COLA with massive neutrinos
  The effect of massive neutrinos on the growth of cold dark matter
perturbations acts as a scale-dependent Newton's constant and leads to
scale-dependent growth factors just as we often find in models of gravity
beyond General Relativity. We show how to compute growth factors for
$\Lambda$CDM and general modified gravity cosmologies combined with massive
neutrinos in Lagrangian perturbation theory for use in COLA and extensions
thereof. We implement this together with the grid-based massive neutrino method
of Brandbyge and Hannestad in $\texttt{MG-PICOLA}$ and compare COLA simulations
to full $\it N$-body simulations of $\Lambda$CDM and $f(R)$ gravity with
massive neutrinos. Our implementation is computationally cheap if the
underlying cosmology already has scale-dependent growth factors and it is shown
to be able to produce results that match $\it N$-body to percent level accuracy
for both the total and CDM matter power-spectra up to $k\lesssim 1 h/$Mpc.
