Equations, inequations and inequalities characterizing the configurations of two real projective conics

Abstract

Ordered pairs of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The results are well--adapted to the study of the relative position of two conics defined by equations depending on parameters.