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The Groebner basis of a polynomial system related to the Jacobian conjecture
(Pontificia Universidad Católica del Perú, 2014)
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
A short proof of Jung’s theorem
(Pontificia Universidad Católica del Perú, 2016)
We give a short and elementary proof of Jung’s theorem, which states that for a field K of characteristic zero the automorphisms of K[x, y] are generated by elementary automorphisms and linear automorphisms.
A differential equation for polynomials related to the Jacobian conjecture
(Pontificia Universidad Católica del Perú, 2013)
We analyze a possible minimal counterexample to theJacobian Conjecture P;Q with gcd(deg(P); deg(Q)) = 16 and show that its existence depends only on the existence of solutions for a certain Abel dierential equation of the ...