  Proving linear inequalities and identities of Shannon's information measures,
possibly with linear constraints on the information measures, is an important
problem in information theory. For this purpose, ITIP and other variant
algorithms have been developed and implemented, which are all based on solving
a linear program (LP). In particular, an identity $f = 0$ is verified by
solving two LPs, one for $f \ge 0$ and one for $f \le 0$. In this paper, we
develop a set of algorithms that can be implemented by symbolic computation.
Based on these algorithms, procedures for verifying linear information
inequalities and identities are devised. Compared with LP-based algorithms, our
procedures can produce analytical proofs that are both human-verifiable and
free of numerical errors. Our procedures are also more efficient
computationally. For constrained inequalities, by taking advantage of the
algebraic structure of the problem, the size of the LP that needs to be solved
can be significantly reduced. For identities, instead of solving two LPs, the
identity can be verified directly with very little computation.
