def test_Domain_interface():
pytest.raises(TypeError, lambda: DomainElement().parent)
assert RR(1).parent is RR
assert CC(1).parent is CC
assert RR.has_default_precision
assert CC.has_default_precision
RR3 = RealField(prec=53, dps=3)
assert str(RR3(1.7611107002)) == '1.76'
assert RealField(tol=3).tolerance == 3.0
assert RealField(tol=0.1).tolerance == 0.1
assert RealField(tol='0.1').tolerance == 0.1
pytest.raises(ValueError, lambda: RealField(tol=object()))
pytest.raises(AttributeError, lambda: CC.ring)
pytest.raises(DomainError, lambda: CC.get_exact())
assert str(EX(1)) == 'EX(1)'
assert EX(1).as_expr() == Integer(1)
assert bool(EX(1)) is True
assert bool(EX(0)) is False
def test___eq__():
assert not QQ.inject(x) == ZZ.inject(x)
assert not QQ.inject(x).field == ZZ.inject(x).field
assert EX(1) != EX(2)
F11 = FF(11)
assert F11(2) != F11(3)
assert F11(2) != object()
def test_composite_option():
assert construct_domain({(1, ): sin(y)}, composite=False) == (EX, {
(1, ):
EX(sin(y))
})
assert construct_domain({(1, ): y}, composite=False) == (EX, {
(1, ): EX(y)
})
assert construct_domain({(1, 1): 1}, composite=False) == (ZZ, {(1, 1): 1})
assert construct_domain({(1, 0): y}, composite=False) == (EX, {
(1, 0): EX(y)
})
def test_Domain_convert():
assert QQ.convert(10e-52) == QQ(
1684996666696915,
1684996666696914987166688442938726917102321526408785780068975640576)
R, x = ring('x', ZZ)
assert ZZ.convert(x - x) == 0
assert ZZ.convert(x - x, R) == 0
F3 = FF(3)
assert F3.convert(Float(2.0)) == F3.dtype(2)
assert F3.convert(PythonRational(2, 1)) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(PythonRational(1, 2)))
assert F3.convert(2.0) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(2.1))
assert RR.convert(CC(1)) == RR(1)
pytest.raises(CoercionFailed, lambda: RR.convert(CC(1, 2)))
assert QQ.convert(ALG(1), ALG) == QQ(1)
pytest.raises(CoercionFailed, lambda: QQ.convert(ALG([1, 1]), ALG))
assert ZZ.convert(ALG(1), ALG) == ZZ(1)
pytest.raises(CoercionFailed, lambda: ZZ.convert(ALG([1, 1]), ALG))
assert EX.convert(ALG([1, 1]), ALG) == sqrt(2) + sqrt(3) + 1
ALG2 = QQ.algebraic_field(sqrt(2))
a2 = ALG2.convert(sqrt(2))
a = ALG.convert(a2, ALG2)
assert a.rep.all_coeffs() == [0, -QQ(9, 2), 0, QQ(1, 2)]
assert RR.convert(a) == RR(1.4142135623730951)
assert CC.convert(a) == CC(1.4142135623730951)
assert ZZ_python.convert(3.0) == ZZ_python.dtype(3)
pytest.raises(CoercionFailed, lambda: ZZ_python.convert(3.2))
assert CC.convert(QQ_python(1, 2)) == CC(0.5)
CC01 = ComplexField(tol=0.1)
assert CC.convert(CC01(0.3)) == CC(0.3)
assert RR.convert(complex(2 + 0j)) == RR(2)
pytest.raises(CoercionFailed, lambda: RR.convert(complex(2 + 3j)))
assert ALG.convert(EX(sqrt(2)), EX) == ALG.from_expr(sqrt(2))
pytest.raises(CoercionFailed, lambda: ALG.convert(EX(sqrt(5)), EX))
pytest.raises(CoercionFailed, lambda: ALG2.convert(ALG.unit))
def test_factor_list():
R, x = ring('x', FF(2))
assert (x**2 + 1).factor_list() == (1, [(x + 1, 2)])
R, x = ring('x', ZZ)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
assert (x**2 + 2 * x + 1).factor_list() == (1, [(x + 1, 2)])
# issue sympy/sympy#8037
assert (6 * x**2 - 5 * x - 6).factor_list() == (1, [(2 * x - 3, 1),
(3 * x + 2, 1)])
R, x = ring('x', QQ)
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
assert (x**2 / 2 + x + QQ(1, 2)).factor_list() == (QQ(1, 2), [(x + 1, 2)])
R, x = ring('x', QQ.algebraic_field(I))
f = x**4 + 2 * x**2
assert f.factor_list() == (1, [(x, 2), (x**2 + 2, 1)])
R, x = ring('x', RR)
assert (1.0 * x**2 + 2.0 * x + 1.0).factor_list() == (1.0, [(1.0 * x + 1.0,
