def test_PolyElement___sub__():
Rt, t = ring("t", ZZ)
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
assert u - x == -x + u
assert (x + u) - 2*u == x - u
assert dict(x - 3*y) == {(1, 0, 0): 1, (0, 1, 0): -3}
assert dict(-u + x) == dict(x - u) == {(1, 0, 0): 1, (0, 0, 0): -u}
assert dict(-u + x*y) == dict(x*y - u) == {(1, 1, 0): 1, (0, 0, 0): -u}
assert dict(-u + x*y + z) == dict(x*y + z - u) == {(1, 1, 0): 1, (0, 0, 1): 1, (0, 0, 0): -u}
assert dict(-u*x + x) == dict(x - u*x) == {(1, 0, 0): -u + 1}
assert dict(-u*x + x*y) == dict(x*y - u*x) == {(1, 1, 0): 1, (1, 0, 0): -u}
assert dict(-u*x + x*y + z) == dict(x*y + z - u*x) == {(1, 1, 0): 1, (0, 0, 1): 1, (1, 0, 0): -u}
pytest.raises(TypeError, lambda: t - x)
pytest.raises(TypeError, lambda: x - t)
pytest.raises(TypeError, lambda: t - u)
pytest.raises(TypeError, lambda: u - t)
Fuv, u, v = field("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Fuv)
assert dict(-u + x) == dict(x - u) == {(1, 0, 0): 1, (0, 0, 0): -u}
Rxyz, x, y, z = ring("x,y,z", EX)
assert dict(-EX(pi) + x*y*z) == dict(x*y*z - EX(pi)) == {(1, 1, 1): EX(1), (0, 0, 0): -EX(pi)}
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_EX():
assert EX.is_positive(EX(2))
assert EX.is_nonnegative(EX(2))
assert EX.is_negative(EX(-1))
assert EX.is_nonpositive(EX(-1))
assert (EX(1) / 2).numerator == 1
assert (EX(1) / 2).denominator == 2
def test_dmp_lift():
A = QQ.algebraic_field(I)
f = [A(1), A(0), A(0), A(I), A(17*I)]
assert dmp_lift(f, 0, A) == [1, 0, 0, 0, 0, 0, 2, 0, 578, 0, 0, 0,
1, 0, -578, 0, 83521]
pytest.raises(DomainError, lambda: dmp_lift([EX(1), EX(2)], 0, EX))
def test_EX():
assert EX.is_positive(EX(2))
assert EX.is_nonnegative(EX(2))
assert EX.is_negative(EX(-1))
assert EX.is_nonpositive(EX(-1))
assert (EX(1)/2).numerator == 1
assert (EX(1)/2).denominator == 2
def test___eq__():
assert not QQ.poly_ring(x) == ZZ.poly_ring(x)
assert not QQ.frac_field(x) == ZZ.frac_field(x)
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.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_PolyElement___mul__():
Rt, t = ring("t", ZZ)
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
assert dict(u*x) == dict(x*u) == {(1, 0, 0): u}
assert dict(2*u*x + z) == dict(x*2*u + z) == {(1, 0, 0): 2*u, (0, 0, 1): 1}
assert dict(u*2*x + z) == dict(2*x*u + z) == {(1, 0, 0): 2*u, (0, 0, 1): 1}
assert dict(2*u*x + z) == dict(x*2*u + z) == {(1, 0, 0): 2*u, (0, 0, 1): 1}
assert dict(u*x*2 + z) == dict(x*u*2 + z) == {(1, 0, 0): 2*u, (0, 0, 1): 1}
assert dict(2*u*x*y + z) == dict(x*y*2*u + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(u*2*x*y + z) == dict(2*x*y*u + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(2*u*x*y + z) == dict(x*y*2*u + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(u*x*y*2 + z) == dict(x*y*u*2 + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(2*u*y*x + z) == dict(y*x*2*u + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(u*2*y*x + z) == dict(2*y*x*u + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(2*u*y*x + z) == dict(y*x*2*u + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(u*y*x*2 + z) == dict(y*x*u*2 + z) == {(1, 1, 0): 2*u, (0, 0, 1): 1}
