Roots of algebraic equations and Clifford algebra

Abstract

If an algebraic equation onIR admits real roots it admits hyperbolic roots which are elements of the set (x0 + ey0) where e is a Clifford number having a square equal to 1. The equation can have hyperbolic or real roots $${{(a_1 + a_2 )} \over 2} + \varepsilon {{(a_1 - a_2 )} \over 2}$$ ifa1 anda2 are two real roots obtained for e=1 or e=−1. Ifn is the degree of an equation the maximum number of hyperbolic or real roots isn2. We apply our analysis to the intersection of plane curves with a real straight line and to differential linear equations with constant coefficients. *** DIRECT SUPPORT *** A00PF004 00003