PathSignatures - A Macaulay2 package for working with signature tensors

The signature of a path is a non-commutative power series whose coefficients are given by certain iterated integrals over the path components. This series almost uniquely characterizes the path up to translation and reparametrization. Projections of these series to their homogeneous components yield the so-called signature tensors.

Our package PathSignatures simplifies the study of these interesting objects in Macaulay2 for piecewise polynomial paths. It allows for the creation and manipulation of paths and the straight-forward computation of the associated signature tensors.

This is joint work with Carlos Améndola, Oriol Reig and Angelo El Saliby.