Summary: Numer. Math. 36, 53-62 (1980) Numerische
9 by Springer-Verlag1980
An Implementation of Vineent's Theorem
Alkiviadis G. Akritas
Universityof Kansas, Departmentof ComputerScience,Lawrence,Kansas66045,USA
Summary. A new method is presented for the isolation of the real roots of a
polynomial equation; it is based on Vincenrs forgotten theorem of 1836 and
has been implemented using exact (infinite precision) integer arithmetic
algorithms. A theoretical analysis of the computing time of this method is
given along with some empirical results.
Subject Classifications: AMS(MOS): 26A78, 68A15; CR: 5.7.
Isolation of the real roots of a polynomial equation (or, simply, isolation) is the
process of finding real, disjoint intervals such that each contains exactly one real
root and every real root is contained in some interval. This process, in itself, is of
great interest and use in several areas; as an example we mention Tarskrs
decision method 1-16].
In this paper we shall restrict our atten(ion to those isolation methods which
have been implemented in computer algebra systems using exact (infinite