The Groebner basis of a polynomial system
Christian Valqui, Marco Solorzano
TL;DR
This paper presents a method to compute the Groebner basis of polynomial systems related to the Jacobian conjecture, utilizing a recursive formula involving Catalan numbers.
Contribution
It introduces a novel recursive approach for calculating Groebner bases linked to the Jacobian conjecture, connecting algebraic geometry with combinatorial sequences.
Findings
Successful computation of Groebner bases using the recursive formula
Establishment of a link between Catalan numbers and polynomial system solutions
Potential implications for the Jacobian conjecture
Abstract
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · History and Theory of Mathematics