Author

ALAA  JONY, SHAWKI AL-RASHED

Published in

Al Baath University Journal, Vol. 38, Issue 13, 2016

Abstract

In this paper we have studied a well-known problem called Jacobian problem, in section 4 we introduce some new results in the framework of this problem, more over in section 5 we give a proof to this problem in special case by reducing the resultant of general polynomial using some MAPLE command. In the same way, we can deduce the general case.

In section 3 we generalize Sakkalis theorem (1)  from two polynomial in two unknowns to n polynomial in n unknowns, we use different way from .

Which lead us to the consideration of resultants of the type :

R_i (x_i,u₁…..u_n)= Res _{x1…..xi,xi+1……xn} (f₁-u₁…., f_n – u_n); i=  1,…n

here ki=deg_xi (R_i) , then we gave a criterion in theorem (4 -1) to decide when a polynomial map F: Cⁿ -> Cⁿ is invertible.

Keywords: Resultant, Grobner basis.