Source code for surface_dynamics.databases.flat_surfaces

r"""
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
"""

from __future__ import absolute_import, print_function

import os
import sage.misc.misc

from sage.env import SAGE_SHARE

from . import __path__ as db_path
if len(db_path) != 1:
    raise RuntimeError("problem with setting paths")
db_path = os.path.abspath(db_path[0])

[docs]def line_count(filename): r""" Returns the number of lines in the file whose name is filename. """ from sage.rings.integer import Integer f = open(filename) lines = 0 read_f = f.read # loop optimization buf = read_f(0X100000) while buf: lines += buf.count('\n') buf = read_f(0X100000) # 1024 x 1024 f.close() return Integer(lines)
[docs]class GenericRepertoryDatabase: r""" Database that consists of a list of files in a repertory. """ default_name = "generic_db" default_path = sage.misc.misc.SAGE_TMP def __init__(self, path=None, name=None, read_only=True): r""" INPUT: - ``path`` - string (default is SAGE_TMP) - path to the database. If the repertory does not exists, it is created. - ``name`` - string (default is 'generic_db') - name of the repertory that will contain files of the database. - ``read_only`` - boolean """ if path is None: path = self.default_path if name is None: name = self.default_name full_path = os.path.join(path,name) if not os.path.isdir(full_path): if read_only: raise ValueError("you must set read_only to `False` if the database does not already exist") try: os.makedirs(full_path) except OSError: raise ValueError("not able to create the database at {}".format(full_path)) self.path = os.path.abspath(full_path) self.read_only = read_only def __eq__(self, other): r""" TESTS:: sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: import os sage: rep1 = os.path.join(tmp_dir()) sage: rep2 = os.path.join(tmp_dir()) sage: C1 = CylinderDiagrams(rep1,read_only=False) sage: C2 = CylinderDiagrams(rep1,read_only=False) sage: C3 = CylinderDiagrams(rep2,read_only=False) sage: C1 == C1 True sage: C1 == C2 True sage: C1 == C3 False """ return self.__class__ is other.__class__ and other.path == self.path def __ne__(self, other): r""" TESTS:: sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: import os sage: rep1 = os.path.join(tmp_dir()) sage: rep2 = os.path.join(tmp_dir()) sage: C1 = CylinderDiagrams(rep1,read_only=False) sage: C2 = CylinderDiagrams(rep1,read_only=False) sage: C3 = CylinderDiagrams(rep2,read_only=False) sage: C1 != C1 False sage: C1 != C2 False sage: C1 != C3 True """ return not self.__eq__(other)
[docs] def clean(self): r""" Clean the database. EXAMPLES:: sage: from surface_dynamics.all import * sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: C = CylinderDiagrams(tmp_dir(), "cylinder_diagrams", read_only=False) sage: C.update(AbelianStratum(4)) 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) [] """ assert not self.read_only for filename in os.listdir(self.path): os.remove(os.path.join(self.path,filename))
[docs]class IrregularComponentTwins(GenericRepertoryDatabase): r""" Twin data of generalized permutation of irregular components of strata of Abelian differentials. """ default_name = "generalized_permutation_twins" default_path = db_path def __repr__(self): r""" String representation TESTS:: sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins sage: D = IrregularComponentTwins() sage: D.__repr__() 'Database of twins of irregular components at ...' """ return "Database of twins of irregular components at %s"%self.path
[docs] def filename(self, stratum): r""" Returns the name of the file for the given component. EXAMPLES:: sage: from surface_dynamics.all import * sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins sage: D = IrregularComponentTwins() sage: D.filename(QuadraticStratum(12)) 'twins-12-irr' sage: D.filename(QuadraticStratum(2,2)) Traceback (most recent call last): ... AssertionError: the stratum has no irregular component """ from surface_dynamics.flat_surfaces.quadratic_strata import QuadraticStratum assert isinstance(stratum, QuadraticStratum) assert stratum.has_regular_and_irregular_components(), "the stratum has no irregular component" return ('twins-' + '_'.join(str(z) for z in stratum.zeros(poles=False)) + '_p' * stratum.nb_poles() + '-irr')
[docs] def has_stratum(self, stratum): r""" Test whether the component is in the database. EXAMPLES:: sage: from surface_dynamics.all import * sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins sage: D = IrregularComponentTwins() sage: D.has_stratum(QuadraticStratum(12)) True """ return os.path.isfile(os.path.join(self.path,self.filename(stratum)))
[docs] def update(self, stratum=None): r""" Update the database with the component comp. If comp is None update the whole database. The database should be not in read only mode. """ assert not self.read_only f = open(os.path.join(selfr.path, self.filename(stratum))) p = stratum.irregular_component().permutation_representative() res = [] for q in p.rauzy_diagram(symmetric=True): if q.is_cylindric(): res.append(q._twin) res.sort() for twin in res: f.write(str(twin) + '\n')
