Main Article Content
This paper introduces a relation between resultant and the Jacobian determinant
by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type: , and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.
Published Online First 20/9/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
Garland W. An introduction to the Jacobian conjectures. Mich. Math. J. 2018. Sep;1-9.
Keller O. Ganze Cremona-Transformationen. Mon Hefte Math. 1939. Dec;47:299-306.
Sakkalis T. On relations between jacobians and resultants of polynomials in two variables. Bull Aust Math Soc. 1993. Jun; 47(3): 473-481.
Jiang L. An Optimization Approach to Jacobian Conjecture. Chon Inst Green Inte Tech CAS. 2020. Feb;1-13.
Omar M. Combinatorial Approaches To The Jacobian Conjecture. Canada: University of Waterloo; 2007. Available from: http://hdl.handle.net/10012/3181.
Moh T. On the Jacobian conjecture and the configuration of roots. J. für die Reine und Angew. Math. 1983; 340:140-212.
Wang S. A Jacobian Criterion for Separability. J Algebra. 1980 Aug; 65(2):453-494.
Cox D, Little J, O’Shea D. Using Algebraic Geometry. 2nd ed. New York Springer; 1998. 572 p.
Peretz R. The 2-dimensional Jacobian Conjecture: A Computational Approach. InAlgorithmic Algebraic Combinatorics and Gröbner Bases 2009 (pp. 151-203). Springer, Berlin, Heidelberg.
Van D E. Polynomial Automorphisms and the Jacobian Conjecture. Switzerland: Birkhauser, Basel Springer; 2000.329p.