2)])
assert (2.0 * x**2 + 4.0 * x + 2.0).factor_list() == (2.0, [(1.0 * x + 1.0,
2)])
f = 6.7225336055071 * x**2 - 10.6463972754741 * x - 0.33469524022264
assert f.factor_list() == (1.0, [(f, 1)])
# issue diofant/diofant#238
f = 0.1 * x**2 + 1.1 * x + 1.0
assert f.factor_list() == (10.0, [(0.1 * x + 0.1, 1), (0.1 * x + 1.0, 1)])
f = 0.25 + 1.0 * x + 1.0 * x**2
assert f.factor_list() == (4.0, [(0.25 + 0.5 * x, 2)])
Rt, t = ring('t', ZZ)
R, x = ring('x', Rt)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
assert (4 * t * x**2 + 4 * t**2 * x).factor_list() == (4 * t, [(x, 1),
(x + t, 1)])
Rt, t = ring('t', QQ)
R, x = ring('x', Rt)
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
assert (t * x**2 / 2 + t**2 * x / 2).factor_list() == (t / 2, [(x, 1),
(x + t, 1)])
R, x = ring('x', EX)
pytest.raises(DomainError, lambda: R(EX(sin(1))).factor_list())
R, x, y = ring('x y', FF(2))
pytest.raises(NotImplementedError, lambda: (x**2 + y**2).factor_list())
R, x, y = ring('x y', ZZ)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
assert (x**2 + 2 * x + 1).factor_list() == (1, [(x + 1, 2)])
assert (4 * x**2 * y + 4 * x * y**2).factor_list() == (4, [(y, 1), (x, 1),
(x + y, 1)])
R, x, y = ring('x y', QQ)
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
assert (x**2 / 2 + x + QQ(1, 2)).factor_list() == (QQ(1, 2), [(x + 1, 2)])
assert (x**2 * y / 2 + x * y**2 / 2).factor_list() == (QQ(1,
2), [(y, 1),
(x, 1),
(x + y, 1)])
R, x, y = ring('x y', QQ.algebraic_field(I))
f, r = x**2 + y**2, (1, [(x - I * y, 1), (x + I * y, 1)])
for method in ('trager', 'modular'):
with using(aa_factor_method=method):
assert f.factor_list() == r
R, x, y = ring('x y', RR)
f = 2.0 * x**2 - 8.0 * y**2
assert f.factor_list() == (2.0, [(1.0 * x - 2.0 * y, 1),
(1.0 * x + 2.0 * y, 1)])
f = 6.7225336055071 * x**2 * y**2 - 10.6463972754741 * x * y - 0.33469524022264
assert f.factor_list() == (1.0, [(f, 1)])
Rt, t = ring('t', ZZ)
R, x, y = ring('x y', Rt)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
assert (4 * t * x**2 + 4 * t**2 * x).factor_list() == (4 * t, [(x, 1),
(x + t, 1)])
Rt, t = ring('t', QQ)
R, x, y = ring('x y', Rt)
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
assert (t * x**2 / 2 + t**2 * x / 2).factor_list() == (t / 2, [(x, 1),
(x + t, 1)])
R, x, y = ring('x y', EX)
pytest.raises(DomainError, lambda: R(EX(sin(1))).factor_list())
# issue diofant/diofant#238
R, x, y, z = ring('x y z', RR)
f = x * y + x * z + 0.1 * y + 0.1 * z
assert f.factor_list() == (10.0, [(x + 0.1, 1), (0.1 * y + 0.1 * z, 1)])
f = 0.25 * x**2 + 1.0 * x * y * z + 1.0 * y**2 * z**2
assert f.factor_list() == (4.0, [(0.25 * x + 0.5 * y * z, 2)])
R, *X = ring('x:200', ZZ)
f, g = X[0]**2 + 2 * X[0] + 1, X[0] + 1
assert f.factor_list() == (1, [(g, 2)])
f, g = X[-1]**2 + 2 * X[-1] + 1, X[-1] + 1
assert f.factor_list() == (1, [(g, 2)])
def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([1, 2, 3],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([Integer(1), Integer(2),
Integer(3)]) == (ZZ, [ZZ(1), ZZ(2),
ZZ(3)])
assert construct_domain(
[Integer(1), Integer(2), Integer(3)],
field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([Rational(1, 2),
Integer(2)]) == (QQ, [QQ(1, 2), QQ(2)])
assert construct_domain([3.14, 1, Rational(1, 2)
]) == (RR, [RR(3.14), RR(1.0),
RR(0.5)])
assert construct_domain([3.14, sqrt(2)],
extension=False) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)]) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain([sqrt(2), 3.14]) == (EX, [EX(sqrt(2)), EX(3.14)])
assert construct_domain([1, sqrt(2)],