assert dict(3*u*(x + y) + z) == dict((x + y)*3*u + z) == {(1, 0, 0): 3*u, (0, 1, 0): 3*u, (0, 0, 1): 1}
pytest.raises(TypeError, lambda: t*x + z)
pytest.raises(TypeError, lambda: x*t + z)
pytest.raises(TypeError, lambda: t*u + z)
pytest.raises(TypeError, lambda: u*t + z)
Fuv, u, v = field("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Fuv)
assert dict(u*x) == dict(x*u) == {(1, 0, 0): u}
Rxyz, x, y, z = ring("x,y,z", EX)
assert dict(EX(pi)*x*y*z) == dict(x*y*z*EX(pi)) == {(1, 1, 1): EX(pi)}
assert (x + 2*y).mul_ground(0) == Rxyz.zero
R, x, y = ring("x,y", ZZ)
p = x + y**2
p1 = p.imul_num(3)
assert p == p1 and p1 == 3*x + 3*y**2
p2 = p.imul_num(0)
assert p == p2 and p2 == R.zero
def test_PolyElement___add__():
Rt, t = ring("t", ZZ)
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
assert dict(+x) == dict(x)
assert dict(x + 3*y) == {(1, 0, 0): 1, (0, 1, 0): 3}
assert dict(u + x) == dict(x + u) == {(1, 0, 0): 1, (0, 0, 0): u}
assert dict(u + x*y) == dict(x*y + u) == {(1, 1, 0): 1, (0, 0, 0): u}
assert dict(u + x*y + z) == dict(x*y + z + u) == {(1, 1, 0): 1, (0, 0, 1): 1, (0, 0, 0): u}
assert dict(u*x + x) == dict(x + u*x) == {(1, 0, 0): u + 1}
assert dict(u*x + x*y) == dict(x*y + u*x) == {(1, 1, 0): 1, (1, 0, 0): u}
assert dict(u*x + x*y + z) == dict(x*y + z + u*x) == {(1, 1, 0): 1, (0, 0, 1): 1, (1, 0, 0): u}
pytest.raises(TypeError, lambda: t + x)
pytest.raises(TypeError, lambda: x + t)
pytest.raises(TypeError, lambda: t + u)
pytest.raises(TypeError, lambda: u + t)
Fuv, u, v = field("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Fuv)
assert u + (x - u) == x
assert dict(u + x) == dict(x + u) == {(1, 0, 0): 1, (0, 0, 0): u}
Rxyz, x, y, z = ring("x,y,z", EX)
assert dict(EX(pi) + x*y*z) == dict(x*y*z + EX(pi)) == {(1, 1, 1): EX(1), (0, 0, 0): EX(pi)}
R, x, y = ring('x, y', ZZ)
p = x**4 + 2*y
m = (1, 2)
p1 = p._iadd_monom((m, 5))
assert p == p1 and p1 == x**4 + 5*x*y**2 + 2*y
p2 = p._iadd_monom(((0, 1), 2))
assert p == p2 and p2 == x**4 + 5*x*y**2 + 4*y
p3 = p._iadd_monom(((0, 1), -4))
assert p == p3 and p3 == x**4 + 5*x*y**2
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 ALG.get_exact() == ALG
assert ZZ.poly_ring(x).get_exact() == ZZ.poly_ring(x)
assert QQ.poly_ring(x).get_exact() == QQ.poly_ring(x)
assert ZZ.poly_ring(x, y).get_exact() == ZZ.poly_ring(x, y)
assert QQ.poly_ring(x, y).get_exact() == QQ.poly_ring(x, y)
assert ZZ.frac_field(x).get_exact() == ZZ.frac_field(x)
assert QQ.frac_field(x).get_exact() == QQ.frac_field(x)
assert ZZ.frac_field(x, y).get_exact() == ZZ.frac_field(x, y)
assert QQ.frac_field(x, y).get_exact() == QQ.frac_field(x, y)
