Title:
A new solution of the quartic problem: with application to integration

D.J. Jeffrey
Department of Applied Mathematics
The University of Western Ontario
London, Ontario, Canada

Abstract:
The Quantifier Elimination problem "For all x, P(x) is positive, where P(x) is
a 4th degree polynomial in R[x]" is solved.  In contrast to previous solutions,
the present solution takes the form of a single inequality.  This inequality,
however, is a more complicated expression than the expressions appearing in
earlier solutions.  Therefore the new solution reduces the number of
inequalities but at the price of a more complicated expression. The problem of
integrating trigonometric functions is then presented, and the place where the
QE problem arises is described.