On The Determination Of Parameters by Means of Functional Inversion

Abstract

This paper attempts to discover how to determine the parameters of a function using the zeroes of the function. Generalizing affine algebraic varieties, we define and develop the locus of a function, to that end. Specific depth of exploration is given to such varieties and their straightforward generalization to a type of loci. Full results are given for those well-behaved cases through the methods of linear algebra, especially Cramer's Rule. Partial results are given for less-well-behaved cases.