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 ALG.get_exact() == ALG
assert ZZ.poly_ring(x).get_exact() == ZZ.poly_ring(x)
assert QQ.poly_ring(x).get_exact() == QQ.poly_ring(x)
assert ZZ.poly_ring(x, y).get_exact() == ZZ.poly_ring(x, y)
assert QQ.poly_ring(x, y).get_exact() == QQ.poly_ring(x, y)
assert ZZ.frac_field(x).get_exact() == ZZ.frac_field(x)
assert QQ.frac_field(x).get_exact() == QQ.frac_field(x)
assert ZZ.frac_field(x, y).get_exact() == ZZ.frac_field(x, y)
assert QQ.frac_field(x, y).get_exact() == QQ.frac_field(x, 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.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_sympyissue_11538():
assert construct_domain(E)[0] == ZZ.poly_ring(E)
assert (construct_domain(x**2 + 2 * x + E) == (ZZ.poly_ring(
x, E), ZZ.poly_ring(x, E)(x**2 + 2 * x + E)))
assert (construct_domain(x + y + GoldenRatio) == (EX,
EX(x + y + GoldenRatio)))
def test_dmp_factor_list():
R, x, y = ring("x,y", ZZ)
assert R.dmp_factor_list(0) == (ZZ(0), [])
assert R.dmp_factor_list(7) == (7, [])
R, x, y = ring("x,y", QQ)
assert R.dmp_factor_list(0) == (QQ(0), [])
assert R.dmp_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
Rt, t = ring("t", ZZ)
R, x, y = ring("x,y", Rt)
assert R.dmp_factor_list(0) == (0, [])
assert R.dmp_factor_list(7) == (ZZ(7), [])
Rt, t = ring("t", QQ)
R, x, y = ring("x,y", Rt)
assert R.dmp_factor_list(0) == (0, [])
assert R.dmp_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
R, x, y = ring("x,y", ZZ)
assert R.dmp_factor_list_include(0) == [(0, 1)]
assert R.dmp_factor_list_include(7) == [(7, 1)]
R, *X = ring("x:200", ZZ)
f, g = X[0]**2 + 2 * X[0] + 1, X[0] + 1
assert R.dmp_factor_list(f) == (1, [(g, 2)])
f, g = X[-1]**2 + 2 * X[-1] + 1, X[-1] + 1
assert R.dmp_factor_list(f) == (1, [(g, 2)])
R, x = ring("x", ZZ)
assert R.dmp_factor_list(x**2 + 2 * x + 1) == (1, [(x + 1, 2)])
R, x = ring("x", QQ)
assert R.dmp_factor_list(x**2 / 2 + x + QQ(1, 2)) == (QQ(1,
2), [(x + 1, 2)])
R, x, y = ring("x,y", ZZ)
assert R.dmp_factor_list(x**2 + 2 * x + 1) == (1, [(x + 1, 2)])
R, x, y = ring("x,y", QQ)
assert R.dmp_factor_list(x**2 / 2 + x + QQ(1, 2)) == (QQ(1,
2), [(x + 1, 2)])
R, x, y = ring("x,y", ZZ)
f = 4 * x**2 * y + 4 * x * y**2
assert R.dmp_factor_list(f) == \
(4, [(y, 1),
(x, 1),
(x + y, 1)])
assert R.dmp_factor_list_include(f) == \
[(4*y, 1),
(x, 1),
(x + y, 1)]
R, x, y = ring("x,y", QQ)
f = x**2 * y / 2 + x * y**2 / 2
assert R.dmp_factor_list(f) == \
(QQ(1, 2), [(y, 1),
(x, 1),
(x + y, 1)])
R, x, y = ring("x,y", RR)
f = 2.0 * x**2 - 8.0 * y**2
assert R.dmp_factor_list(f) == \
(RR(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
coeff, factors = R.dmp_factor_list(f)
assert coeff == RR(1.0) and len(factors) == 1 and factors[0][0].almosteq(
f, 1e-10) and factors[0][1] == 1
# 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 R.dmp_factor_list(f) == (10.0, [(0.1 * y + 0.1 * z, 1),
(x + 0.1, 1)])
