def test_convert():
F3 = FF(3)
F3_gmpy = FF_gmpy(3)
F3_python = FF_python(3)
assert F3.convert(gmpy.mpz(2)) == F3.dtype(2)
assert F3.convert(gmpy.mpq(2, 1)) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(gmpy.mpq(1, 2)))
assert ZZ_gmpy.convert(F3_python(1)) == ZZ_gmpy.dtype(1)
assert ZZ_gmpy.convert(F3_gmpy(1)) == ZZ_gmpy.dtype(1)
assert ZZ_gmpy.convert(PythonRational(2)) == ZZ_gmpy.dtype(2)
pytest.raises(CoercionFailed,
lambda: ZZ_gmpy.convert(PythonRational(2, 3)))
assert QQ_python.convert(gmpy.mpz(3)) == QQ_python.dtype(3)
assert QQ_python.convert(gmpy.mpq(2, 3)) == QQ_python.dtype(2, 3)
assert QQ_gmpy.convert(PythonRational(2, 3)) == QQ_gmpy.dtype(2, 3)
assert ZZ_python.convert(F3_gmpy(1)) == ZZ_python.dtype(1)
assert ZZ_python.convert(gmpy.mpz(3)) == ZZ_python.dtype(3)
assert ZZ_python.convert(gmpy.mpq(3, 1)) == ZZ_python.dtype(3)
pytest.raises(CoercionFailed, lambda: ZZ_python.convert(gmpy.mpq(3, 2)))
assert CC.convert(gmpy.mpz(3)) == CC(3)
assert CC.convert(gmpy.mpq(1, 2)) == CC(0.5)
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_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_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_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_python.factorial(QQ_python(7, 2)) == 6
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_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.new(1), ALG) == QQ(1)
pytest.raises(CoercionFailed, lambda: QQ.convert(ALG.new([1, 1]), ALG))
assert ZZ.convert(ALG.new(1), ALG) == ZZ(1)
pytest.raises(CoercionFailed, lambda: ZZ.convert(ALG.new([1, 1]), ALG))
assert EX.convert(ALG.new([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.to_dense() == [QQ(1, 2), 0, -QQ(9, 2), 0]
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_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.to_dense() == [QQ(1, 2), 0, -QQ(9, 2), 0]
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_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_python.factorial(QQ_python(7, 2)) == 6
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.poly_ring(x)) == F3.poly_ring(x)
assert unify(F3, ZZ.frac_field(x)) == F3.frac_field(x)
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.poly_ring(x)) == ZZ.poly_ring(x)
assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x)
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.poly_ring(x)) == QQ.poly_ring(x)
assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x)
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.poly_ring(x)) == RR.poly_ring(x)
assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x)
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.poly_ring(x)) == CC.poly_ring(x)
assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x)
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.poly_ring(x), F3) == F3.poly_ring(x)
assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x)
assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x)
assert unify(ZZ.poly_ring(x), ALG) == ALG.poly_ring(x)
assert unify(ZZ.poly_ring(x), RR) == RR.poly_ring(x)
assert unify(ZZ.poly_ring(x), CC) == CC.poly_ring(x)
assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x)
assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.poly_ring(x), EX) == EX
assert unify(ZZ.frac_field(x), F3) == F3.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x)
assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x)
assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), 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.poly_ring(x)) == EX
assert unify(EX, ZZ.frac_field(x)) == 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
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.poly_ring(x)) == F3.poly_ring(x)
assert unify(F3, ZZ.frac_field(x)) == F3.frac_field(x)
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.poly_ring(x)) == ZZ.poly_ring(x)
assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x)
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.poly_ring(x)) == QQ.poly_ring(x)
assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x)
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.poly_ring(x)) == RR.poly_ring(x)
assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x)
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.poly_ring(x)) == CC.poly_ring(x)
assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x)
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.poly_ring(x), F3) == F3.poly_ring(x)
assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x)
assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x)
assert unify(ZZ.poly_ring(x), ALG) == ALG.poly_ring(x)
assert unify(ZZ.poly_ring(x), RR) == RR.poly_ring(x)
assert unify(ZZ.poly_ring(x), CC) == CC.poly_ring(x)
assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x)
assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.poly_ring(x), EX) == EX
assert unify(ZZ.frac_field(x), F3) == F3.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x)
assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x)
assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), 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.poly_ring(x)) == EX
assert unify(EX, ZZ.frac_field(x)) == EX
assert unify(EX, EX) == EX
def test_to_expr():
assert CC.to_expr(1 - 2j) == 1 - 2*I