One of the most useful functions exposed by the Fermat interface is
FerSolve that is vastly superior to Mathematica’s
Solve when dealing with very large symbolic systems of
equations.
A typical situation where one needs to solve such equations is the
derivation of tensor decomposition formulas. To this aim FeynCalc’s
Tdec can directly use FerSolve, once
FeynHelpers is loaded. One just needs to set the option
Solve to FerSolve.
The following example calculates tensor reduction formula for a rank 6 integral with 2 loop momenta and two external momenta. The Fermat part requires only 40 seconds on a modern laptop to solve the corresponding 52 \times 52 symbolic system.
Tdec[{{p1, mu1}, {p1, mu2}, {p1, mu3}, {p1, mu4}, {p2, mu5}, {p2, mu6}},
{Q1, Q2}, Solve -> FerSolve, UseTIDL -> False, FCVerbose -> 1]