Groebner bases and differential algebra
Proceedings of the 5th international conference, AAECC-5 on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Non-commutative Gröbner bases in algebras of solvable type
Journal of Symbolic Computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Solving zero-dimensional involutive systems
Algorithms in algebraic geometry and applications
Involution approach to investigating polynomial systems
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Standard Bases of Differential Ideals
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Computer algebra methods in the study of nonlinear differential systems
Computational Mathematics and Mathematical Physics
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In this paper, we consider and illustrate by examples some recently developed computer algebra methods for analyzing and solving nonlinear algebraic and differential equations. The foundation of these methods is either the transformation of the initial equations to an equivalent, often called standard, form or their reduction to a finite set of subsystems in standard form. As a standard form we consider various Grobner bases with special emphasis on its involutive extension. Applications to the symmetry and integrability analysis of partial differential equations as well as to solving systems of polynomial equations are discussed.