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Romanovski, Valery G.; Prešern, Mateja

An approach to solving systems of polynomials via modular arithmetics with applications. (English) Zbl 1225.13029

J. Comput. Appl. Math. 236, No. 2, 196-208 (2011).
Summary: The objective of this paper is twofold. First, we describe a method to solve large systems of polynomial equations using modular arithmetics. Then, we apply the approach to the study of the problem of linearizability for a quadratic system of ordinary differential equations.

Cited in 31 Documents

MSC:

13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
13P15 Solving polynomial systems; resultants
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
65Y04 Numerical algorithms for computer arithmetic, etc.

Keywords:

polynomial systems of ODEs; linearizability of ODEs; decomposition of affine varieties

Software:

SINGULAR; primdec
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\textit{V. G. Romanovski} and \textit{M. Prešern}, J. Comput. Appl. Math. 236, No. 2, 196--208 (2011; Zbl 1225.13029)
Full Text: DOI

References:

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