Vladimir Gerdt

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Vladimir Gerdt is affiliated with the following schools: Dubna State University, Saratov State University, Moscow State University

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Vladimir Gerdt

Mathematics

#3533

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#5194

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Measure Theory

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#4148

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Mathematics

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According to Wikipedia, Vladimir P. Gerdt was a Russian mathematician and a full professor at the Joint Institute for Nuclear Research where he was the head of the Group of Algebraic and Quantum Computations. His research interests were concentrated in computer algebra, symbolic and algebraic computations, algebraic and numerical analysis of nonlinear differential equations, polynomial equations, applications to mathematics and physics, and quantum computation with over 210 published articles.

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Vladimir Gerdt's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Involutive bases of polynomial ideals (1998) (214)
Lecture Notes in Computer Science (LNCS) (2011) (139)
Minimal involutive bases (1997) (78)
Involutive Algorithms for Computing Groebner Bases (2005) (66)
Algorithmic Thomas decomposition of algebraic and differential systems (2011) (62)
Construction of Janet Bases I. Monomial Bases (2001) (51)
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations (2006) (39)
Involutive Division Techniques: Some Generalizations and Optimizations (1999) (33)
A Case Study on the Parametric Occurrence of Multiple Steady States (2017) (32)
Gröbner bases and involutive methods for algebraic and differential equations (1997) (31)
On Decomposition of Algebraic PDE Systems into Simple Subsystems (2008) (28)
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 (2008) (26)
A Maple Package for Computing Groebner Bases for Linear Recurrence Relations (2005) (26)
Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems (2011) (25)
On the Relation between Pommaret and Janet Bases (2000) (24)
On Consistency of Finite Difference Approximations to the Navier-Stokes Equations (2013) (23)
Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks (2019) (23)
Thomas Decomposition of Algebraic and Differential Systems (2010) (23)
Involution and Difference Schemes for the Navier-Stokes Equations (2009) (22)
Gröbner Bases in Perturbative Calculations (2004) (21)
Janet-Like Monomial Division (2005) (21)
Symbolic-Numerical Algorithms to Solve the Quantum Tunneling Problem for a Coupled Pair of Ions (2011) (21)
Consistency of finite difference approximations for linear PDE systems and its algorithmic verification (2010) (21)
Phase structure of the SU(2) lattice gauge Higgs theory (1986) (20)
Construction of Finitely Presented Lie Algebras and Superalgebras (1996) (19)
Completion of Linear Differential Systems to Involution (1999) (19)
A pommaret division algorithm for computing Grobner bases in boolean rings (2008) (19)
The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs (2018) (17)
Noetherian quotients of the algebra of partial difference polynomials and Grobner bases of symmetric ideals (2013) (17)
A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem (2007) (17)
Analytic calculations on digital computers for applications in physics and mathematics (1980) (16)
Involutive bases algorithm incorporating F5 criterion (2013) (16)
Fast Search for the Janet Divisor (2004) (16)
On the ring of local polynomial invariants for a pair of entangled qubits (2010) (16)
Entanglement Sudden Death and Birth Effects in Two Qubits Maximally Entangled Mixed States Under Quantum Channels (2019) (15)
Computer generation of necessary integrability conditions for polynomial-nonlinear evolution systems (1990) (15)
Computer Algebra Application for Classification of Integrable Non-Linear Evolution Equations (1985) (15)
Computer Algebra, Symmetry Analysis And Integrability Of Nonlinear Evolution Equations (1993) (14)
Algorithmic Verification of Linearizability for Ordinary Differential Equations (2017) (14)
Construction of Janet Bases II. Polynomial Bases (2001) (14)
