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
one 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.
This paper is part of the author's work on
resultants of composed polynomials.