FCLoopCreateFactorizingRules[ints, topos] processes the
given list of GLIs and corresponding topologies and returns a list of
rules for replacing all factorizing integrals by simpler integrals with
less loops.
Notice that we automatically generate suitable
FCTopology objects for the simpler integrals. Using the
options PreferredTopologies or
PreferredIntegrals those can be mapped to a desired
set.
Overview, FCLoopFactorizingQ, FCLoopCreateFactorizingRules.
masters = Get@FileNameJoin[{$FeynCalcDirectory, "Documentation", "Examples", "MasterIntegrals",
"mastersBMixing3L.m"}];topos = Get@FileNameJoin[{$FeynCalcDirectory, "Documentation", "Examples", "MasterIntegrals",
"toposBMixing3L.m"}];```mathematica FCLoopCreateFactorizingRules[masters[[1 ;; 50]], topos]
```mathematica
\text{FCLoopCreateFactorizingRules: }\;\text{Number of factorizing integrals: }11
\text{FCLoopCreateFactorizingRules: }\;\text{Number of simpler integrals: }6
\left\{\left\{G^{\text{prop2Ltopo00011}}(0,0,0,1,1)\to G^{\text{loopint1}}(1)^2,G^{\text{prop2Ltopo00011}}(1,1,0,0,1)\to G^{\text{loopint1}}(1) G^{\text{loopint7}}(1,1),G^{\text{prop2Ltopo00110}}(1,1,1,1,0)\to G^{\text{loopint11}}(1,1) G^{\text{loopint7}}(1,1),G^{\text{prop2Ltopo00111}}(0,0,1,1,1)\to G^{\text{loopint1}}(1) G^{\text{loopint11}}(1,1),G^{\text{prop2Ltopo00303}}(0,0,1,0,1)\to G^{\text{loopint3}}(1)^2,G^{\text{prop2Ltopo01013}}(0,0,0,1,1)\to G^{\text{loopint1}}(1) G^{\text{loopint3}}(1),G^{\text{prop2Ltopo01310}}(0,1,1,1,0)\to G^{\text{loopint1}}(1) G^{\text{loopint12}}(1,1),G^{\text{prop2Ltopo01313}}(0,0,1,1,1)\to G^{\text{loopint3}}(1) G^{\text{loopint12}}(1,1),G^{\text{prop2Ltopo02020}}(0,1,0,1,0)\to G^{\text{loopint13}}(1)^2,G^{\text{prop2Ltopo02023}}(0,0,0,1,1)\to G^{\text{loopint13}}(1) G^{\text{loopint3}}(1),G^{\text{prop2Ltopo02102}}(0,0,1,0,1)\to G^{\text{loopint1}}(1) G^{\text{loopint13}}(1)\right\},\left\{G^{\text{loopint1}}(1),G^{\text{loopint11}}(1,1),G^{\text{loopint12}}(1,1),G^{\text{loopint13}}(1),G^{\text{loopint3}}(1),G^{\text{loopint7}}(1,1)\right\},\left\{\text{FCTopology}\left(\text{loopint1},\left\{\frac{1}{(-\text{p1}^2+\text{m1}^2+i \eta )}\right\},\{\text{p1}\},\{\},\{\},\{\}\right),\text{FCTopology}\left(\text{loopint11},\left\{\frac{1}{(-\text{p3}^2+\text{m1}^2+i \eta )},\frac{1}{(-(\text{p3}+\text{q1})^2+\text{m1}^2+i \eta )}\right\},\{\text{p3}\},\{\text{q1}\},\{\},\{\}\right),\text{FCTopology}\left(\text{loopint12},\left\{\frac{1}{(-\text{p3}^2+\text{m3}^2+i \eta )},\frac{1}{(-(\text{p3}+\text{q1})^2+\text{m1}^2+i \eta )}\right\},\{\text{p3}\},\{\text{q1}\},\{\},\{\}\right),\text{FCTopology}\left(\text{loopint13},\left\{\frac{1}{(-(\text{p3}+\text{q1})^2+\text{m2}^2+i \eta )}\right\},\{\text{p3}\},\{\text{q1}\},\{\},\{\}\right),\text{FCTopology}\left(\text{loopint3},\left\{\frac{1}{(-\text{p1}^2+\text{m3}^2+i \eta )}\right\},\{\text{p1}\},\{\},\{\},\{\}\right),\text{FCTopology}\left(\text{loopint7},\left\{\frac{1}{(-\text{p1}^2+i \eta )},\frac{1}{(-(\text{p1}+\text{q1})^2+i \eta )}\right\},\{\text{p1}\},\{\text{q1}\},\{\},\{\}\right)\right\}\right\}