sage-surface_dynamics.ipynb

Kernel: SageMath (stable)

Sage Surface Dynamics Module

https://pypi.org/project/surface_dynamics/

version()

'SageMath version 8.2, Release Date: 2018-05-05'

from surface_dynamics.all import *

o = Origami('(1,2)','(1,3)')
o

(1,2)(3)
(1,3)(2)

o.sum_of_lyapunov_exponents()

4/3

o.lyapunov_exponents_approx()    # abs tol 0.05

[0.332969411376565]

o.veech_group()

Arithmetic subgroup with permutations of right cosets
 S2=(2,3)
 S3=(1,2,3)
 L=(1,2)
 R=(1,3)

q = QuadraticStratum(1,1,1,1)
q.orientation_cover()

H_5(2^4)

q.components()

[Q_2(1^4)^hyp]

c = q.components()[0]
c

Q_2(1^4)^hyp

c.orientation_cover_component()

H_5(2^4)^odd

AbelianStrata(genus=3).list()

[H_3(4), H_3(3, 1), H_3(2^2), H_3(2, 1^2), H_3(1^4)]

O = OrigamiDatabase()
q = O.query(("stratum","=",AbelianStratum(2)), ("nb_squares","=",5))
q.number_of()

2

for o in q:
     print("%s\n- - - - - - - -" % o)

(1)(2)(3)(4,5)
(1,2,3,4)(5)
- - - - - - - -
(1)(2)(3,4,5)
(1,2,3)(4)(5)
- - - - - - - -

Q12_reg = QuadraticStratum(12).regular_component()
Q12_reg.lyapunov_exponents_H_plus(nb_iterations=2**20)   # abs tol 0.05

[0.6638979772769612,
 0.4496320367320795,
 0.22949766392391907,
 0.08700850585592607]

Q12_reg.lyapunov_exponents_H_minus(nb_iterations=2**20)  # abs tol 0.05

[1.0001683654623874, 0.3116877930036588, 0.11979408029348164]