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Author: Harald Schilly
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Description: sage surface dynamics module

Sage Surface Dynamics Module

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

In [1]:
version()
'SageMath version 8.2, Release Date: 2018-05-05'
In [2]:
from surface_dynamics.all import *
In [3]:
o = Origami('(1,2)','(1,3)') o
(1,2)(3) (1,3)(2)
In [4]:
o.sum_of_lyapunov_exponents()
4/3
In [5]:
o.lyapunov_exponents_approx() # abs tol 0.05
[0.332969411376565]
In [6]:
o.veech_group()
Arithmetic subgroup with permutations of right cosets S2=(2,3) S3=(1,2,3) L=(1,2) R=(1,3)
In [7]:
q = QuadraticStratum(1,1,1,1) q.orientation_cover()
H_5(2^4)
In [8]:
q.components()
[Q_2(1^4)^hyp]
In [9]:
c = q.components()[0] c
Q_2(1^4)^hyp
In [10]:
c.orientation_cover_component()
H_5(2^4)^odd
In [11]:
AbelianStrata(genus=3).list()
[H_3(4), H_3(3, 1), H_3(2^2), H_3(2, 1^2), H_3(1^4)]
In [12]:
O = OrigamiDatabase() q = O.query(("stratum","=",AbelianStratum(2)), ("nb_squares","=",5)) q.number_of()
2
In [13]:
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) - - - - - - - -
In [14]:
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]
In [15]:
Q12_reg.lyapunov_exponents_H_minus(nb_iterations=2**20) # abs tol 0.05
[1.0001683654623874, 0.3116877930036588, 0.11979408029348164]
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