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_almosteq():
assert CC.almosteq(CC(2), 3) is False
assert CC.almosteq(2, CC(3)) is False
assert CC.almosteq(2, CC(2.5), 0.1) is False
assert CC.almosteq(2, CC(2.5), 1.0) is True
assert RR.almosteq(5, RR(2), 1) is True
assert RR._context.almosteq(RR(2), 1, None, 1) is True
def test_PolyElement():
Ruv, u, v = ring('u v', ZZ)
_, x, y, _ = ring('x y z', Ruv)
assert str(x - x) == '0'
assert str(x - 1) == 'x - 1'
assert str(x + 1) == 'x + 1'
assert str((u**2 + 3 * u * v + 1) * x**2 * y + u +
1) == '(u**2 + 3*u*v + 1)*x**2*y + u + 1'
assert str((u**2 + 3 * u * v + 1) * x**2 * y +
(u + 1) * x) == '(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x'
assert str((u**2 + 3 * u * v + 1) * x**2 * y + (u + 1) * x +
1) == '(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1'
assert str((-u**2 + 3 * u * v - 1) * x**2 * y - (u + 1) * x -
1) == '-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1'
assert str(-(v**2 + v + 1) * x + 3 * u * v +
1) == '-(v**2 + v + 1)*x + 3*u*v + 1'
assert str(-(v**2 + v + 1) * x - 3 * u * v +
1) == '-(v**2 + v + 1)*x - 3*u*v + 1'
K, t = field('t', ZZ)
_, x = ring('x', K)
assert str(x / t) == '1/t*x'
assert str(CC.inject(w).convert(I)) == '(0.0 + 1.0j)'
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)
pytest.raises(CoercionFailed, lambda: ALG2.convert(CC(1j)))
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_Domain_get_exact():
assert EX.get_exact() == EX
assert ZZ.get_exact() == ZZ
assert QQ.get_exact() == QQ
assert RR.get_exact() == QQ
assert CC.get_exact() == QQ.algebraic_field(I)
assert ALG.get_exact() == ALG
assert ZZ.inject(x).get_exact() == ZZ.inject(x)
assert QQ.inject(x).get_exact() == QQ.inject(x)
assert ZZ.inject(x, y).get_exact() == ZZ.inject(x, y)
assert QQ.inject(x, y).get_exact() == QQ.inject(x, y)
assert ZZ.inject(x).field.get_exact() == ZZ.inject(x).field
assert QQ.inject(x).field.get_exact() == QQ.inject(x).field
assert ZZ.inject(x, y).field.get_exact() == ZZ.inject(x, y).field
assert QQ.inject(x, y).field.get_exact() == QQ.inject(x, y).field
def test_FracElement_from_expr():
x, y, z = symbols('x y z')
F, X, Y, Z = field((x, y, z), ZZ)
f = F.convert(1)
assert f == 1 and isinstance(f, F.dtype)
f = F.convert(Rational(3, 7))
assert f == F(3) / 7 and isinstance(f, F.dtype)
f = F.convert(x)
assert f == X and isinstance(f, F.dtype)
f = F.convert(Rational(3, 7) * x)
assert f == 3 * X / 7 and isinstance(f, F.dtype)
f = F.convert(1 / x)
assert f == 1 / X and isinstance(f, F.dtype)
f = F.convert(x * y * z)
assert f == X * Y * Z and isinstance(f, F.dtype)
f = F.convert(x * y / z)
assert f == X * Y / Z and isinstance(f, F.dtype)
f = F.convert(x * y * z + x * y + x)
assert f == X * Y * Z + X * Y + X and isinstance(f, F.dtype)
f = F.convert((x * y * z + x * y + x) / (x * y + 7))
assert f == (X * Y * Z + X * Y + X) / (X * Y + 7) and isinstance(
f, F.dtype)
f = F.convert(x**3 * y * z + x**2 * y**7 + 1)
assert f == X**3 * Y * Z + X**2 * Y**7 + 1 and isinstance(f, F.dtype)
pytest.raises(CoercionFailed, lambda: F.convert(2**x))
pytest.raises(CoercionFailed, lambda: F.convert(7 * x + sqrt(2)))
F, X, Y = field((2**x, y), ZZ)
f = F.convert(2**(2 * x) + 1)
assert f == X**2 + 1
# issue sympy/sympy#20985
F, X = field(x, CC)
assert F.convert(I / x) == F.convert(CC(0, 1)) / X
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 QQ.lcm(QQ(2, 3), QQ(4, 9)) == QQ(4, 3)
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_Domain_unify():
F3 = GF(3)
