# Descartes Signature Explorer

Descartes Signature Explorer

The Descartes signature of a polynomial gives the maximum number of roots in each angular direction of the complex plane. It arises from the Descartes rule of sweeps, which extends the well-known rule of signs to polynomials with non-real coefficients. Whereas the rule of signs counts the sign changes of a polynomial's coefficient sequence, the rule of sweeps considers the polynomial's "angular sweep". This Demonstration provides a laboratory for investigating the relationships among coefficients, their sweeps, and the corresponding Descartes signature.