Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Essential components of an algebraic differential equation
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
Journal of Symbolic Computation
Examples of Computation of Generators of a Differential Ideal by Its Characteristic Set
Programming and Computing Software
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Characteristic sets for ordinary differential equations
Programming and Computing Software
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In this paper, the characterizability of radical differential ideals is discussed and the characterizability criterion for them is proved. This criterion is based on the known algorithm for decomposing a radical differential ideal into characterizable components. The inclusion problem is also considered, in the light of which the algorithm for minimal characteristic decomposition of principal ideals is discussed. This algorithm is improved by using the proven characterizability criterion. Differential and algebraic properties of autoreduced sets are discussed, and the structure of differential chains and characteristic sets of radical differential ideals is revealed. The corresponding algorithms are constructed and discussed.