The databases.flat_surfaces Module

The databases.flat_surfaces Module#

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)#

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: 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: (C.path / C.filename(a, 2)).is_file()
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 = PosixPath('/home/runner/work/surface-dynamics/surface-dynamics/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: 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: 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: 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(f.name for f in C.path.iterdir())
['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)#

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: sorted(f.name for f in C.path.iterdir())
['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: list(C.path.iterdir())
[]

default_name = 'generic_db'#

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

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 = PosixPath('/home/runner/work/surface-dynamics/surface-dynamics/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.

The databases.flat_surfaces Module

Contents

The databases.flat_surfaces Module#