Debugging the monodromy group of a genus 43 curve

incorrect monodromy

(-0.8236030133558490? - 1.432315805459161?*I, [(4, 8)])
(-1.003926469820694? - 1.312699285291610?*I, [(7, 10)])
(-0.6292719323035824? - 1.527276805764545?*I, [(1, 2)])
(-1.167115733368246? - 1.170457245420270?*I, [(1, 5)])
(-0.4242938073167455? - 1.595984245201483?*I, [(3, 10)])
(-1.310334542487599? - 1.008018012406511?*I, [(0, 4)])
(-0.2122033047349114? - 1.637297596524009?*I, [(0, 9)])
(0.003353190880725522? - 1.650551001929049?*I, [(5, 6)])
(-1.431088452408990? - 0.8281670339311812?*I, [(6, 10)])
(0.2186811865807071? - 1.635561892212205?*I, [(4, 6)])
(-0.5346088735260990? - 1.170266804235750?*I, [(8, 10)])
(-0.6956929536582253? - 1.082260891448253?*I, [(7, 9)])
(-0.3626350214089086? - 1.234457005669015?*I, [(2, 4)])
(0.4301017574225731? - 1.592631107458204?*I, [(0, 1)])
(-0.1832704436745978? - 1.273522568728736?*I, [(1, 3)])
(-0.8426104516372692? - 0.9722324057786133?*I, [(1, 3)])
(-1.527270479244535? - 0.6339987867667903?*I, [(5, 9)])
(-0.0001653393692074800? - 1.286665606216596?*I, [(5, 7)])
(0.634014162972467? - 1.522534720269269?*I, [(7, 9)])
(-0.9723733062442276? - 0.8424220601695606?*I, [(2, 4)])
(0.1829531584424494? - 1.273615728834950?*I, [(8, 10)])
(0.8269563494091244? - 1.426507908496946?*I, [(6, 8)])
(0.3623568320478668? - 1.234635780015786?*I, [(2, 4)])
(-1.082342808738414? - 0.6954724540003671?*I, [(8, 10)])
(0.5343923161981249? - 1.170516711964818?*I, [(1, 3)])
(1.005662372449717? - 1.306221350319643?*I, [(0, 4)])
(-1.597199899970955? - 0.4288626529733614?*I, [(0, 3)])
(0.6955555729213048? - 1.082561689107675?*I, [(5, 7)])
(-1.170283081927089? - 0.5343742709125206?*I, [(5, 7)])
(1.167115878559294? - 1.163750718492437?*I, [(1, 9)])
(0.8425633789720717? - 0.9725597265059753?*I, [(8, 10)])
(1.308598891336851? - 1.001539932243499?*I, [(5, 6)])
(0.9724203577049965? - 0.8427493871231044?*I, [(2, 4)])
(-1.234406365943711? - 0.3624054589640381?*I, [(0, 1)])
(1.427735261546770? - 0.8223588854906939?*I, [(3, 9, 6, 10)])
(1.082480175003162? - 0.6957732683615668?*I, [(0, 1)])
(-1.639653362220268? - 0.2163037713027747?*I, [(2, 6)])
(1.522528248575658? - 0.6292564108894109?*I, [(2, 9, 3, 4)])
(1.170499636109959? - 0.534624200516265?*I, [(5, 7)])
(-1.273409208351774? - 0.1830646265848356?*I, [(4, 6)])
(1.591391804674080? - 0.4255092637517972?*I, [(0, 2)])
(1.234684564485265? - 0.3625842534133297?*I, [(8, 10)])
(1.633175228896190? - 0.2145679217999130?*I, [(3, 5)])
(1.273726512175305? - 0.1831577986390063?*I, [(4, 6)])
(-1.653887616329582?, [(8, 9)])
(-1.286498839270547?, [(9, 10)])
(0, [(0, 1), (4, 6), (5, 7), (9, 10)])
(1.286829540108581?, [(0, 1)])
(1.647180944186020?, [(8, 10)])
(1.273726512175305? + 0.1831577986390063?*I, [(5, 7)])
(1.633175228896190? + 0.2145679217999130?*I, [(2, 4)])
(1.234684564485265? + 0.3625842534133297?*I, [(9, 10)])
