Algorithms and implementations for differential elimination
Algorithms and implementations for differential elimination
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra
Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra
Sufficient Set of Integrability Conditions of an Orthonomic System
Foundations of Computational Mathematics
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
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Differential algebra of convergent power series that depend on an arbitrary finite number of variables is considered. The concept of a passive family of generators is defined for a differential ideal of this algebra. It is a further extension of the concept of the Groebner basis. The theorem that allows checking whether a family of generators is passive and ensures that the point solution of an infinite system of equations exists and is unique in this algebra is proved.