Section:
New Results
Subresultants of and , Jacobi polynomials and complexity
A previous article in 2017 described explicit expressions for the coefficients
of the order- polynomial subresultant of and
with respect to Bernstein's set of polynomials , for .
In [8], Alin Bostan,
together with T. Krick, M. Valdettaro (U. Buenos Aires, Argentina) and
A. Szanto (U. North Carolina, Raleigh, USA) further developed the study of
these structured polynomials and showed that the coefficients of the
subresultants of and with respect to the monomial
basis can be computed in linear arithmetic complexity, which is
faster than for arbitrary polynomials. The result is obtained as a
consequence of the amazing though seemingly unnoticed fact that these
subresultants are scalar multiples of Jacobi polynomials up to an affine
change of variables.