One-loop examples. One-loop propagator diagram with the masses m and 0. Massless on-shell box diagram.
An example of a twofold MB integral. Strategy A.
Strategy B [Tausk]
Implementation of Strategy B in Czakon's code MB.m. One-loop examples. One-loop propagator diagram with the masses m and 0 (.nb file). Massless on-shell box diagram (.nb file).
Barnes lemmas and their corollaries.
A two-loop example: the massless non-planar 2-loop vertex diagram. The derivation of a twofold MB representation. The evaluation (.nb file).
An example where an auxiliary analytic regularization is necessary (.nb file).
An algorithm based on Strategy A. An application of the corresponding code (MBresolve.m) in the same examples (.nb file).
The massless on-shell double-box. "Horizontal" and "vertical" checks and the evaluation (.nb file). Summing up series, nested sums and HPL.
An example where an auxiliary analytic regularization is necessary: the massless on-shell double-box with a numerator (.nb file).
A warning: the loop-by-loop strategy can be problematic for nonplanar diagrams. The massless non-planar 2-loop vertex diagram (.nb file).
Using PSLQ for MB integrals (.nb file).
Proceeding in 4 loops with a 10fold MB integral (.nb file).
Perspectives.