  We propose a factorizability ansatz for angular bispectra which permits fast
algorithms for forecasting, analysis, and simulation, yet is general enough to
encompass many interesting CMB bispectra. We describe a suite of general
algorithms which apply to any bispectrum which can be represented in
factorizable form. First, we present algorithms for Fisher matrix forecasts and
the related problem of optimizing the factorizable representation, giving a
Fisher forecast for Planck as an example. We show that the CMB can give
independent constraints on the amplitude of primordial bispectra of both local
and equilateral shape as well as those created by secondary anisotropies. We
also show that the ISW-lensing bispectrum should be detected by Planck and
could bias estimates of the local type of non-Gaussianity if not properly
accounted for. Second, we implement a bispectrum estimator which is fully
optimal in the presence of sky cuts and inhomogeneous noise, extends the
generality of fast estimators which have been limited to a few specific forms
of the bispectrum, and improves the running time of existing implementations by
several orders of magnitude. Third, we give an algorithm for simulating random,
weakly non-Gaussian maps with prescribed power spectrum and factorizable
bispectrum.
