This issue tracks progress covering as many theorems / algorithms and examples as possible from http://arxiv.org/abs/2007.01749
[x] Section 3 "Clusters"
[x] All notation for clusters
[ ] some issues with theta still when extending by sqrt
[x] Example 3.6
[x] Example 3.7
[x] Section 4 "BY trees"
[x] Definitions
[ ] Plotting automorphisms
[x] Example 4.9
[ ] Example 4.11 not done yet, I think I did it once but its a bit fiddly
[ ] Example 4.12 not done
[ ] Section 5 "Reduction typee"
[x] semistability criterion
[x] good reduction criterion
[x] good reduction jacobian criterion
[x] pot. good reduction
[x] pot. toric rank
[ ] tame reduction criterion
[x] Example 5.8
[x] Example 5.10
[x] Section 6 "special fibre ss"
[x] red map
[x] component equations
[x] dual graph
[x] Example 6.9
[x] Example 6.10
[ ] Section 7 "min reg model" nothing done at all
[ ] Theorems
[ ] Example 7.6
[ ] Example 7.7
[x] Section 8 "dual special fibre and homology" done I think, maybe galois action needs a bit more work
[x] Theorem 8.1 have dual_graph which I implement based on section 6, so should be double checked?
[x] Theorem 8.2
[x] Example 8.4 just added
[x] Example 8.5
[x] Example 8.6
[ ] Section 9 "snc model, tame" nothing
[ ] Theorems
[ ] Example 1
[ ] Example 2
[x] Section 10 "tamagawa"
[x] Theorems
[x] Example 10.4
[x] Example 10.5
[x] Example 10.6
[x] Example 10.7
[ ] Section 11 "gal reps" nothing, not clear even how to represent the info in sage
[ ] Theorems
[ ] Example 11.5
[ ] Example 11.6
[ ] Section 12 "conductors"
[x] tame conductor
[ ] wild conductor not really done as getting the full galois group in the case of a wild field seems hard
[x] Example 12.5 (should also check that the wild part returns 0)
[ ] Example 12.6 (tame case only)
[x] Example 12.7 (should also check that the wild part returns 0)
[x] Example 12.8 (should also check that the wild part returns 0)
[ ] Section 13 "root numbers tame" #27
[ ] theorems (these look doable to me)
[ ] Example 13.7 (done using semistable stuff from homology section)
[x] Example 13.8 (done using semistable stuff from homology section)
[x] Example 13.9 (done using semistable stuff from homology section)
[x] Section 14 "differentials"
[x] Theorems half done
[x] Example 14.8
[x] Example 14.9
[ ] Example 14.10
[x] Section 15 "min disc"
[x] Theorem 15.1, the discriminant function of a cluster
[x] Theorem 15.2, the minimal_discriminant function of a cluster
[x] notation 15.4, the weight function of a BY_tree
[x] Theorem 15.5, the minimal_discriminant function of a BY_tree
[x] Example 15.6
[ ] Example 15.7 (missing the base changed example, in general our stuff is not well tested over extensions)
[x] Section 16 "min weier" pretty much done once again the only limitation is that galois action, so we should chcek root field is tame also
[x] Theorem 16.1
[x] Theorem 16.2
[x] Theorem 16.3
[x] Example 16.4
[x] Example 16.5
[x] Example 16.6
[x] Example 16.7
[ ] Section 17 "isomorphisms/ equivalence"
[ ] def 17.2, we don't have these operations on cluster pictures, they would be quite easy to do, probably best as a function on a cluster tthat returns an updated one rather than mutating.
[ ] theorem 17.5, we have a function to pass from a BY tree to a cluster, but i'm unsure if it is doing exactly the right thing as I dont "attach an open yellow edge to the center"
This issue tracks progress covering as many theorems / algorithms and examples as possible from http://arxiv.org/abs/2007.01749