def test_element():
from pyeantic import eantic
from sage.all import ZZ, QQ
K = eantic.renf('x^2 - 2', 'x', '[1.4142 +/- 0.0001]')
assert str(eantic.renf_elem(K, [ZZ(2), ZZ(3)])) == "(3*x+2 ~ 6.2426407)"
assert str(eantic.renf_elem(K, [1/ZZ(2), 1/ZZ(3)])) == "(1/3*x+1/2 ~ 0.97140452)"
def __init__(self, embedded, category=None):
r"""
TESTS::
sage: from pyeantic import eantic, RealEmbeddedNumberField
sage: K = NumberField(x**2 - 2, 'a', embedding=sqrt(AA(2)))
sage: K = RealEmbeddedNumberField(K)
sage: from pyeantic.real_embedded_number_field import RealEmbeddedNumberField
sage: isinstance(K, RealEmbeddedNumberField)
True
sage: TestSuite(K).run()
"""
self.number_field = embedded
var = self.number_field.variable_name()
self.renf = eantic.renf(
repr(self.number_field.polynomial().change_variable_name(var)),
var, str(RBF(self.number_field.gen())))
Field.__init__(self, QQ, category=category)
self.register_coercion(self.number_field)
self.number_field.register_conversion(ConversionNumberFieldRenf(self))
def test_arithmetic():
from pyeantic import eantic
from sage.all import ZZ, QQ
K = eantic.renf('x^2 - 2', 'x', '[1.4142 +/- 0.0001]')
a = K.gen()
assert (a + ZZ(1)) * (a - ZZ(1)) == (a*a - ZZ(1))
assert (a + 1/ZZ(2)) * (a - 1/ZZ(2)) == (a*a - 1/ZZ(4))
def test_eantic():
from pyeantic import eantic
L = eantic.renf("a^3 - a^2 - a - 1", "a", "[1.84 +/- 0.01]")
lengths = []
lengths.append(eantic.renf_elem(L, "a"))
lengths.append(eantic.renf_elem(L, "2*a^2 - 3"))
iet = IntervalExchangeTransformation(lengths, [1, 0])
iet_10_check(iet)
def test_arithmetic():
K = eantic.renf("x^2 - 3", "x", "1.73 +/- 0.1")
x = K.gen()
assert x + x == 2 * x
assert not (x - x)
assert (x + 1) * (x - 1) == x * x - 1
assert x**2 == 3
assert -x != x
def test_cmp():
from pyeantic import eantic
from sage.all import ZZ, QQ
K = eantic.renf('x^2 - 2', 'x', '[1.4142 +/- 0.0001]')
a = K.gen()
assert a == a
assert a <= a
assert a >= a
assert a > 0
assert 0 < a
assert a != 0
def test_construct():
K = eantic.renf("A^3 - 3", "A", "1.44 +/- 0.1")
zero = K.zero()
one = K.one()
A = K.gen()
assert eantic.renf_elem(K) == zero
assert eantic.renf_elem(K, "A") == A
assert eantic.renf_elem(K, "A - 3") == A - 3
assert eantic.renf_elem(K, "1") == one
assert eantic.renf_elem(A) == A
assert eantic.renf_elem(K, 1) == one
assert eantic.renf_elem(K, [0, 0, 0]) == zero
assert eantic.renf_elem(K, [1, 0, 0]) == one
assert eantic.renf_elem(K, [0, 1, 0]) == A
def lengths(coefficients, permutation):
r"""
Produces lengths for the given permutation in a ring represented by coefficients.
"""
if len(permutation) == 2:
lengths = [18, 3]
elif len(permutation) == 7:
lengths = [4, 56, 23, 11, 21, 9, 65]
else:
lengths = [1] * len(permutation)
if coefficients == "mpz":
from gmpxxyy import mpz
return [mpz(l) for l in lengths]
elif coefficients == "mpq":
from gmpxxyy import mpq
return [mpq(l) for l in lengths]
elif coefficients == "renf_elem":
from pyeantic import eantic
L = eantic.renf("a^3 - a^2 - a - 1", "a", "[1.84 +/- 0.01]")
return [eantic.renf_elem(L, l) for l in lengths]
else:
raise NotImplementedError(
f"Cannot create lengths for {coefficients} yet.")
def test_delete_parent_before_binop():
K = eantic.renf("x^3 - 3", "x", "1.44 +/- 0.1")
x = K.gen()
y = K.gen() + 1
del K
z = x + y
def test_repr():
K = eantic.renf("x^2 - 3", "x", "1.73 +/- 0.1")
x = K.gen()
assert repr(x) == "(x ~ 1.7320508)"
def __init__(self, embedded, category=None):
r"""
TESTS::
sage: import pyeantic
sage: from pyeantic import RealEmbeddedNumberField
sage: K = RealEmbeddedNumberField(QQ)
sage: isinstance(K, pyeantic.real_embedded_number_field.RealEmbeddedNumberField)
True
sage: TestSuite(K).run()
::
sage: K = NumberField(x**2 - 2, 'a', embedding=sqrt(AA(2)))
sage: K = RealEmbeddedNumberField(K)
sage: import pyeantic.real_embedded_number_field
sage: isinstance(K, pyeantic.real_embedded_number_field.RealEmbeddedNumberField)
True
sage: TestSuite(K).run()
::
sage: K = NumberField(x**2 - 2, 'b', embedding=sqrt(AA(2)))
sage: K = RealEmbeddedNumberField(K)
sage: isinstance(K, pyeantic.real_embedded_number_field.RealEmbeddedNumberField)
True
sage: TestSuite(K).run()
::
sage: K.an_element() in K.number_field
True
sage: K.an_element() in QQbar
True
sage: K.number_field.an_element() in K
True
sage: 1 in K
True
::
sage: type(K.one() - K.number_field.one())
<class 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic'>
sage: type(K.number_field.one() - K.one())
<class 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic'>
sage: type(K.one() - 1)
<class 'pyeantic.real_embedded_number_field.RealEmbeddedNumberField_with_category.element_class'>
sage: type(1 - K.one())
<class 'pyeantic.real_embedded_number_field.RealEmbeddedNumberField_with_category.element_class'>
"""
self.number_field = embedded
var = self.number_field.variable_name()
self.renf = eantic.renf(
repr(self.number_field.polynomial().change_variable_name(var)),
var, str(RBF(self.number_field.gen())))
CommutativeRing.__init__(self, QQ, category=category)
# It is usually not a good idea to introduce cycles in the coercion
# framework: when performing a + b with a in A and b in B, it's a bit
# random whether the result will be in A or in B. So we make the map
# into the SageMath number field a coercion since it makes lots of
# stuff work that depends on having coercions to other number fields
# and AA, QQbar, …. We register this coercion as an embedding so
# transitive coercions are detected by the coercion framework such as
# the coercion into AA.
self.register_embedding(CoercionNumberFieldRenf(self))
self.register_conversion(self.number_field)
# Allow coercion of rationals and integers so arithmetic with integers
# works on the SageMath prompt.
self.register_coercion(QQ)
def test_repr():
K = eantic.renf("x^2 - 3", "x", "1.73 +/- 0.1")
assert str(K) == repr(K)
assert str(K) == "NumberField(x^2 - 3, [1.7320508075688772935274463415058723669 +/- 5.08e-38])"
