  We design algorithms to efficiently evaluate modular equations of Siegel and
Hilbert type for abelian surfaces over number fields using complex
approximations. Their output can be made provably correct if an explicit
description of the associated graded ring of modular forms over Z is known;
this includes the Siegel case, and the Hilbert case for the quadratic fields of
discriminant 5 and 8. Our algorithms also apply to finite fields via lifting.
