Démonstration de la continuité des racines d'une équation algébrique
Démonstration du théorème de Cauchy : toute équation à une racine
Die Kombinationen gegebenen Profils. II
Die Kombinationen gegebenen Profils. III
Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5
∗ Research partially supported by INTAS grant 97-1644A real polynomial of one real variable is hyperbolic (resp. strictly hyperbolic) if it has only real roots (resp. if its roots are real and distinct). We prove that there are 116 possible non-degenerate configurations between the roots of a degree 5 strictly hyperbolic polynomial and of its derivatives (i.e. configurations without equalities between roots). The standard Rolle theorem allows 286 such configurations. To obtain the result we study...