Software
Here is a list of the software packages I maintain.
Levy area simulation
Levy's area describes the area enclosed by a two-dimensional Brownian motion and the chord connecting the start with the end point. It has a deep connection with iterated Ito integrals and is notoriously difficult to simulate.
Since the Levy areas are the key to higher-order numerical approximations for S(P)DEs it is crucial that we have efficient implementations of the current state-of-the-art algorithms for their simulation. These are provided by the LevyArea packages.
LevyArea.jl for Julia
LevyArea.m for Matlab
For more information see the accompanying paper "An analysis of approximation algorithms for iterated stochastic integrals and a Julia and MATLAB simulation toolbox"
Nice numbers
This package was inspired by two insights:
Students don't like ''complicated'' numbers and
every number that is not a rational number or a square root of an integer is complicated.
Thus, during the design of tractable exercises it is helpful to have the computer complain as soon as numbers get too complicated. The numbers from NiceNumbers.jl accomplish this. All nice numbers consist of a rational number and possibly a square root of a rational number. They can be added, subtracted, multiplied even divided, as long as the result can still be represented as a nice number. The package supports also Cholesky and LU decompositions of matrices of nice numbers and can therefore easily be used to design exercises involving these decompositions.