Symbolic-Numerical Algorithms for Solving the Parametric Self-adjoint 2D Elliptic Boundary-Value Problem Using High-Accuracy Finite Element Method (2017) (13)
Computer Classification of Integrable Coupled KdV-like Systems (1990) (13)
Isomorphism Verification for Complex and Real Lie Algebras by Gröbner Basis Technique (1993) (13)
Computation of Difference Gröbner Bases (2012) (12)
On an Algorithmic Optimization in Computation of Involutive Bases (2002) (12)
The Circuit Model of Quantum Computation and Its Simulation with Mathematica (2011) (12)
A mathematica program for constructing quantum circuits and computing their unitary matrices (2009) (12)
New exact solutions for polynomial oscillators in large dimensions (2003) (11)
Involutive Division Generated by an Antigraded Monomial Ordering (2011) (11)
A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in the Magnetic Field: Cylindrical Coordinates (2007) (11)
On computation of Gröbner bases for linear difference systems (2005) (11)
Quantum information scrambling and entanglement in bipartite quantum states (2020) (10)
Computer Algebra in the Theory of Ordinary Differential Equations of Halphen Type (1989) (10)
Constrained Hamiltonian Systems and Gröbner Bases (1999) (10)
A Mathematica Package for Simulation of Quantum Computation (2009) (10)
Computation of Difference Groebner Bases (2012) (9)
On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2) (2005) (9)
Simulation of Quantum Error Correction with Mathematica (2013) (9)
Analysis of constraints in light-cone version of SU(2) Yang-Mills mechanics (2002) (9)
Improved Kolchin–Ritt Algorithm (2003) (9)
Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models (2010) (9)
On the algorithmic linearizability of nonlinear ordinary differential equations (2020) (9)
Specialized computer algebra system GINV (2008) (9)
Symbolic-Numerical Algorithms for Solving Parabolic Quantum Well Problem with Hydrogen-Like Impurity (2009) (9)
Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations (2017) (9)
On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases (2013) (9)
Formint — A program for the classification of integrable nonlinear evolution equations (1985) (9)
Simulation of quantum error correction by means of QuantumCircuit package (2013) (8)
Construction of Involutive Monomial Sets for Different Involutive Divisions (1999) (8)
Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow (2019) (8)
A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in Magnetic Field (2006) (8)
Experimental Analysis of Involutive Criteria (2005) (8)
Some algorithms for calculating unitary matrices for quantum circuits (2010) (8)
Involutive Algorithms for Computing (2005) (8)
A software package to construct polynomial sets over Z2 for determining the output of quantum computations (2005) (7)
Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method (2017) (7)
Involutive divisions in mathematica: Implementation and some applications (1998) (7)
Towards an algorithmisation of the Dirac constraint formalism (2006) (7)
Effectiveness of involutive criteria in computation of polynomial Janet bases (2006) (7)
Solving algebraic systems which arise as necessary integrability conditions for polynomial-nonlinear evolution equations (1990) (7)
SU(6) Casimir invariants and SU(2) ⊗ SU(3) scalars for a mixed qubit-qutrit state (2011) (7)
Lie Symmetry Analysis for Cosserat Rods (2014) (6)
Computer algebra applications for investigating integrability of nonlinear evolution systems (1987) (6)
Lagrangian Constraints and Differential Thomas Decomposition (2015) (6)
On the properties of numerical solutions of dynamical systems obtained using the midpoint method (2019) (6)
On selection of nonmultiplicative prolongations in computation of Janet bases (2007) (6)
Symbolic Algorithm for Generating Irreducible Bases of Point Groups in the Space of SO(3) Group (2015) (6)
Parallel computation of Janet and Gröbner bases over rational numbers (2005) (6)
On Computing Janet Bases for Degree Compatible Orderings (2006) (6)
Local form of a solution of the Chew-Low equations (1975) (6)
Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing (2009) (6)
The phase structure of the SU(3) lattice gauge-Higgs model (1986) (6)
Symbolic-Numeric Algorithms for Solving BVPs for a System of ODEs of the Second Order: Multichannel Scattering and Eigenvalue Problems (2016) (5)
