Database of cylinder diagrams and quadratic permutations

Databases for translation surfaces.

This file contain different databases (with different implementations) for algorithms related to translation surfaces:

• structure of Strebel differentials for quadratic differentials in order to differentiate

• database of separatrix and cylinder diagrams up to isomorphism

• database of volume of connected components of Abelian strata

class surface_dynamics.databases.flat_surfaces.CylinderDiagrams(path=None, read_only=True)

Bases: GenericRepertoryDatabase

Database of cylinder diagrams.

The database consists of several files with the following name convention: “stratum-component-ncyls”. As an example, the list of 3-cylinder diagrams in the odd component of H(2,2) is named “2_2-odd-3”.

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams
sage: import os

sage: C = CylinderDiagrams()
sage: a = Stratum([3,1,1,1], k=1).unique_component()
sage: C.filename(a, 2)
'cyl_diags-3_1_1_1-c-2'
sage: os.path.isfile(os.path.join(C.path, C.filename(a, 2)))
True
sage: l = list(C.get_iterator(a, 2))
sage: l[0]
(0,9)-(0,5,7,8,6) (1,6,2,5,3,8,4,7)-(1,2,3,9,4)
sage: l[0].ncyls()
2
sage: l[0].stratum()
H_4(3, 1^3)

count(comp, ncyls=None)

Returns the number of cylinder diagrams for a stratum or a component of stratum with given number of cylinders.

default_path = '/usr/share/miniconda3/envs/test/lib/python3.10/site-packages/surface_dynamics/databases/cylinder_diagrams'

filename(comp, ncyls)

Returns the name of the file for the given component comp and the given of number of cylinders ncyls.

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams
sage: C = CylinderDiagrams()
sage: C.filename(Stratum([4], k=1).odd_component(), 3)
'cyl_diags-4-odd-3'
sage: C.filename(Stratum([3,3], k=1).hyperelliptic_component(), 2)
'cyl_diags-3_3-hyp-2'

get_iterator(comp, ncyls=None)

Returns an iterator over the list of cylinder diagrams for the component comp read from the database.

INPUT:

• comp - a component of stratum

• ncyls - number of cylinders

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams
sage: import os

sage: C = CylinderDiagrams(tmp_dir(), read_only=False)

sage: A = Stratum([2], k=1)
sage: a = A.unique_component()
sage: C.update(A)
sage: list(C.get_iterator(a)) == A.cylinder_diagrams()
True

sage: C.clean()
sage: C.get_iterator(a)
Traceback (most recent call last):
...
ValueError: not in the database

has_component(comp)

Test whether the database has the component comp.

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams
sage: import tempfile

sage: tmp_dir = tempfile.TemporaryDirectory()
sage: C = CylinderDiagrams(tmp_dir.name, read_only=False)
sage: C.clean()

sage: a1 = Stratum([4], k=1).odd_component()
sage: a2 = Stratum([1,1,1,1], k=1).unique_component()

sage: C.has_component(a1)
False
sage: C.has_component(a2)
False
sage: C.update(Stratum([4], k=1))
sage: C.has_component(a1)
True

sage: C.has_component(a2)
False

sage: C.has_component(-19)
Traceback (most recent call last):
...
AssertionError: the argument must be a component of stratum of Abelian differentials

has_stratum(stratum)

Test whether the database contains the data for a given stratum.

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams

sage: import os

sage: C = CylinderDiagrams(tmp_dir(), read_only=False)
sage: C.clean()

sage: a1 = Stratum([4], k=1)
sage: a2 = Stratum([1,1,1,1], k=1)

sage: C.has_stratum(a1)
False
sage: C.has_stratum(a2)
False
sage: C.update(Stratum([4], k=1))
sage: C.has_stratum(a1)
True

sage: C.has_stratum(a2)
False

sage: C.has_stratum(1)
Traceback (most recent call last):
...
AssertionError: the argument must be a stratum of Abelian differential

list_strata()

List available strata in that database.

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams
sage: import os

sage: C = CylinderDiagrams(tmp_dir(), read_only=False)
sage: C.clean()

sage: C.list_strata()
[]
sage: C.update(Stratum([1,1], k=1))
sage: C.list_strata()
[H_2(1^2)]
sage: C.update(Stratum([2], k=1))
sage: C.list_strata()
[H_2(2), H_2(1^2)]

update(stratum, verbose=False)

Compute once for all the given cylinder diagrams of the given stratum.