f = 0.25 * x**2 + 1.0 * x * y * z + 1.0 * y**2 * z**2
assert R.dmp_factor_list(f) == (4.0, [(0.25 * x + 0.5 * y * z, 2)])
Rt, t = ring("t", ZZ)
R, x, y = ring("x,y", Rt)
f = 4 * t * x**2 + 4 * t**2 * x
assert R.dmp_factor_list(f) == \
(4*t, [(x, 1),
(x + t, 1)])
Rt, t = ring("t", QQ)
R, x, y = ring("x,y", Rt)
f = t * x**2 / 2 + t**2 * x / 2
assert R.dmp_factor_list(f) == (t / 2, [(x, 1), (x + t, 1)])
R, x, y = ring("x,y", FF(2))
pytest.raises(NotImplementedError, lambda: R.dmp_factor_list(x**2 + y**2))
R, x, y = ring("x,y", EX)
pytest.raises(DomainError, lambda: R.dmp_factor_list(EX(sin(1))))
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=None) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)],
extension=True) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([sqrt(2), 3.14],
extension=True) == (EX, [EX(sqrt(2)),
EX(3.14)])
assert construct_domain([1, sqrt(2)],
extension=None) == (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)],
extension=True) == (alg, [alg(7),
alg(Rational(1, 2)),
alg(sqrt(2))]))
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert (construct_domain([7, sqrt(2), sqrt(3)], extension=True) == (alg, [
alg(7), alg(sqrt(2)), alg(sqrt(3))
]))
dom = ZZ.poly_ring(x)
assert construct_domain([2 * x, 3]) == (dom, [dom(2 * x), dom(3)])
dom = ZZ.poly_ring(x, y)
assert construct_domain([2 * x, 3 * y]) == (dom, [dom(2 * x), dom(3 * y)])
dom = QQ.poly_ring(x)
assert construct_domain([x / 2, 3]) == (dom, [dom(x / 2), dom(3)])
dom = QQ.poly_ring(x, y)
assert construct_domain([x / 2, 3 * y]) == (dom, [dom(x / 2), dom(3 * y)])
dom = RR.poly_ring(x)
assert construct_domain([x / 2, 3.5]) == (dom, [dom(x / 2), dom(3.5)])
dom = RR.poly_ring(x, y)
assert construct_domain([x / 2,
3.5 * y]) == (dom, [dom(x / 2),
dom(3.5 * y)])
dom = ZZ.frac_field(x)
assert construct_domain([2 / x, 3]) == (dom, [dom(2 / x), dom(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2 / x, 3 * y]) == (dom, [dom(2 / x), dom(3 * y)])
dom = RR.frac_field(x)
assert construct_domain([2 / x, 3.5]) == (dom, [dom(2 / x), dom(3.5)])
dom = RR.frac_field(x, y)
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, {})
def test_dmp_clear_denoms():
assert dmp_clear_denoms([[]], 1, QQ, ZZ) == (ZZ(1), [[]])
assert dmp_clear_denoms([[QQ(1)]], 1, QQ, ZZ) == (ZZ(1), [[QQ(1)]])
assert dmp_clear_denoms([[QQ(7)]], 1, QQ, ZZ) == (ZZ(1), [[QQ(7)]])
assert dmp_clear_denoms([[QQ(7, 3)]], 1, QQ) == (ZZ(3), [[QQ(7)]])
assert dmp_clear_denoms([[QQ(7, 3)]], 1, QQ, ZZ) == (ZZ(3), [[QQ(7)]])
assert dmp_clear_denoms(
[[QQ(3)], [QQ(1)], []], 1, QQ, ZZ) == (ZZ(1), [[QQ(3)], [QQ(1)], []])
assert dmp_clear_denoms([[QQ(
1)], [QQ(1, 2)], []], 1, QQ, ZZ) == (ZZ(2), [[QQ(2)], [QQ(1)], []])
assert dmp_clear_denoms([QQ(3), QQ(
1), QQ(0)], 0, QQ, ZZ, convert=True) == (ZZ(1), [ZZ(3), ZZ(1), ZZ(0)])
assert dmp_clear_denoms([QQ(1), QQ(1, 2), QQ(
