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Pleating ray API #18

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4 tasks done
aelzenaar opened this issue Aug 10, 2023 · 1 comment
Closed
4 tasks done

Pleating ray API #18

aelzenaar opened this issue Aug 10, 2023 · 1 comment
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enhancement New feature or request

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@aelzenaar
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aelzenaar commented Aug 10, 2023 •
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  • 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)
  • selection of correct cusp from roots of Farey polynomial
  • continued fraction approximation of cusp groups
  • add subclass CuspGroup of ClassicalRileyGroup
@aelzenaar aelzenaar added the enhancement New feature or request label Aug 10, 2023
@aelzenaar aelzenaar modified the milestones: v0.0.99, 0.1.0 Aug 10, 2023
@aelzenaar aelzenaar modified the milestones: 0.1.0, 0.2 Jan 21, 2024
@aelzenaar
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  1. Fix starting radius R.
  2. Solve (Im Phi_p/q = 0) on the circle |z| = R.
  3. 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)
  4. 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.

@aelzenaar aelzenaar modified the milestones: 0.2, 0.1.1 Feb 8, 2024
aelzenaar added a commit that referenced this issue Feb 9, 2024
@aelzenaar
Add algorithms to compute rational pleating rays
2bfac7d 
In farey.py we now have an implementation of Newton's algorithm
and other paraphernalia to compute points on pleating rays.

There is also a new example, parabolic_slice_pleating_rays.py.

This is the first half of the features listed in #18.
aelzenaar added a commit that referenced this issue Feb 11, 2024
@aelzenaar
Add cusp group class to riley module
3ce15a2 
Final piece of pleating ray API, issue #18
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