assert unify(F3, F3) == F3
assert unify(F3, ZZ) == F3
assert unify(F3, QQ) == QQ
assert unify(F3, ALG) == ALG
assert unify(F3, RR) == RR
assert unify(F3, CC) == CC
assert unify(F3, ZZ.inject(x)) == F3.inject(x)
assert unify(F3, ZZ.inject(x).field) == F3.inject(x).field
assert unify(F3, EX) == EX
assert unify(ZZ, F3) == F3
assert unify(ZZ, ZZ) == ZZ
assert unify(ZZ, QQ) == QQ
assert unify(ZZ, ALG) == ALG
assert unify(ZZ, RR) == RR
assert unify(ZZ, CC) == CC
assert unify(ZZ, ZZ.inject(x)) == ZZ.inject(x)
assert unify(ZZ, ZZ.inject(x).field) == ZZ.inject(x).field
assert unify(ZZ, EX) == EX
assert unify(QQ, F3) == QQ
assert unify(QQ, ZZ) == QQ
assert unify(QQ, QQ) == QQ
assert unify(QQ, ALG) == ALG
assert unify(QQ, RR) == RR
assert unify(QQ, CC) == CC
assert unify(QQ, ZZ.inject(x)) == QQ.inject(x)
assert unify(QQ, ZZ.inject(x).field) == QQ.inject(x).field
assert unify(QQ, EX) == EX
assert unify(RR, F3) == RR
assert unify(RR, ZZ) == RR
assert unify(RR, QQ) == RR
assert unify(RR, ALG) == RR
assert unify(RR, RR) == RR
assert unify(RR, CC) == CC
assert unify(RR, ZZ.inject(x)) == RR.inject(x)
assert unify(RR, ZZ.inject(x).field) == RR.inject(x).field
assert unify(RR, EX) == EX
assert unify(CC, F3) == CC
assert unify(CC, ZZ) == CC
assert unify(CC, QQ) == CC
assert unify(CC, ALG) == CC
assert unify(CC, RR) == CC
assert unify(CC, CC) == CC
assert unify(CC, ZZ.inject(x)) == CC.inject(x)
assert unify(CC, ZZ.inject(x).field) == CC.inject(x).field
assert unify(CC, EX) == EX
CC2 = ComplexField(prec=20)
assert unify(CC, CC2) == unify(CC2, CC) == ComplexField(prec=CC.precision,
tol=CC2.tolerance)
RR2 = RealField(prec=20)
assert unify(RR, RR2) == unify(RR2, RR) == RealField(prec=RR.precision,
tol=RR2.tolerance)
assert unify(ZZ.inject(x), F3) == F3.inject(x)
assert unify(ZZ.inject(x), ZZ) == ZZ.inject(x)
assert unify(ZZ.inject(x), QQ) == QQ.inject(x)
assert unify(ZZ.inject(x), ALG) == ALG.inject(x)
assert unify(ZZ.inject(x), RR) == RR.inject(x)
assert unify(ZZ.inject(x), CC) == CC.inject(x)
assert unify(ZZ.inject(x), ZZ.inject(x)) == ZZ.inject(x)
assert unify(ZZ.inject(x), ZZ.inject(x).field) == ZZ.inject(x).field
assert unify(ZZ.inject(x), EX) == EX
assert unify(ZZ.inject(x).field, F3) == F3.inject(x).field
assert unify(ZZ.inject(x).field, ZZ) == ZZ.inject(x).field
assert unify(ZZ.inject(x).field, QQ) == QQ.inject(x).field
assert unify(ZZ.inject(x).field, ALG) == ALG.inject(x).field
assert unify(ZZ.inject(x).field, RR) == RR.inject(x).field
assert unify(ZZ.inject(x).field, CC) == CC.inject(x).field
assert unify(ZZ.inject(x).field, ZZ.inject(x)) == ZZ.inject(x).field
assert unify(ZZ.inject(x).field, ZZ.inject(x).field) == ZZ.inject(x).field
assert unify(ZZ.inject(x).field, EX) == EX
assert unify(EX, F3) == EX
assert unify(EX, ZZ) == EX
assert unify(EX, QQ) == EX
assert unify(EX, ALG) == EX
assert unify(EX, RR) == EX
assert unify(EX, CC) == EX
assert unify(EX, ZZ.inject(x)) == EX
assert unify(EX, ZZ.inject(x).field) == EX
assert unify(EX, EX) == EX
def test_to_expr():
assert CC.to_expr(1 - 2j) == 1 - 2 * I
def test_CC_double():
assert CC(3.14).real > 1e-50
assert CC(1e-13).real > 1e-50
assert CC(1e-14).real > 1e-50
assert CC(1e-15).real > 1e-50
assert CC(1e-20).real > 1e-50
assert CC(1e-40).real > 1e-50
assert CC(3.14j).imag > 1e-50
assert CC(1e-13j).imag > 1e-50
assert CC(1e-14j).imag > 1e-50
assert CC(1e-15j).imag > 1e-50
assert CC(1e-20j).imag > 1e-50
assert CC(1e-40j).imag > 1e-50
a = CC(2.1 + 1j)
assert a.numerator == a and a.denominator == 1