
Formal Power Series Solutions of First Order Autonomous Algebraic Ordinary Differential Equations
Given a first order autonomous algebraic ordinary differential equation,...
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Regular cylindrical algebraic decomposition
We show that a strong wellbased cylindrical algebraic decomposition P o...
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Computational Understanding and Manipulation of Symmetries
For natural and artificial systems with some symmetry structure, computa...
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Wilf classes of nonsymmetric operads
Two operads are said to belong to the same Wilf class if they have the s...
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Notes on Computational Graph and Jacobian Accumulation
The optimal calculation order of a computational graph can be represente...
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Algebraic Statistics in Model Selection
We develop the necessary theory in computational algebraic geometry to p...
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Geometric vs Algebraic Nullity for Hyperpaths
We consider the question of how the eigenvarieties of a hypergraph relat...
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Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them as algebraic systems. Afterwards we apply differential elimination and analyze the behavior of the dimension in the resulting Thomas decomposition. For such systems of algebraic dimension one, we show that all formal Puiseux series solutions can be approximated up to an arbitrary order by convergent solutions. We show that the existence of Puiseux series and algebraic solutions can be decided algorithmically. Moreover, we present a symbolic algorithm to compute all algebraic solutions. The output can either be represented by triangular systems or by their minimal polynomials.
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