[docs] def list_strata(self): r""" 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)] """ from surface_dynamics.flat_surfaces.quadratic_strata import QuadraticStratum from sage.rings.integer import Integer s = set() for f in os.listdir(self.path): if f.startswith('twins-'): g = f[6:] i = g.index('-') comp = g[:i].replace('p','-1') s.add(comp) return sorted(QuadraticStratum(map(Integer,g.split('_'))) for g in s)
[docs] def get(self, stratum): r""" Get the list of twins for the stratum of quadratic differentials ``stratum``. EXAMPLES:: sage: from surface_dynamics.all import * sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins sage: D = IrregularComponentTwins() sage: l = D.get(QuadraticStratum(6,3,-1)) sage: l[0][0] [(1, 8), (1, 5), (1, 4), (0, 4), (0, 3), (1, 7), (1, 6)] sage: l[0][1] [(1, 2), (1, 3), (1, 0), (1, 1), (0, 2), (0, 1), (0, 6), (0, 5), (0, 0)] sage: len(l) 1634 """ assert self.has_stratum(stratum) f = open(os.path.join(self.path, self.filename(stratum))) res = [] s = f.readline() while s: res.append(eval(s)) s = f.readline() return res
[docs] def count(self, stratum): r""" Returns the number of twins for that stratum. EXAMPLES:: sage: from surface_dynamics.all import * sage: from surface_dynamics.databases.flat_surfaces import IrregularComponentTwins sage: D = IrregularComponentTwins() sage: Q = QuadraticStratum(12) sage: len(D.get(Q)) 6993 sage: D.count(Q) 6993 """ return line_count(os.path.join(self.path, self.filename(stratum)))
[docs]class CylinderDiagrams(GenericRepertoryDatabase): r""" 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.all import * sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: import os sage: C = CylinderDiagrams() sage: a = AbelianStratum(3,1,1,1).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) """ default_name = "cylinder_diagrams" default_path = db_path def __repr__(self): r""" String representation. TEST:: sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: C = CylinderDiagrams(tmp_dir(), read_only=False) sage: print(C) # indirect doctest Database of cylinder diagrams at ... """ return "Database of cylinder diagrams at %s"%self.path
[docs] def filename(self, comp, ncyls): r""" Returns the name of the file for the given component ``comp`` and the given of number of cyliders ``ncyls``. EXAMPLES:: sage: from surface_dynamics.all import * sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: C = CylinderDiagrams() sage: C.filename(AbelianStratum(4).odd_component(), 3) 'cyl_diags-4-odd-3' sage: C.filename(AbelianStratum(3,3).hyperelliptic_component(), 2) 'cyl_diags-3_3-hyp-2' """ return ('cyl_diags-' + '_'.join(str(z) for z in comp.stratum().zeros()) + '-' + comp._name + '-' + str(ncyls))
[docs] def has_component(self, comp): r""" Test wheter the database has the component ``comp``. EXAMPLES:: sage: from surface_dynamics.all import * 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 = AbelianStratum(4).odd_component() sage: a2 = AbelianStratum(1,1,1,1).unique_component() sage: C.has_component(a1) False sage: C.has_component(a2) False sage: C.update(AbelianStratum(4)) 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 """ from surface_dynamics.flat_surfaces.abelian_strata import AbelianStratumComponent assert isinstance(comp, AbelianStratumComponent), "the argument must be a component of stratum of Abelian differentials" return os.path.isfile(os.path.join(self.path,self.filename(comp, 1)))
[docs] def has_stratum(self, stratum): r""" Test whether the database contains the data for a given stratum. EXAMPLES:: sage: from surface_dynamics.all import * 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 = AbelianStratum(4) sage: a2 = AbelianStratum(1,1,1,1) sage: C.has_stratum(a1) False sage: C.has_stratum(a2) False sage: C.update(AbelianStratum(4)) 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 """ from surface_dynamics.flat_surfaces.abelian_strata import AbelianStratum assert isinstance(stratum, AbelianStratum), "the argument must be a stratum of Abelian differential" return self.has_component(stratum.one_component())
def _files(self): r""" Iterator over the list of files. TESTS:: sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: C = CylinderDiagrams() sage: C._files() <generator object _files at ...> sage: it = C._files() sage: it.next() # random 'cyl_diags-...' sage: it.next() # random 'cyl_diags-...' """ for f in os.listdir(self.path): if f.startswith('cyl_diags-'): yield f