(1.591391804674080? + 0.4255092637517972?*I, [(1, 3)])
(-1.273409208351774? + 0.1830646265848356?*I, [(5, 7)])
(1.170499636109959? + 0.534624200516265?*I, [(4, 6)])
(1.522528248575658? + 0.6292564108894109?*I, [(2, 5, 3, 8)])
(-1.639653362220268? + 0.2163037713027747?*I, [(3, 7)])
(1.082480175003162? + 0.6957732683615668?*I, [(0, 1)])
(1.427735261546770? + 0.8223588854906939?*I, [(2, 8, 7, 10)])
(-1.234406365943711? + 0.3624054589640381?*I, [(0, 1)])
(0.9724203577049965? + 0.8427493871231044?*I, [(3, 5)])
(1.308598891336851? + 1.001539932243499?*I, [(4, 7)])
(0.8425633789720717? + 0.9725597265059753?*I, [(9, 10)])
(1.167115878559294? + 1.163750718492437?*I, [(0, 8)])
(-1.170283081927089? + 0.5343742709125206?*I, [(4, 6)])
(0.6955555729213048? + 1.082561689107675?*I, [(4, 6)])
(-1.597199899970955? + 0.4288626529733614?*I, [(1, 2)])
(1.005662372449717? + 1.306221350319643?*I, [(1, 5)])
(0.5343923161981249? + 1.170516711964818?*I, [(0, 2)])
(-1.082342808738414? + 0.6954724540003671?*I, [(9, 10)])
(0.3623568320478668? + 1.234635780015786?*I, [(3, 5)])
(0.8269563494091244? + 1.426507908496946?*I, [(7, 9)])
(0.1829531584424494? + 1.273615728834950?*I, [(9, 10)])
(-0.9723733062442276? + 0.8424220601695606?*I, [(3, 5)])
(0.634014162972467? + 1.522534720269269?*I, [(6, 8)])
(-0.0001653393692074800? + 1.286665606216596?*I, [(4, 6)])
(-1.527270479244535? + 0.6339987867667903?*I, [(4, 8)])
(-0.8426104516372692? + 0.9722324057786133?*I, [(0, 2)])
(-0.1832704436745978? + 1.273522568728736?*I, [(0, 2)])
(0.4301017574225731? + 1.592631107458204?*I, [(0, 1)])
(-0.3626350214089086? + 1.234457005669015?*I, [(3, 5)])
(-0.6956929536582253? + 1.082260891448253?*I, [(6, 8)])
(-0.5346088735260990? + 1.170266804235750?*I, [(9, 10)])
(0.2186811865807071? + 1.635561892212205?*I, [(5, 7)])
(-1.431088452408990? + 0.8281670339311812?*I, [(7, 10)])
(0.003353190880725522? + 1.650551001929049?*I, [(4, 7)])
(-0.2122033047349114? + 1.637297596524009?*I, [(1, 8)])
(-1.310334542487599? + 1.008018012406511?*I, [(1, 5)])
(-0.4242938073167455? + 1.595984245201483?*I, [(2, 10)])
(-1.167115733368246? + 1.170457245420270?*I, [(0, 4)])
(-0.6292719323035824? + 1.527276805764545?*I, [(0, 3)])
(-1.003926469820694? + 1.312699285291610?*I, [(6, 10)])
(-0.8236030133558490? + 1.432315805459161?*I, [(5, 9)])

The following are two different ways of computing the permutation of sheets about the branch point 1.427735261546770? - 0.8223588854906939?*I. Below, gamma_mon was constructed using RiemannSurfacePathFactory.monodromy_path whereas gamma_man was manually constructed by creating a ComplexArc around the target branch point.

sage: phi1 = matching_permutation(gamma_mon.get_y(0), gamma_mon.get_y(1))
sage: phi1
[(3, 9, 6, 10)]
sage: phi2 = matching_permutation(gamma_man.get_y(0), gamma_man.get_y(1))
sage: phi2
[(8, 9)]

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