  We show that questions concerning the topological B-model on a Calabi-Yau
manifold in the Landau-Ginzburg phase can be rephrased in the language of
commutative algebra. This yields interesting and very practical methods for
analyzing the model. We demonstrate how the relevant "Ext" groups and
superpotentials can be computed efficiently by computer algebra packages such
as Macaulay. This picture leads us to conjecture a general description of
D-branes in linear sigma models in terms of triangulated categories. Each phase
of the linear sigma model is associated with a different presentation of the
category of D-branes.