[docs] def list_strata(self): r""" List available strata in that database. EXAMPLES:: sage: from surface_dynamics.all import * 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(AbelianStratum(1,1)) sage: C.list_strata() [H_2(1^2)] sage: C.update(AbelianStratum(2)) sage: C.list_strata() [H_2(2), H_2(1^2)] """ from surface_dynamics.flat_surfaces.abelian_strata import AbelianStratum from sage.rings.integer import Integer s = set() for f in self._files(): g = f[10:] s.add(g[:g.index('-')]) return [AbelianStratum(map(Integer, g.split('_'))) for g in s]
[docs] def get_iterator(self, comp, ncyls=None): r""" 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.all import * sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: import os sage: C = CylinderDiagrams(tmp_dir(), read_only=False) sage: A = AbelianStratum(2) sage: a = A.unique_component() sage: C.update(A) sage: list(C.get_iterator(a)) [(0,2,1)-(0,2,1), (0,1)-(0,2) (2)-(1)] sage: C.clean() sage: C.get_iterator(a) Traceback (most recent call last): ... ValueError: not in the database """ from surface_dynamics.flat_surfaces.strata import Stratum, StratumComponent if not isinstance(comp,StratumComponent): raise TypeError("comp should be a component of stratum") if ncyls is None: from itertools import chain g = comp.stratum().genus() s = comp.stratum().nb_zeros() return chain(*(self.get_iterator(comp,i) for i in xrange(1,g+s))) filename = os.path.join(self.path, self.filename(comp,ncyls)) if not os.path.isfile(filename): raise ValueError("not in the database") return self._one_file_iterator(filename)
def _one_file_iterator(self, filename): f = open(filename) from surface_dynamics.flat_surfaces.separatrix_diagram import CylinderDiagram line = f.readline() while line: yield CylinderDiagram(line[:-1]) line = f.readline() f.close() def _check_symmetries(self, filename): r""" TESTS:: sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: C = CylinderDiagrams() sage: C._check_symmetries('cyl_diags-4_2-odd-5') # not tested -- to be fixed sage: for filename in C._files(): # not tested -- very long time, ~1h ....: C._check_symmetries(filename) # not tested -- very long time, ~1h """ filename = os.path.join(self.path, filename) for c in self._one_file_iterator(filename): if c != c.canonical_label(inplace=False): raise ValueError("in file {}, {} does not have canonical labels".format( filename, c)) c1 = c.horizontal_symmetry() c1.canonical_label(inplace=True) if c1 < c: raise ValueError("in file {}, {} is not minimal... {} is the good one!".format( filename, c,c1)) c1 = c.vertical_symmetry() c1.canonical_label(inplace=True) if c1 < c: raise ValueError("in file {}, {} is not minimal... {} is the good one!".format( filename, c,c1)) c1 = c.inverse() c1.canonical_label(inplace=True) if c1 < c: raise ValueError("in file {}, {} is not minimal... {} is the good one!".format( filename,c,c1)) def _remove_symmetries(self, filename): r""" Use this at your own risk! It modifies the file of the database inplace!!! """ filename = os.path.join(self.path, filename) n = 0 s = set() garbage = set() for c in self._one_file_iterator(filename): n += 1 if c in garbage: continue cc = [c] c1 = c.horizontal_symmetry() c1.canonical_label(inplace=True) cc.append(c1) c1 = c.vertical_symmetry() c1.canonical_label(inplace=True) cc.append(c1) c1 = c.inverse() c1.canonical_label(inplace=True) cc.append(c1) s.add(min(cc)) garbage.update(cc) print("old cardinality: %d" % n) print("new cardinality: %d" % len(s)) print("gain : %d" % (n-len(s))) f = open(filename, "w") for c in sorted(s): f.write(str(c) + "\n") f.close()
[docs] def update(self, stratum, verbose=False): r""" 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.all import * sage: from surface_dynamics.databases.flat_surfaces import CylinderDiagrams sage: C = CylinderDiagrams(tmp_dir(), read_only=False) sage: C.update(AbelianStratum(4), verbose=True) computation for H_3(4) ncyls = 1 2 cyl. diags for H_3(4)^odd 1 cyl. diags for H_3(4)^hyp ncyls = 2 4 cyl. diags for H_3(4)^odd 2 cyl. diags for H_3(4)^hyp ncyls = 3 4 cyl. diags for H_3(4)^odd 2 cyl. diags for H_3(4)^hyp 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'] """ import sys if verbose: print("computation for %s"%stratum) sys.stdout.flush() for ncyls in xrange(1, stratum.genus() + stratum.nb_zeros()): if verbose: print(" ncyls = %d"%ncyls) sys.stdout.flush() d = stratum.cylinder_diagrams_by_component(ncyls, force_computation = True) for c in d: if verbose: print(" %d cyl. diags for %s"%(len(d[c]),c)) f = open(os.path.join(self.path,self.filename(c,ncyls)), "w") for cyl in sorted(d[c]): f.write(str(cyl) + "\n") f.close()
[docs] def count(self, comp, ncyls=None): r""" Returns the number of cylinder diagrams for a stratum or a component of stratum with given number of cylinders. """ from surface_dynamics.flat_surfaces.abelian_strata import AbelianStratum if isinstance(comp, AbelianStratum): return sum(self.count(cc, ncyls) for cc in comp.components()) if ncyls is None: g = comp.stratum().genus() s = comp.stratum().nb_zeros() return sum((self.count(comp,i) for i in xrange(1,g+s))) return line_count(os.path.join(self.path, self.filename(comp, ncyls)))