Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 21, 17:00 ~ 17:30 UTC-3

A Macaulay formula for the sparse resultant

Martín Sombra

ICREA and Universitat de Barcelona, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Compact and easy-to-evaluate formulae for resultants is a kind of "Philosopher's Stone" in computer algebra. In this search, determinantal formulae are important pearls that are hard to find. Macaulay showed in 1902 that homogeneous resultants can be computed as the quotient of two determinants 'à la Sylvester'. In 1993, Canny and Emiris extended his construction to sparse resultants, and conjectured that these can also be computed as the quotient of two determinants 'a la Sylvester'. In this talk, we will review the history of this problem and show how we managed to solve this conjecture.

Joint work with Carlos D'Andrea (Universitat de Barcelona, Spain) and Gabriela Jeronimo (Universidad de Buenos Aires, Argentina).

View abstract PDF