CoCalc Public Filessage-surface_dynamics.ipynb
Author: Harald Schilly
Views : 86
Description: sage surface dynamics module
Compute Environment: Ubuntu 18.04 (Deprecated)

# 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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