On application of involutivity analysis of differential equations to constrained dynamical systems (2003) (5)
Symbolic-Numerical Algorithms for Solving Elliptic Boundary-Value Problems Using Multivariate Simplex Lagrange Elements (2018) (5)
Symbolic Algorithm for Generating Irreducible Rotational-Vibrational Bases of Point Groups (2016) (5)
Algorithm for reduction of boundary-value problems in multistep adiabatic approximation (2010) (5)
Interpolation Hermite Polynomials For Finite Element Method (2018) (5)
Construction of a Lie algebra by a subset of generators and commutation relations (1990) (5)
Light cone SU(2) Yang-Mills theory and conformal mechanics (2002) (5)
On the General Analytical Solution of the Kinematic Cosserat Equations (2016) (5)
Erratum to: Program AEAA_v1_0, "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" [Computer Physics Communications 178 (2008) 301] (2009) (4)
An algorithm for analysis of the structure of finitely presented Lie algebras (1997) (4)
Symbolic-Numerical Algorithm for Solving the Time-Dependent Schrödinger Equation by Split-Operator Method (2005) (4)
Algebraically simple involutive differential systems and the Cauchy problem (2010) (4)
On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits (2016) (4)
Homogeneity of integrability conditions for multi-parametric families of polynomial-non-linear evolution equations (1996) (4)
Milestone Developments in Quantum Information and No-Go Theorems (2018) (4)
Specialized computer algebra system GINV (2008) (4)
Discretization of quasilinear evolution equations by computer algebra methods (2017) (4)
Symbolic Algorithm for Generating the Orthonormal Bargmann-Moshinsky Basis for \mathrm SU(3) Group (2018) (4)
A Variant of Gerdt's Algorithm for Computing Involutive Bases (2011) (4)
On the Consistency Analysis of Finite Difference Approximations (2019) (4)
Uniformization of the forward-scattering amplitude at high energy (1976) (4)
Computer algebra in physical research of jinr (1987) (3)
SU(2) lattice gauge-Higgs model (1985) (3)
Symbolic-Numerical Algorithm for Large Scale Calculations the Orthonormal SU(3) BM Basis (2019) (3)
Janet Bases of Toric Ideals (2005) (3)
Involutive method for computing Gröbner bases over $$ \mathbb{F}_2 $$ (2008) (3)
U(1) LATTICE GAUGE HIGGS MODEL (1985) (3)
Strong Consistency and Thomas Decomposition of Finite Difference Approximations to Systems of Partial Differential Equations (2020) (3)
A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations (2018) (3)
An algorithm for constructing polynomial systems whose solution space characterizes quantum circuits (2005) (3)
Analytical calculations in high energy physics by computer (1980) (2)
Symbolic algorithm for factorization of the evolution operator of the time-dependent Schrödinger equation (2006) (2)
Implementation of the FGLM Algorithm and Finding Roots of Polynomial Involutive Systems (2003) (2)
Estimations of positive roots of polynomials (2010) (2)
High-Accuracy Finite Element Method: Benchmark Calculations (2018) (2)
Computer Algebra Tools for Higher Symmetry Analysis of Nonlinear Evolution Equations (1991) (2)
On the Partial Analytical Solution of the Kirchhoff Equation (2015) (2)
On computation of Boolean involutive bases (2010) (2)
A program for constructing finitely presented Lie algebras and superalgebras (1997) (2)
Gröbner bases applied to systems of linear difference equations (2008) (2)
Phase transitions in the Euclidean and Hamiltonian approaches to lattice gauge theories at a finite temperature (1983) (2)
On Exact Solvability of Anharmonic Oscillators in Large Dimensions (2003) (2)
Computer classification of integrable seventh order MKdV-like equations (1987) (2)
IV International Conference on Computer Algebra in Physical Research : memorial volume for N.N. Govorun, Dubna, USSR, 22-26 May 1990 (1991) (2)
Global structure of the general solution of the Chew-Low equations (1981) (2)
Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method (2020) (1)
The construction of finitely represented Lie algebras (1996) (1)
On the Quadratization of the Integrals for the Many-Body Problem (2021) (1)
On symbolic-numerical representation of the evolution operator for finite-dimensional quantum systems (2007) (1)
Solution of Chew-Low equations in the quadratic approximation (1982) (1)
On precession of entangled spins in a strong laser field (2009) (1)
