23 citations · 43 across the 33 of their papers we have counts for
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Some algorithms related to the Jacobian Conjecture
Jorge A. Guccione, Juan J. Guccione, Rodrigo Horruitiner +1
We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible…
The two-dimensional Jacobian conjecture and the lower side of the Newton polygon
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We prove that if the Jacobian Conjecture in two variables is false and (P,Q) is a standard minimal pair, then the Newton polygon HH(P) of P must satisfy several restrictions that h…
The Groebner basis of a polynomial system
Christian Valqui, Marco Solorzano
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
On the shape of possible counterexamples to the Jacobian Conjecture
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We improve the algebraic methods of Abhyankar for the Jacobian Conjecture in dimension two and describe the shape of possible counterexamples. We give an elementary proof of the re…