Resultants of partially composed polynomials

  • Authors:

  • Manfred Minimair

  • Affiliations:

  • Department of Mathematics and Computer Science, Seton Hall University, 400 South Orange Avenue, South Orange, NJ 07079, USA

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2006

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Abstract

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.