Resultants of partially composed polynomials

We study the structure of resultants of two homogeneous partially composed polynomials. By two homogeneous partially composed polynomials we mean a pair of polynomials of which one does not have any given composition structure and the other is obtained by composing a bivariate homogeneous polynomial with two bivariate homogeneous polynomials. The main contributions are two equivalent formulas, each representing the resultant of two partially composed polynomials as a certain iterated resultant of the component polynomials. Furthermore, in many cases, this iterated resultant can be computed with dramatically increased efficiency, as demonstrated by experiments.