Warning:

Depending on the dimension of the stratum, it may be very long!

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams

sage: C = CylinderDiagrams(tmp_dir(), read_only=False)
sage: C.update(Stratum([4], k=1), verbose=True) # random
computation for H_3(4)
 ncyls = 1
 1 cyl. diags for H_3(4)^hyp
 2 cyl. diags for H_3(4)^odd
 ncyls = 2
 2 cyl. diags for H_3(4)^hyp
 4 cyl. diags for H_3(4)^odd
 ncyls = 3
 2 cyl. diags for H_3(4)^hyp
 4 cyl. diags for H_3(4)^odd
sage: sorted(os.listdir(C.path))
['cyl_diags-4-hyp-1',
 'cyl_diags-4-hyp-2',
 'cyl_diags-4-hyp-3',
 'cyl_diags-4-odd-1',
 'cyl_diags-4-odd-2',
 'cyl_diags-4-odd-3']

class surface_dynamics.databases.flat_surfaces.GenericRepertoryDatabase(path=None, read_only=True)

Bases: object

Database that consists of a list of files in a repertory.

clean()

Clean the database.

EXAMPLES:

sage: from surface_dynamics import Stratum
sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams
sage: import tempfile

sage: tmp_dir = tempfile.TemporaryDirectory()
sage: C = CylinderDiagrams(tmp_dir.name, read_only=False)
sage: C.update(Stratum([4], k=1))
sage: import os
sage: sorted(os.listdir(C.path))
['cyl_diags-4-hyp-1',
 'cyl_diags-4-hyp-2',
 'cyl_diags-4-hyp-3',
 'cyl_diags-4-odd-1',
 'cyl_diags-4-odd-2',
 'cyl_diags-4-odd-3']
sage: C.clean()
sage: os.listdir(C.path)
[]

default_name = 'generic_db'

class surface_dynamics.databases.flat_surfaces.IrregularComponentTwins(path=None, read_only=True)

Bases: GenericRepertoryDatabase

Twin data of generalized permutation of irregular components of strata of Abelian differentials.

count(stratum)

Returns the number of twins for that stratum.

EXAMPLES:

sage: from surface_dynamics import *

sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins
sage: D = IrregularComponentTwins()
sage: Q = Stratum([12], k=2)
sage: len(D.get(Q))
82
sage: D.count(Q)
82

default_path = '/usr/share/miniconda3/envs/test/lib/python3.10/site-packages/surface_dynamics/databases/generalized_permutation_twins'

filename(stratum)

Returns the name of the file for the given component.

EXAMPLES:

sage: from surface_dynamics import *
sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins
sage: D = IrregularComponentTwins()
sage: D.filename(Stratum([12], k=2))
'twins-12-irr'
sage: D.filename(Stratum([3,3,3,-1], k=2))
'twins-3_3_3_p-irr'
sage: D.filename(Stratum([2,2], k=2))
Traceback (most recent call last):
...
AssertionError: the stratum has no irregular component

get(stratum)

Get the list of twins for the stratum of quadratic differentials stratum.

EXAMPLES:

sage: from surface_dynamics import *

sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins
sage: D = IrregularComponentTwins()
sage: l = D.get(Stratum([6,3,-1], k=2))
sage: l[0]
((1, 2, 0, 4, 6, 7, 8, 9, 10, 11, 12, 13, 5, 3),)
sage: len(l)
32

has_stratum(stratum)

Test whether the component is in the database.

EXAMPLES:

sage: from surface_dynamics import *

sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins
sage: D = IrregularComponentTwins()
sage: D.has_stratum(Stratum([12], k=2))
True

list_strata()

Returns the list of components for which the list of twins is stored.

EXAMPLES:

sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins
sage: G = IrregularComponentTwins()
sage: G.list_strata()
[Q_3(9, -1), Q_3(6, 3, -1), Q_4(12), Q_3(3^3, -1), Q_4(6^2), Q_4(9, 3), Q_4(6, 3^2), Q_4(3^4)]

update(stratum)

Update the database with the irregular component of the given stratum.

The database should not be in read only mode.

surface_dynamics.databases.flat_surfaces.line_count(filename)

Returns the number of lines in the file whose name is filename.