0)], 0, QQ, ZZ, convert=True) == (ZZ(2), [ZZ(2), ZZ(1), ZZ(0)])
assert dmp_clear_denoms([[QQ(3)], [QQ(
1)], []], 1, QQ, ZZ, convert=True) == (ZZ(1), [[QQ(3)], [QQ(1)], []])
assert dmp_clear_denoms([[QQ(1)], [QQ(1, 2)], []], 1, QQ, ZZ,
convert=True) == (ZZ(2), [[QQ(2)], [QQ(1)], []])
assert dmp_clear_denoms(
[[EX(Rational(3, 2))], [EX(Rational(9, 4))]], 1, EX) == (EX(4), [[EX(6)], [EX(9)]])
assert dmp_clear_denoms([[EX(7)]], 1, EX) == (EX(1), [[EX(7)]])
assert dmp_clear_denoms([[EX(sin(x)/x), EX(0)]], 1, EX) == (EX(x), [[EX(sin(x)), EX(0)]])
def test_dmp_factor_list():
R, x = ring("x", ZZ)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
R, x = ring("x", QQ)
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
R, x = ring("x", ZZ.poly_ring('t'))
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
R, x = ring("x", QQ.poly_ring('t'))
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
R, x = ring("x", ZZ)
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 (x**2 / 2 + x + QQ(1, 2)).factor_list() == (QQ(1, 2), [(x + 1, 2)])
R, x = ring("x", FF(2))
assert (x**2 + 1).factor_list() == (1, [(x + 1, 2)])
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
coeff, factors = f.factor_list()
assert coeff == 1.0 and len(factors) == 1 and factors[0][0].almosteq(
f, 1e-10) and factors[0][1] == 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)
f = 4 * t * x**2 + 4 * t**2 * x
assert f.factor_list() == (4 * t, [(x, 1), (x + t, 1)])
Rt, t = ring("t", QQ)
R, x = ring("x", Rt)
f = t * x**2 / 2 + t**2 * x / 2
assert f.factor_list() == (t / 2, [(x, 1), (x + t, 1)])
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", EX)
pytest.raises(DomainError, lambda: R(EX(sin(1))).factor_list())
R, x, y = ring("x,y", ZZ)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
R, x, y = ring("x,y", QQ)
assert R(0).factor_list() == (0, [])
assert R(QQ(1, 7)).factor_list() == (QQ(1, 7), [])
Rt, t = ring("t", ZZ)
R, x, y = ring("x,y", Rt)
assert R(0).factor_list() == (0, [])
assert R(7).factor_list() == (7, [])
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), [])
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)])
R, x = ring("x", ZZ)
assert (x**2 + 2 * x + 1).factor_list() == (1, [(x + 1, 2)])
R, x = ring("x", QQ)
assert (x**2 / 2 + x + QQ(1, 2)).factor_list() == (QQ(1, 2), [(x + 1, 2)])
R, x, y = ring("x,y", ZZ)
assert (x**2 + 2 * x + 1).factor_list() == (1, [(x + 1, 2)])
R, x, y = ring("x,y", QQ)
assert (x**2 / 2 + x + QQ(1, 2)).factor_list() == (QQ(1, 2), [(x + 1, 2)])
R, x, y = ring("x,y", ZZ)
f = 4 * x**2 * y + 4 * x * y**2
assert f.factor_list() == (4, [(y, 1), (x, 1), (x + y, 1)])
R, x, y = ring("x,y", QQ)
f = x**2 * y / 2 + x * y**2 / 2
assert f.factor_list() == (QQ(1, 2), [(y, 1), (x, 1), (x + y, 1)])
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
coeff, factors = f.factor_list()
assert coeff == 1.0 and len(factors) == 1 and factors[0][0].almosteq(
