Pleating ray API - Githubissues

aelzenaar / bella

New computational package for small-rank matrix groups

BSD 3-Clause "New" or "Revised" License

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Closed aelzenaar closed 7 months ago

aelzenaar commented 1 year ago

[x] generator walking down r/s pleating ray from -10 to -2 (say) with a step either uniform in [-10,2] or in the moduli space (general for all polynomials)
[x] selection of correct cusp from roots of Farey polynomial
[x] continued fraction approximation of cusp groups
[x] add subclass CuspGroup of ClassicalRileyGroup

aelzenaar commented 7 months ago

Fix starting radius R.
Solve (Im Phi_p/q = 0) on the circle |z| = R.
Choose the solution z_0 to (2) with angle closest to pi*p/q. Set L_0 = Phi_p/q(z_0). This should be in (-infty, -2)
Let N be the desired number of points, set epsilon = |L_0 + 2|/N. Iterate Newton's method to find z_n (n in 1 to N), starting from z_n-1, that solves Phi_p/q = L_0 + N*epsilon.