def test_gothic_generic():
x = polygen(QQ)
K = NumberField(x**3 - 2, 'a', embedding=AA(2)**QQ((1, 3)))
a = K.gen()
S = translation_surfaces.cathedral(a, a**2)
O = GL2ROrbitClosure(S)
assert O.ambient_stratum() == AbelianStratum(2, 2, 2)
for d in O.decompositions(4, 50):
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == O.absolute_dimension() == 4
assert O.field_of_definition() == QQ
def test_D9_number_field():
x = polygen(QQ)
K = NumberField(x**3 - 2, 'a', embedding=AA(2)**QQ((1,3)))
a = K.gen()
S = translation_surfaces.mcmullen_genus2_prototype(2,1,0,-1,a/4)
O = GL2ROrbitClosure(S)
for d in O.decompositions(5):
ncyl, nmin, nund = d.num_cylinders_minimals_undetermined()
assert (nund == 0)
assert ((nmin == 0) or (ncyl == 0 and 1 <= nmin <= 2))
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == 3
assert O.field_of_definition() == QQ
def test_gothic_exact_reals():
pytest.importorskip('pyexactreal')
from pyexactreal import ExactReals
x = polygen(QQ)
K = NumberField(x**3 - 2, 'a', embedding=AA(2)**QQ((1, 3)))
R = ExactReals(K)
S = translation_surfaces.cathedral(K.gen(), R.random_element([0.1, 0.2]))
O = GL2ROrbitClosure(S)
assert O.ambient_stratum() == AbelianStratum(2, 2, 2)
for d in O.decompositions(4, 50):
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == O.absolute_dimension() == 4
def test_back_and_forth_nf():
p = iet.Permutation("a b c", "c b a")
x = polygen(QQ)
K = NumberField(x**2 - 2, 'sqrt2', embedding=AA(2).sqrt())
sqrt2 = K.gen()
T = iet.IntervalExchangeTransformation(p, [1, sqrt2, sqrt2 - 1])
T2 = iet_to_pyintervalxt(T)
T3 = iet_from_pyintervalxt(T2)
assert T == T3
r1 = vector(ZZ, (0, 0, 0, 1, 1, 0))
r2 = vector(ZZ, (3, 1, 0, 1, 0, 2))
r3 = vector(ZZ, (5, 0, 1, 2, 0, 3))
K = NumberField(x**3 - 3, 'cbrt3', embedding=AA(3)**QQ((1, 3)))
cbrt3 = K.gen()
p = iet.Permutation(["a", "b", "c", "d", "e", "f"],
["f", "d", "c", "b", "a", "e"])
l = r1 + (cbrt3 - 1) * r2 + cbrt3**2 * r3
T = iet.IntervalExchangeTransformation(p, l)
assert T.sah_arnoux_fathi_invariant().is_zero()
T2 = iet_to_pyintervalxt(T)
assert list(T2.safInvariant()) == [0, 0, 0]
T3 = iet_from_pyintervalxt(T2)
assert T == T3
def test_D9_exact_real():
pytest.importorskip('pyexactreal')
from pyexactreal import ExactReals
R = ExactReals(QQ)
x = polygen(QQ)
K = NumberField(x**3 - 2, 'a', embedding=AA(2)**QQ((1,3)))
a = K.gen()
S = translation_surfaces.mcmullen_genus2_prototype(2,1,0,-1,R.random_element([0.1, 0.2]))
O = GL2ROrbitClosure(S)
for d in O.decompositions(5):
ncyl, nmin, nund = d.num_cylinders_minimals_undetermined()
assert (nund == 0)
assert ((nmin == 0) or (ncyl == 0 and 1 <= nmin <= 2))
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == 3
def test_gothic_veech():
x = polygen(QQ)
K = NumberField(x**2 - 2, 'sqrt2', embedding=AA(2)**QQ((1, 2)))
sqrt2 = K.gen()
x = QQ((1, 2))
y = 1
a = x + y * sqrt2
b = -3 * x - QQ((3, 2)) + 3 * y * sqrt2
S = translation_surfaces.cathedral(a, b)
O = GL2ROrbitClosure(S)
assert O.ambient_stratum() == AbelianStratum(2, 2, 2)
for d in O.decompositions(4, 50):
assert d.parabolic()
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == O.absolute_dimension() == 2
assert O.field_of_definition() == O.V2._isomorphic_vector_space.base_ring()
def test_nf():
from sage.all import NumberField, QQ, AA, Rational, polygen
from pyeantic.sage_conversion import sage_nf_to_eantic
x = polygen(QQ)
# linear
K = NumberField(x - 3, 'x', embedding=QQ(3))
L = sage_nf_to_eantic(K)
# quadratic
K = NumberField(2*x**2 - 3, 'A', embedding=AA(Rational((3,2)))**Rational((1,2)))
L = sage_nf_to_eantic(K)
# cubic
p = x**3 - x**2 - x - 1
s = p.roots(AA, False)[0]
K = NumberField(x**3 - x**2 - x - 1, 's', embedding=s)
L = sage_nf_to_eantic(K)
def __classcall__(cls, embed, category=None):
