Dixon Resultant without Extraneous Factors

Extraneous factors are unwanted parameters which appear in the process of eliminating variables in a symbolic polynomial system. This paper is intended to present the conditions, under which the Dixon resultant formulation is exact which implied as there is not any extraneous factors in determinante of Dixon matrix. Like other matrix based methods, the Dixon method is not exempt from the existence of extraneous factors along with the resultant which together is called projection operator; however, recognition of these factors takes a long process, and sometimes the presence of them can make computing the projection operator impractical. As a matter of fact, under such conditions, the projection operators are exactly, up to a constant factor, resultant.

Keywords:

Elimination Theory , Resultant , Dixon Construction , Extraneous Factors