  We calculate the electromagnetic corrections needed to obtain isospin
invariant hadronic pion-pion s-wave scattering lengths a^0, a^2 from the
elements a_cc, a_0c of the s-wave scattering matrix for the (\pi^+ \pi^-, \pi^0
\pi^0) system at the \pi^+ \pi^- threshold. These elements can be extracted
from experiments on pionium. Our calculation uses energy independent hadronic
pion-pion potentials that satisfactorily reproduce the low-energy phase shifts
given by two-loop chiral pertur- bation theory. We also take into account an
important relativistic effect whose inclusion influences the corrections
considerably.