On computer algebra application to simulation of quantum computation (2007) (1)
INVESTIGATION OF NONLINEAR WATER WAVES USING COMPUTER ALGEBRA SYSTEM REDUCE-2 (1983) (1)
On conservative difference schemes for the many-body problem (2020) (1)
Construction of a New Implicit Difference Scheme for 2D Boussinesq Paradigm Equation (2019) (1)
Simulation of quantum circuits with Mathematica (2008) (1)
Symbolic-Numeric Algorithm for Computing Orthonormal Basis of O(5)˟ SU(1, 1) Group (2020) (1)
Local invariants for mixed qubit-qutrit states (2011) (1)
Lie Algebras and Superalgebras Defined by a Finite Number of Relations: Computer Analysis (1995) (1)
An algorithmic approach to solving polynomial equations associated with quantum circuits (2009) (1)
Mikhail Grigor'evich Meshcheryakov (Obituary) (1994) (1)
Involutive method for computing Grbner bases over (2008) (1)
Comprehensive Involutive Systems (2012) (1)
Some laws governing neutron spectra behind the shielding of proton accelerators (1977) (1)
The Teleportation of the Bell States Has Been Carried Out on the Five-Qubit Quantum IBM Computer (2019) (1)
A C# PACKAGE FOR ASSEMBLING QUANTUM CIRCUITS AND GENERATING ASSOCIATED POLYNOMIAL SETS (2007) (1)
Symbolic-Numerical Calculations of High-|m| Rydberg States and Decay Rates in Strong Magnetic Fields (2012) (1)
Separability of two-qubit state in terms of local invariants (2011) (1)
Symbolic numerical algorithms and programs for the solution of boundary-value problems of dynamics of few-body quantum systems (2016) (1)
Constructing the SU(2) × U(1) Orbit Space for Qutrit Mixed States (2015) (1)
Computer algebra in scientific computing : 14th International Workshop, CASC 2012, Maribor, Slovenia, September 3-6, 2012 : proceedings (2012) (1)
Computer Algebra in Scientific Computing, 11th International Workshop, CASC 2009, Kobe, Japan, September 13-17, 2009. Proceedings (2009) (1)
Analytical Asymptotic Expressions for the Green's Function of the Electron in a Single-Level Quantum Dot at the Kondo and the Fano Resonances (2008) (1)
ON ADAPTIVE APPROXIMATION AND D-FINITE FUNCTIONS (2000) (0)
ec 1 99 9 Constrained Hamiltonian Systems and Gröbner Bases ⋆ (1999) (0)
2 0 Se p 19 99 Completion of Linear Differential Systems to Involution ⋆ (2009) (0)
Describing the Orbit Space of the Global Unitary Actions for Mixed Qudit States (2014) (0)
Laboratory of Information Technologies Joint Institute for Nuclear Research 141980 Dubna , Russia gerdt @ jinr (2006) (0)
Computer Algebra in Physical Research: Memorial Volume for N N Govorun Proceedings of the IV International Conference (1991) (0)
Computer Algebra in Scientific Computing (2015) (0)
ASYS: a computer algebra package for analysis of nonlinear algebraic equations systems (1992) (0)
Analytic calculation of the invariant curve of the chew-low equations (1979) (0)
Kvarki, glyuony i reshetki (1985) (0)
Cubic approximation and local restrictions on the functional arbitrariness in the general solution of the Chew-Low equations (1983) (0)
Computer Algebra in Scientific Computing - 12th International Workshop (Tsakhkadzor, Armenia, September 6-12, 2010) (2010) (0)
On the Consistency Analysis of Finite Difference Approximations (2019) (0)
Thomas decomposition and its applications (2011) (0)
Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301 (2015) (0)
Differential Gröbner Bases, Resultants, etc. (2008) (0)
Teleportation of the Bell States on IBM Q Computers Under Their Hardware Errors (2020) (0)
Bounds for Proto-Galois Groups (2018) (0)
ANALYTICAL CALCULATIONS IN HIGHENERGYPHYSICSBYCOMPUTER (1980) (0)
Generation and Analysis of a New Implicit Difference Scheme for the Korteweg-de Vries Equation (2018) (0)
New type of sum rules for $pi$N-scattering in subthreshold region (1973) (0)
On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits (2017) (0)
Lie-Bäcklund symmetries of coupled nonlinear Schrödinger equations (1991) (0)
Multi-layer evolution schemes for the finite-dimensional quantum systems in external fields (2009) (0)
Groebner Bases Applied to Systems of Linear Difference Equations (2006) (0)
On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases (2013) (0)
Symbolic-Numeric Algorithm for Computing Orthonormal Basis of Group (2020) (0)
POTHMF , a Program to Compute Matrix Elements of the Coupled Radial Equations for a Hydrogen-like Atom in a Homogeneous Magnetic Field (2007) (0)
