On the Real Waring Rank of a Biharmonic Form

Abstract

We develop an effective method for determining the real Waring rank and the real border rank of biharmonic binary forms. By means of real apolarity, we convert both of these problems into membership questions for regions bounded by a hypocycloid and an epicycloid. We further provide a computable algebraic criterion for the relevant memberships, which involves only the signs of certain real-valued resultants.