FCLoopCanonicalize[exp, {q1, q2, ...}, loopHead] is an
auxiliary internal function that canonicalizes indices of multi-loop
integrals with loop momenta q1, q2, ... that are wrapped
with loopHead. The output is given as a list of 4 entries,
of which the last one contains a list of all the unique loop integrals
in the given expression. After those are simplified, the original output
of FCLoopCanonicalize together with the list of the
simplified unique integrals should be inserted into
FCLoopSolutionList to obtain the final replacement list
that will be applied to the original expression.
FCLoopCanonicalize[myHead[FVD[q, \[Mu]]], q, myHead]\left( \begin{array}{c} \;\text{myHead}\left(q^{\mu }\right) \\ \{\text{FCGV}(\text{cli191})\to \mu \} \\ \;\text{myHead}\left(q^{\text{FCGV}(\text{cli191})}\right) \\ \;\text{myHead}\left(q^{\text{FCGV}(\text{cli191})}\right) \\ \end{array} \right)
FCLoopCanonicalize[myHead[FVD[q, \[Mu]] FVD[q, \[Nu]] FAD[q, {q + p, m}]] + myHead[FVD[q, \[Rho]] FVD[q, \[Sigma]] FAD[q, {q + p, m}]], q, myHead]\left\{\left\{\text{myHead}\left(\frac{q^{\mu } q^{\nu }}{q^2.\left((p+q)^2-m^2\right)}\right),\text{myHead}\left(\frac{q^{\rho } q^{\sigma }}{q^2.\left((p+q)^2-m^2\right)}\right)\right\},\{\{\text{FCGV}(\text{cli201})\to \mu ,\text{FCGV}(\text{cli202})\to \nu \},\{\text{FCGV}(\text{cli201})\to \rho ,\text{FCGV}(\text{cli202})\to \sigma \}\},\left\{\text{myHead}\left(\frac{q^{\text{FCGV}(\text{cli201})} q^{\text{FCGV}(\text{cli202})}}{q^2.\left((p+q)^2-m^2\right)}\right),\text{myHead}\left(\frac{q^{\text{FCGV}(\text{cli201})} q^{\text{FCGV}(\text{cli202})}}{q^2.\left((p+q)^2-m^2\right)}\right)\right\},\left\{\text{myHead}\left(\frac{q^{\text{FCGV}(\text{cli201})} q^{\text{FCGV}(\text{cli202})}}{q^2.\left((p+q)^2-m^2\right)}\right)\right\}\right\}
FCLoopCanonicalize[myHead[FVD[q1, \[Mu]] FVD[q2, \[Nu]]], {q1, q2}, myHead]\left( \begin{array}{c} \;\text{myHead}\left(\text{q1}^{\mu } \;\text{q2}^{\nu }\right) \\ \{\text{FCGV}(\text{cli211})\to \mu ,\text{FCGV}(\text{cli212})\to \nu \} \\ \;\text{myHead}\left(\text{q1}^{\text{FCGV}(\text{cli211})} \;\text{q2}^{\text{FCGV}(\text{cli212})}\right) \\ \;\text{myHead}\left(\text{q1}^{\text{FCGV}(\text{cli211})} \;\text{q2}^{\text{FCGV}(\text{cli212})}\right) \\ \end{array} \right)