r"""
Normalize parameters so embedded real number fields are unique::
sage: from pyeantic import eantic, RealEmbeddedNumberField
sage: K = NumberField(x**2 - 2, 'a', embedding=sqrt(AA(2)))
sage: K = RealEmbeddedNumberField(K)
sage: L = NumberField(x**2 - 2, 'a')
sage: L = RealEmbeddedNumberField(L.embeddings(AA)[1])
sage: M = eantic.renf_class.make("a^2 - 2", "a", "1.4 +/- .1")
sage: M = RealEmbeddedNumberField(M)
sage: K is L
True
sage: K is M
True
"""
if isinstance(embed, eantic.renf_class):
# Since it is quite annoying to convert an fmpz polynomial, we parse
# the printed representation of the renf_class. This is of course
# not very robust…
import re
match = re.match("^NumberField\\(([^,]+), (\\[[^\\]]+\\])\\)$",
repr(embed))
assert match, "renf_class printed in an unexpected way"
minpoly = match.group(1)
root_str = match.group(2)
match = re.match("^\\d*\\*?([^\\^ *]+)[\\^ ]", minpoly)
assert match, "renf_class printed leading coefficient in an unexpected way"
minpoly = QQ[match.group(1)](minpoly)
roots = []
AA_roots = minpoly.roots(AA, multiplicities=False)
for prec in [53, 64, 128, 256]:
R = RealBallField(prec)
root = R(root_str)
roots = [aa for aa in AA_roots if R(aa).overlaps(root)]
if len(roots) == 1:
break
if len(roots) != 1:
raise RuntimeError(
"cannot distinguish roots with limited ball field precision"
)
embed = NumberField(minpoly,
minpoly.variable_name(),
embedding=roots[0])
if embed in NumberFields():
if not RR.has_coerce_map_from(embed):
raise ValueError(
"number field must be endowed with an embedding into the reals"
)
if not embed.is_absolute():
raise NotImplementedError("number field must be absolute")
# We recreate our NumberField from the embedding since number
# fields with the same embedding might differ by other parameters
# and therefore do not serve immediately as unique keys.
embed = AA.coerce_map_from(embed)
if isinstance(embed, Map):
K = embed.domain()
if K not in NumberFields():
raise ValueError("domain must be a number field")
if not AA.has_coerce_map_from(embed.codomain()):
raise ValueError("codomain must coerce into RR")
if not K.is_absolute():
raise NotImplementedError("number field must be absolute")
# We explicitly construct an embedding from the given embedding to
# make sure that we get a useable key.
minpoly = (QQ['x'].gen() - 1) if K is QQ else K.polynomial()
minpoly = minpoly.change_variable_name('x')
embedding = AA.one() if K is QQ else embed(K.gen())
embed = NumberField(minpoly,
K.variable_name(),
embedding=embedding)
else:
raise TypeError(
"cannot build RealEmbeddedNumberField from embedding %s" %
(type(embed)))
category = category or Fields()
return super(RealEmbeddedNumberField,
cls).__classcall__(cls, embed, category)
import sys
import pytest
import itertools
pytest.importorskip('pyflatsurf')
from sage.all import AA, QQ
from flatsurf import EquiangularPolygons, similarity_surfaces, GL2ROrbitClosure
# TODO: the test for field of definition with is_isomorphic() does not check
# for embeddings... though for quadratic fields it does not matter much.
@pytest.mark.parametrize("a,b,c,d,l1,l2,veech,discriminant",
[(1, 1, 1, 7, 1, 1, True, 5),
(1, 1, 1, 7, AA(2).sqrt(), 1, False, 5),
(1, 1, 1, 9, 1, 1, True, 3),
(1, 1, 1, 9, AA(2).sqrt(), 1, False, 1),
(2, 2, 3, 13, 1, 1, False, 5),
(1, 1, 2, 8, 1, 1, False, 1),
(1, 1, 2, 12, 1, 1, False, 2),
(1, 2, 2, 11, 1, 1, False, 2),
(1, 2, 2, 15, 1, 1, False, 5)])
def test_rank2_quadrilateral(a, b, c, d, l1, l2, veech, discriminant):
E = EquiangularPolygons(a, b, c, d)
P = E([l1, l2], normalized=True)
B = similarity_surfaces.billiard(P, rational=True)
S = B.minimal_cover(cover_type="translation")
S = S.erase_marked_points()
S, _ = S.normalized_coordinates()
O = GL2ROrbitClosure(S)