  Polynomial chaos expansion (PCE) is an increasingly popular technique for
uncertainty propagation and quantification in systems and control. Based on the
theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying
mathematical framework to study systems under arbitrary uncertainties of finite
variance; we introduce this problem as a so-called mapping under uncertainty.
For practical PCE-based applications we require orthogonal polynomials relative
to given probability densities, and their quadrature rules. With PolyChaos we
provide a Julia software package that delivers the desired functionality: given
a probability density function, PolyChaos offers several numerical routines to
construct the respective orthogonal polynomials, and the quadrature rules
together with tensorized scalar products. PolyChaos is the first PCE-related
software written in Julia, a scientific programming language that combines the
readability of scripted languages with the speed of compiled languages. We
provide illustrating numerical examples that show both PCE and PolyChaos in
action.