extension=False) == (EX, [EX(1),
EX(sqrt(2))])
assert construct_domain([x, sqrt(x)]) == (EX, [EX(x), EX(sqrt(x))])
assert construct_domain([x, sqrt(x), sqrt(y)
]) == (EX, [EX(x),
EX(sqrt(x)),
EX(sqrt(y))])
alg = QQ.algebraic_field(sqrt(2))
assert (construct_domain(
[7, Rational(1, 2),
sqrt(2)]) == (alg, [alg([7]),
alg([Rational(1, 2)]),
alg([1, 0])]))
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert (construct_domain([7, sqrt(2), sqrt(3)]) == (alg, [
alg([7]), alg.from_expr(sqrt(2)),
alg.from_expr(sqrt(3))
]))
dom = ZZ.inject(x)
assert construct_domain([2 * x, 3]) == (dom, [dom(2 * x), dom(3)])
dom = ZZ.inject(x, y)
assert construct_domain([2 * x, 3 * y]) == (dom, [dom(2 * x), dom(3 * y)])
dom = QQ.inject(x)
assert construct_domain([x / 2, 3]) == (dom, [dom(x / 2), dom(3)])
dom = QQ.inject(x, y)
assert construct_domain([x / 2, 3 * y]) == (dom, [dom(x / 2), dom(3 * y)])
dom = RR.inject(x)
assert construct_domain([x / 2, 3.5]) == (dom, [dom(x / 2), dom(3.5)])
dom = RR.inject(x, y)
assert construct_domain([x / 2,
3.5 * y]) == (dom, [dom(x / 2),
dom(3.5 * y)])
dom = ZZ.inject(x).field
assert construct_domain([2 / x, 3]) == (dom, [dom(2 / x), dom(3)])
dom = ZZ.inject(x, y).field
assert construct_domain([2 / x, 3 * y]) == (dom, [dom(2 / x), dom(3 * y)])
dom = RR.inject(x).field
assert construct_domain([2 / x, 3.5]) == (dom, [dom(2 / x), dom(3.5)])
dom = RR.inject(x, y).field
assert construct_domain([2 / x,
3.5 * y]) == (dom, [dom(2 / x),
dom(3.5 * y)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(Rational(2, 3)) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
assert construct_domain([-x * y + x * (y + 42) - 42 * x
]) == (EX, [EX(-x * y + x * (y + 42) - 42 * x)])
def test_sympyissue_11538():
assert construct_domain(E)[0] == ZZ.inject(E)
assert (construct_domain(x**2 + 2 * x + E) == (ZZ.inject(
x, E), ZZ.inject(x, E)(x**2 + 2 * x + E)))
assert (construct_domain(x + y + GoldenRatio) == (EX,
EX(x + y + GoldenRatio)))
def test_arithmetics():
assert ZZ.rem(ZZ(2), ZZ(3)) == 2
assert ZZ.div(ZZ(2), ZZ(3)) == (0, 2)
assert QQ.rem(QQ(2, 3), QQ(4, 7)) == 0
assert QQ.div(QQ(2, 3), QQ(4, 7)) == (QQ(7, 6), 0)
assert CC.gcd(CC(1), CC(2)) == 1
assert CC.lcm(CC(1), CC(2)) == 2
assert EX(Rational(2, 3)).numerator == 2
assert EX(Rational(2, 3)).denominator == 3
assert abs(EX(-2)) == 2
assert -EX(2) == -2
assert 2 + EX(3) == EX(3) + 2 == 5
assert 2 - EX(3) == EX(2) - 3 == -1
assert 2 * EX(3) == EX(3) * 2 == 6
assert 2 / EX(3) == EX(2) / 3 == EX(Rational(2, 3))
assert EX(2)**2 == 4
pytest.raises(TypeError, lambda: EX(2) + object())
pytest.raises(TypeError, lambda: EX(2) - object())
pytest.raises(TypeError, lambda: EX(2) * object())
pytest.raises(TypeError, lambda: EX(2)**object())
pytest.raises(TypeError, lambda: EX(2) / object())
F11 = FF(11)
assert +F11(2) == F11(2)
assert F11(5) + 7 == 7 + F11(5) == F11(1)
assert F11(5) - 7 == 5 - F11(7) == F11(9)
assert F11(5) * 7 == 7 * F11(5) == F11(2)
assert F11(5) / 9 == 5 / F11(9) == F11(3)
assert F11(4) % 9 == 4 % F11(9) == F11(4)
pytest.raises(TypeError, lambda: F11(2) + object())
pytest.raises(TypeError, lambda: F11(2) - object())
pytest.raises(TypeError, lambda: F11(2) * object())
pytest.raises(TypeError, lambda: F11(2)**object())
pytest.raises(TypeError, lambda: F11(2) / object())
pytest.raises(TypeError, lambda: F11(2) % object())
pytest.raises(TypeError, lambda: object() % F11(2))
def test_EX():
assert EX.is_normal(EX(2)) is True
assert EX.is_normal(EX(-1)) is False
assert (EX(1) / 2).numerator == 1
assert (EX(1) / 2).denominator == 2