  Scalar, vector and tensor harmonics on the three-sphere were introduced
originally to facilitate the study of various problems in gravitational
physics. These harmonics are defined as eigenfunctions of the covariant Laplace
operator which satisfy certain divergence and trace identities, and
ortho-normality conditions. This paper provides a summary of these properties,
along with a new notation that simplifies and clarifies some of the key
expressions. Practical methods are described for accurately and efficiently
computing these harmonics numerically, and test results are given that
illustrate how well the analytical identities are satisfied by the harmonics
computed numerically in this way.