On Consistency of Finite Dierence Approximations to the Navier-Stokes Equations (2013) (0)
Computation classification of ODEs: a changelle to differential algebra? (2018) (0)
A ] 2 0 Se p 19 99 Constrained Hamiltonian Systems and Gröbner Bases ⋆ (1999) (0)
Integrability of Polynomial-Nonlinear Evolution Equations and Computer Algebra (1991) (0)
Symbolic-Numeric Integration of the Dynamical Cosserat Equations (2017) (0)
J an 2 00 5 Gröbner Bases in Perturbative Calculations (2005) (0)
ELEMENTARY PARTICLES AND FIELDS Theory On Precession of Entangled Spins in a Strong Laser Field (2009) (0)
Entanglement Sudden Death and Birth Effects in Two Qubits Maximally Entangled Mixed States Under Quantum Channels (2019) (0)
Constructing SU(2) x U(1) orbit space for qutrit mixed states (2014) (0)
S-consistent FDAs for Navier-Stokes Equations (2017) (0)
Complexity of Bounding Polynomial Roots (2009) (0)
NEUTRON SPECTRA OUTSIDE THE PROTON ACCELERATOR SHIELDING. (1972) (0)
s waves of $pi$N scattering and magnitude of the sigma commutator in the statistical model (1974) (0)
The use of computer algebra to investigate the integrability of non-linear evolution systems (1990) (0)
Computer algebra in scientific computing : 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015 : proceedings (2015) (0)
Computer algebra aided numerical solving nonlinear PDEs (2013) (0)
GRéOBNER BASES APPLIED TO SYSTEMS OF LINEAR DIFFERENCE EQUATIONS (2008) (0)
Computer Algebra in Scientific Computing (2017) (0)
Involutive method for computing Gröbner bases over % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqp (2008) (0)
14th International Workshop on Computer Algebra in Scientific Computing (2012) (0)
An Implementation in C of an Algorithm for Construction of Finitely Presented Lie Superalgebrasz (1996) (0)
Computer algebra and computation of Puiseux expansions of algebraic functions (1987) (0)
Computer algebra and solving polynomials (1996) (0)
Linearization of ODEs: algorithmic approach (2015) (0)
Computer Algebra in Scientific Computing (2016) (0)
ANALYTICAL COMPUTER CALCULATIONS AND THEIR APPLICATION IN HIGH-ENERGY PHYSICS. (IN RUSSIAN) (1982) (0)
Discretization of quasilinear evolution equations by computer algebra methods (2017) (0)
Constructing the SU(2) × U(1) Orbit Space for Qutrit Mixed States (2015) (0)
Involutive Bases as a Tool for Multivariate Polynomials over Finite Fields (2010) (0)
Estimates for Positive Roots of Polynomials (2009) (0)
Computer Analysis of Nanoscale Quantum-Dimensional Model Structures in External Fields (2012) (0)
Gröbner Bases as a General Algorithmic Tool for Systems of Equations (2006) (0)
Computer algebra in scientific computing : 15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013, proceedings (2013) (0)
CASIMIR AND (2011) (0)
Ja n 20 05 Gröbner Bases in Perturbative Calculations (0)
Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136 (2013) (0)
U-italic(1) Higgs gauge theory on the lattice (1986) (0)
Simulation of quantum error correction by means of QuantumCircuit package (2013) (0)
Механика Янга - Миллса на световом конусе: $SU(2)$ вместо $SU(3)$@@@Light-cone Yang - Mills mechanics: $SU(2)$ vs. $SU(3)$ (2008) (0)
Deducing the Constraints in the Light-Cone SU (3) Yang-Mills Mechanics Via Gröbner Bases (2007) (0)
Phase transitions in abelian Higgs models on a lattice (1984) (0)
Computation of Difierence Grobner Bases (2012) (0)
Hadronic Vacuum Polarization and Test of Quantum Electrodynamics at Low Energies (2021) (0)
A Maple Implementation of the Finite Element Method for Solving Boundary-Value Problems for Systems of Second-Order Ordinary Differential Equations (2020) (0)
Computer Algebra in Scientific Computing (2013) (0)
Uniformization of the forward scattering amplitude at high energies. [10 to 1000 GeV] (1976) (0)
Measurement of the spectrum of high-energy protons emerging from the shielding of a 680-MeV synchrocyclotron (1976) (0)
Computer algebra in physical research of Joint Institute for Nuclear Research (1987) (0)
Computations on Simple Games using RelView (2018) (0)
Entanglement of spins under a strong laser influence (2013) (0)
Role of involutive criteria in computing Boolean Gröbner bases (2009) (0)
Computer algebra in scientific computing : 16th International Workshop, CASC 2014, Warsaw, Poland, September 8-12, 2014 : proceedings (2014) (0)

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