We approach string phenomenology from the perspective of computational
algebraic geometry, by providing new and efficient techniques for proving
stability and calculating particle spectra in heterotic compactifications. This
is done in the context of complete intersection Calabi-Yau manifolds in a
single projective space where we classify positive monad bundles. Using a
combination of analytic methods and computer algebra we prove stability for all
such bundles and compute the complete particle spectrum, including gauge
singlets. In particular, we find that the number of anti-generations vanishes
for all our bundles and that the spectrum is manifestly moduli-dependent.Comment: 36 pages, Late