Gröbner bases and involutive methods for algebraic and differential equations

DOI10.1016/S0895-7177(97)00060-5zbMath0904.13014OpenAlexW1971064965MaRDI QIDQ1368545

Vladimir P. Gerdt

Publication date: 4 January 1999

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0895-7177(97)00060-5

zbMATH Keywords

Gröbner basespartial differential equationsdifferential algebrainvolutive basesLie methods in differential equations

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Applications of Lie groups to the sciences; explicit representations (22E70) Commutative rings of differential operators and their modules (13N10) Solutions to PDEs in closed form (35C05)

Related Items (9)

Sufficient set of integrability conditions of an orthonomic system ⋮ Some open problems related to creative telescoping ⋮ Maurice Janet's algorithms on systems of linear partial differential equations ⋮ Ext groups of Janet systems. ⋮ Minimal involutive bases ⋮ Parallelization of matrix algorithms for Gröbner basis computation ⋮ From Analytical Mechanics Problems to Rewriting Theory Through M. Janet’s Work ⋮ Parallel algorithms for Gröbner-basis construction ⋮ Computer algebra methods in the study of nonlinear differential systems

Cites Work

• Non-commutative Gröbner bases in algebras of solvable type
• An algorithm for determining the size of symmetry groups
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Involutive bases of polynomial ideals
• Homogeneity of integrability conditions for multi-parametric families of polynomial-nonlinear evolution equations.
• Involutive systems of algebraic equations
• Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
• COMPUTER ALGEBRA, SYMMETRY ANALYSIS AND INTEGRABILITY OF NONLINEAR EVOLUTION EQUATIONS
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