FCLoopFindOverdeterminedTopologies[topos] finds
topologies with overdetermined propagator bases in the given list of
topologies. The function returns a list of two lists, where the first
list contains all overdetermined topologies and the second one the
rest.
Overview, FCTopology, FCLoopFindOverdeterminedTopologies, FCLoopFindTopologies, FCLoopFindTopologyMappings, SubtopologyMarker.
topos = {FCTopology[topo1, {SFAD[k1], SFAD[k1 + p], SFAD[k1 - p]}, {k1}, {p}, {}, {}],
FCTopology[topo2, {SFAD[k1], SFAD[k1 + p]}, {k1}, {p}, {}, {}]}\left\{\text{FCTopology}\left(\text{topo1},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )},\frac{1}{((\text{k1}-p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right),\text{FCTopology}\left(\text{topo2},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right)\right\}
FCLoopFindOverdeterminedTopologies[topos]\left( \begin{array}{c} \;\text{FCTopology}\left(\text{topo1},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )},\frac{1}{((\text{k1}-p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right) \\ \;\text{FCTopology}\left(\text{topo2},\left\{\frac{1}{(\text{k1}^2+i \eta )},\frac{1}{((\text{k1}+p)^2+i \eta )}\right\},\{\text{k1}\},\{p\},\{\},\{\}\right) \\ \end{array} \right)