FCLoopBasisIntegralToGraph: Graph representation from a propagator representation

[vsht]

Initial version of FCLoopBasisIntegralToGraph, a function that converts a propagator representation of a loop integral to a graph representation. The output is a list of edge rules that can immediately processed via Mathematica's GraphPlot

Usage examples:

FAD[p1, p2, q1 + p1, p1 - q2, q1 + p1 - p2, p1 - p2 - q2, 
 p1 - p2 + q1 - q3]
re = FCLoopBasisIntegralToGraph[%, {p1, p2}]
GraphPlot[%]

FAD[p1] FAD[p4] FAD[p1 + q1] FAD[p3 + p4 + q1] FAD[p3] FAD[p1 - p4]
FCLoopBasisIntegralToGraph[%, {p1, p3, p4}, FCVerbose -> 0]
GraphPlot[%]

SFAD[p1, p2, q1 + p1, p1 - q2, q1 + p1 - p2, p1 - p2 - q2]
FCLoopBasisIntegralToGraph[%, {p1, p2}]
GraphPlot[%]

ToDo

• [x] The code works but still requires a lot of polishing
• [x] Support CFADs and especially eikonal propagators
• [ ] If the line momentum flowing through the propagator is unclear, add an option to specify it explicitly
• [x] Better debugging output and more comments
• [ ] Additional output styles/modes (e.g. for GraphViz, EXP etc.)
• [x] Unit tests
• [x] Documentation
• [ ] Mention similar codes somewhere (important for the paper): PlanarityTest, GraphRoutines (is it public???)
• [ ] A connection to IGraph/M as in GraphRoutines would be a good idea
• [x] Use the U and F Polynomials to determine external momenta that really contribute (important e.g. for tadpoles). Requires the merge of #58 !
• [ ] A front-end function for generating nice plots with proper line labelling