We present an efficient method to shorten the analytic integration-by-parts
(IBP) reduction coefficients of multi-loop Feynman integrals. For our approach,
we develop an improved version of Leinartas' multivariate partial fraction
algorithm, and provide a modern implementation based on the computer algebra
system Singular. Furthermore, We observe that for an integral basis with
uniform transcendental (UT) weights, the denominators of IBP reduction
coefficients with respect to the UT basis are either symbol letters or
polynomials purely in the spacetime dimension D. With a UT basis, the partial
fraction algorithm is more efficient both with respect to its performance and
the size reduction. We show that in complicated examples with existence of a UT
basis, the IBP reduction coefficients size can be reduced by a factor of as
large as ∼100. We observe that our algorithm also works well for settings
without a UT basis.Comment: minor changes, typos correcte