Occasional trivialization errors

[plonghi]

In some examples the trivialization produces some errors. It is useful to collect the simplest occurrences to look for what's going wrong case by case.

1) The screenshot below is taken from plot #0 of http://het-math2.physics.rutgers.edu/loom/plot?data=4_equal_punctures_short_3_iter_incomplete

[plonghi]

2) I implemented a set of basic global checks on monodromies. The product of monodromies from branch points and irregular singularities does not match with the monodromy at infinity, in at least two examples: seeding_type_III_A and coset_D_4. Fixing this is somewhat urgent, as it points to potentially serious issues with trivialization of the covering.

UPDATE: it seems that the issue arises in configurations of D-type, where two sheets are identically zero everywhere. The discrepancy between monodromies at branch points (plus irregular singualrities) and the monodromy at infinity involves precisely the switching of the two null sheets. This is now correctly handled in seeding_type_III_A and in coset_D_4. But, the problem now arises in D_4_AD_from_SO_8. Needs further investigation, to find a way of determining this tricky piece of the monodromy. At least, the problem does not appear to be too severe, but will still lead to tangible trouble with trivializing covers, and creating consistent networks.

[plonghi]

3) In this example http://het-math2.physics.rutgers.edu/loom/plot?data=SU_3_N_f_6 there appear to be inconsistent labeling of S-walls by roots. This is not an issue due trivialization, in fact the direct check on global consistency on monodromy indicates that monodromies are OK. The issue is with the routine that assigns roots to single S-walls. It fails at particular phases: below I post a few examples (see picture for the precise phase/step) a) In plot 7 the S-wall emanating from the branch point on the left is green, it should be purple. b) In plot 17 the two green S-walls in the middle intersect each other. This means they can't be of the same root type. c) In plot 64 the S-wall emanating from the bottom-right branch point, and flowing downwards should be Purple, not Blue. d) In the last picture I zoomed in on an artifact occurring close to the bottom-left branch point at step 15, I don't have a good understanding of this artifact right now, bt it's clearly important to correct these things.

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a) b) c) d)