f, 1e-10) and factors[0][1] == 1
# 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, [(0.1 * y + 0.1 * z, 1), (x + 0.1, 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)])
Rt, t = ring("t", ZZ)
R, x, y = ring("x,y", Rt)
f = 4 * t * x**2 + 4 * t**2 * x
assert f.factor_list() == (4 * t, [(x, 1), (x + t, 1)])
Rt, t = ring("t", QQ)
R, x, y = ring("x,y", Rt)
f = t * x**2 / 2 + t**2 * x / 2
assert f.factor_list() == (t / 2, [(x, 1), (x + t, 1)])
R, x, y = ring("x,y", FF(2))
pytest.raises(NotImplementedError, lambda: (x**2 + y**2).factor_list())
R, x, y = ring("x,y", EX)
pytest.raises(DomainError, lambda: R(EX(sin(1))).factor_list())
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)])
assert R.dmp_factor_list(f) == r
with config.using(aa_factor_method='trager'):
assert R.dmp_factor_list(f) == r
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_dup_factor_list():
R, x = ring("x", ZZ)
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(7) == (7, [])
R, x = ring("x", QQ)
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
R, x = ring("x", ZZ.poly_ring('t'))
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(7) == (7, [])
R, x = ring("x", QQ.poly_ring('t'))
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
R, x = ring("x", ZZ)
assert R.dup_factor_list_include(0) == [(0, 1)]
assert R.dup_factor_list_include(7) == [(7, 1)]
assert R.dup_factor_list(x**2 + 2 * x + 1) == (1, [(x + 1, 2)])
assert R.dup_factor_list_include(x**2 + 2 * x + 1) == [(x + 1, 2)]
# issue sympy/sympy#8037
assert R.dup_factor_list(6 * x**2 - 5 * x - 6) == (1, [(2 * x - 3, 1),
(3 * x + 2, 1)])
R, x = ring("x", QQ)
assert R.dup_factor_list(x**2 / 2 + x + QQ(1, 2)) == (QQ(1,
2), [(x + 1, 2)])
R, x = ring("x", FF(2))
assert R.dup_factor_list(x**2 + 1) == (1, [(x + 1, 2)])
R, x = ring("x", RR)
assert R.dup_factor_list(1.0 * x**2 + 2.0 * x + 1.0) == (1.0, [
(1.0 * x + 1.0, 2)
])
assert R.dup_factor_list(2.0 * x**2 + 4.0 * x + 2.0) == (2.0, [
(1.0 * x + 1.0, 2)
])
f = 6.7225336055071 * x**2 - 10.6463972754741 * x - 0.33469524022264
coeff, factors = R.dup_factor_list(f)
assert coeff == RR(1.0) and len(factors) == 1 and factors[0][0].almosteq(
f, 1e-10) and factors[0][1] == 1
# issue diofant/diofant#238
f = 0.1 * x**2 + 1.1 * x + 1.0
assert R.dup_factor_list(f) == (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 R.dup_factor_list(f) == (4.0, [(0.25 + 0.5 * x, 2)])
Rt, t = ring("t", ZZ)
R, x = ring("x", Rt)
f = 4 * t * x**2 + 4 * t**2 * x
assert R.dup_factor_list(f) == \
(4*t, [(x, 1),
(x + t, 1)])
Rt, t = ring("t", QQ)
R, x = ring("x", Rt)
f = t * x**2 / 2 + t**2 * x / 2
assert R.dup_factor_list(f) == (t / 2, [(x, 1), (x + t, 1)])
R, x = ring("x", QQ.algebraic_field(I))
f = x**4 + 2 * x**2
assert R.dup_factor_list(f) == (R.domain(1), [(x, 2), (x**2 + 2, 1)])
R, x = ring("x", EX)
pytest.raises(DomainError, lambda: R.dup_factor_list(EX(sin(1))))