Attacking Jacobian Problem Using Resultant Theory

  • 13 Nov 2021
  • Published Resarch - Mathematics


Alaa Jony and Shawki Al-Rashed

Published in

Baghdad Science Journal, Volume 19, No. 2, 2022, published online first 20 September 2021.


 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:

Ri(Xi,U1,...,Un)= Resx1,...Xi-1,Xi+1,..Xn(f1-u1,...,fn-un),i=1,..n,

 and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.

Keywords: Jacobian conjecture, polynomial map, resultant.

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