  Vacuum polarization, a key prediction of quantum theory, can cause a variety
of intriguing phenomena that can be triggered by high-intensity laser pulses.
The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory
of electromagnetism with nonlinear photon-photon interactions mediated by
vacuum fluctuations. This work presents a numerical solver for the leading
weak-field Heisenberg-Euler corrections. The present code implementation
reaches an accuracy of order thirteen in the numerical scheme and takes into
account up to six-photon interactions. Since theoretical approaches are limited
to approximations and the experimental requirements for signal detection are
high, the need for support from the numerical side is apparent.
