deformable solids (74-XX)
3 History and biography (01-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
3 Number theory (11-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Special functions (33-XX)
2 General and overarching topics; collections (00-XX)
2 Mathematical logic and foundations (03-XX)
2 Difference and functional equations (39-XX)
2 Operator theory (47-XX)
2 Statistical mechanics, structure of matter (82-XX)
2 Relativity and gravitational theory (83-XX)
1 Category theory; homological algebra (18-XX)
1 Functions of a complex variable (30-XX)
1 Approximations and expansions (41-XX)
1 Integral equations (45-XX)
1 Convex and discrete geometry (52-XX)
1 Differential geometry (53-XX)
1 Probability theory and stochastic processes (60-XX)
1 Optics, electromagnetic theory (78-XX)
1 Operations research, mathematical programming (90-XX)

Citations by Year

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