Code and files related to computations of scattering diagrams for Sage Days 64.5
- Scattering Diagrams Code is Sage code which contains the classes
- ScatteringDiagram
- SDWall
- SDTable
- SDVertex
- ScatteringNB is a Sage worksheet which contains a version of the above code, as well as several examples.
- StereoProj is a Sage worksheet which contains some old code for computing stereographic projections of g-fans. Poorly written and uncommented; avoid if possible.
r=2 To-Do List:
- Use knowledge of g-fan to optimize SDTable.multiplicity
- Find out if increasing recursion depth causes stack overflows
- Eliminate as many perturbations as possible!
r=2 Wish List:
- Implement path-ordered products as ring homomorphisms, and compute characteristic automorphism. (Problem: no homomorphisms of multivariate Laurent rings are not implemented yet)
- Broken lines/theta functions. Possibly incorporate this project: https://github.com/Etn40ff/broken-lines
- Verify computed multiplicites (compare with Reineke's result?)
r=3 Wish List:
- Write new or extend existing classes SDWall, SDVertex and ScatteringDiagram to the r=3 case.
- Implement stereographic plots for the above classes
- Implement `affine slice' plots for the above classes. (It may be easier to extend the r=2 code to cover this case)
Research Questions:
- Do the non-cluster theta functions of the Markov quiver coincide with the bracelet basis? (Equivalently,) what is the characteristic automorphism of a scattering diagram of the Markov cluster algebra?
- What is the path ordered product of the path in D(2,2) which goes from the all-positive quadrant to the wild wall? (An answer to this coul answer the previous question)
- Is there a quiver with 3-vertices that has more than two components of open chambers?