FCLoopFindSectors[{GLI[...], ...}] analyzes the indices
of the GLI integrals in the given list and identifies sectors to which
they belong. Notice that only GLIs with integer indices are
supported.
If the option GatherBy is set to True
(default), the output will be a list of two lists, where the former
contains the original integrals sorted w.r.t the identified sectors,
while the latter is a list of all available sectors.
For GatherBy->False, the output is a list containing
all identified sectors without the original integrals.
Setting the option Last to Truewill return
only the top sector.
ints = {
GLI[topo1, {1, 1, 1, 1}],
GLI[topo1, {2, 1, 2, 1}],
GLI[topo2, {1, 0, 1, 1}],
GLI[topo3, {1, 0, 1, -1}]
};FCLoopFindSectors[ints]\left( \begin{array}{ccc} \left\{\{1,0,1,0\},\left\{G^{\text{topo3}}(1,0,1,-1)\right\}\right\} & \left\{\{1,0,1,1\},\left\{G^{\text{topo2}}(1,0,1,1)\right\}\right\} & \left\{\{1,1,1,1\},\left\{G^{\text{topo1}}(1,1,1,1),G^{\text{topo1}}(2,1,2,1)\right\}\right\} \\ \{1,0,1,0\} & \{1,0,1,1\} & \{1,1,1,1\} \\ \end{array} \right)
FCLoopFindSectors[ints, Last -> True]\left\{\{1,1,1,1\},\left\{G^{\text{topo1}}(1,1,1,1),G^{\text{topo1}}(2,1,2,1)\right\}\right\}
FCLoopFindSectors[ints, GatherBy -> False]\left( \begin{array}{cccc} 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ \end{array} \right)
FCLoopFindSectors[ints, GatherBy -> False, Last -> True]\{1,1,1,1\}