AndroidRemoteController/python/py/Lib/site-packages/sympy/plotting/tests/test_series.py

from sympy import (
    latex, exp, symbols, I, pi, sin, cos, tan, log, sqrt,
    re, im, arg, frac, Sum, S, Abs, lambdify,
    Function, dsolve, Eq, floor, Tuple
)
from sympy.external import import_module
from sympy.plotting.series import (
    LineOver1DRangeSeries, Parametric2DLineSeries, Parametric3DLineSeries,
    SurfaceOver2DRangeSeries, ContourSeries, ParametricSurfaceSeries,
    ImplicitSeries, _set_discretization_points, List2DSeries
)
from sympy.testing.pytest import raises, warns, XFAIL, skip, ignore_warnings

np = import_module('numpy')


def test_adaptive():
    # verify that adaptive-related keywords produces the expected results
    if not np:
        skip("numpy not installed.")

    x, y = symbols("x, y")

    s1 = LineOver1DRangeSeries(sin(x), (x, -10, 10), "", adaptive=True,
        depth=2)
    x1, _ = s1.get_data()
    s2 = LineOver1DRangeSeries(sin(x), (x, -10, 10), "", adaptive=True,
        depth=5)
    x2, _ = s2.get_data()
    s3 = LineOver1DRangeSeries(sin(x), (x, -10, 10), "", adaptive=True)
    x3, _ = s3.get_data()
    assert len(x1) < len(x2) < len(x3)

    s1 = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=True, depth=2)
    x1, _, _, = s1.get_data()
    s2 = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=True, depth=5)
    x2, _, _ = s2.get_data()
    s3 = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=True)
    x3, _, _ = s3.get_data()
    assert len(x1) < len(x2) < len(x3)


def test_detect_poles():
    if not np:
        skip("numpy not installed.")

    x, u = symbols("x, u")

    s1 = LineOver1DRangeSeries(tan(x), (x, -pi, pi),
        adaptive=False, n=1000, detect_poles=False)
    xx1, yy1 = s1.get_data()
    s2 = LineOver1DRangeSeries(tan(x), (x, -pi, pi),
        adaptive=False, n=1000, detect_poles=True, eps=0.01)
    xx2, yy2 = s2.get_data()
    # eps is too small: doesn't detect any poles
    s3 = LineOver1DRangeSeries(tan(x), (x, -pi, pi),
        adaptive=False, n=1000, detect_poles=True, eps=1e-06)
    xx3, yy3 = s3.get_data()
    s4 = LineOver1DRangeSeries(tan(x), (x, -pi, pi),
        adaptive=False, n=1000, detect_poles="symbolic")
    xx4, yy4 = s4.get_data()

    assert np.allclose(xx1, xx2) and np.allclose(xx1, xx3) and np.allclose(xx1, xx4)
    assert not np.any(np.isnan(yy1))
    assert not np.any(np.isnan(yy3))
    assert np.any(np.isnan(yy2))
    assert np.any(np.isnan(yy4))
    assert len(s2.poles_locations) == len(s3.poles_locations) == 0
    assert len(s4.poles_locations) == 2
    assert np.allclose(np.abs(s4.poles_locations), np.pi / 2)

    with warns(
            UserWarning,
            match="NumPy is unable to evaluate with complex numbers some of",
            test_stacklevel=False,
        ):
        s1 = LineOver1DRangeSeries(frac(x), (x, -10, 10),
            adaptive=False, n=1000, detect_poles=False)
        s2 = LineOver1DRangeSeries(frac(x), (x, -10, 10),
            adaptive=False, n=1000, detect_poles=True, eps=0.05)
        s3 = LineOver1DRangeSeries(frac(x), (x, -10, 10),
            adaptive=False, n=1000, detect_poles="symbolic")
        xx1, yy1 = s1.get_data()
        xx2, yy2 = s2.get_data()
        xx3, yy3 = s3.get_data()
        assert np.allclose(xx1, xx2) and np.allclose(xx1, xx3)
        assert not np.any(np.isnan(yy1))
        assert np.any(np.isnan(yy2)) and np.any(np.isnan(yy2))
        assert not np.allclose(yy1, yy2, equal_nan=True)
        # The poles below are actually step discontinuities.
        assert len(s3.poles_locations) == 21

    s1 = LineOver1DRangeSeries(tan(u * x), (x, -pi, pi), params={u: 1},
        adaptive=False, n=1000, detect_poles=False)
    xx1, yy1 = s1.get_data()
    s2 = LineOver1DRangeSeries(tan(u * x), (x, -pi, pi), params={u: 1},
        adaptive=False, n=1000, detect_poles=True, eps=0.01)
    xx2, yy2 = s2.get_data()
    # eps is too small: doesn't detect any poles
    s3 = LineOver1DRangeSeries(tan(u * x), (x, -pi, pi), params={u: 1},
        adaptive=False, n=1000, detect_poles=True, eps=1e-06)
    xx3, yy3 = s3.get_data()
    s4 = LineOver1DRangeSeries(tan(u * x), (x, -pi, pi), params={u: 1},
        adaptive=False, n=1000, detect_poles="symbolic")
    xx4, yy4 = s4.get_data()

    assert np.allclose(xx1, xx2) and np.allclose(xx1, xx3) and np.allclose(xx1, xx4)
    assert not np.any(np.isnan(yy1))
    assert not np.any(np.isnan(yy3))
    assert np.any(np.isnan(yy2))
    assert np.any(np.isnan(yy4))
    assert len(s2.poles_locations) == len(s3.poles_locations) == 0
    assert len(s4.poles_locations) == 2
    assert np.allclose(np.abs(s4.poles_locations), np.pi / 2)

    with warns(
            UserWarning,
            match="NumPy is unable to evaluate with complex numbers some of",
            test_stacklevel=False,
        ):
        u, v = symbols("u, v", real=True)
        n = S(1) / 3
        f = (u + I * v)**n
        r, i = re(f), im(f)
        s1 = Parametric2DLineSeries(r.subs(u, -2), i.subs(u, -2), (v, -2, 2),
            adaptive=False, n=1000, detect_poles=False)
        s2 = Parametric2DLineSeries(r.subs(u, -2), i.subs(u, -2), (v, -2, 2),
            adaptive=False, n=1000, detect_poles=True)
    with ignore_warnings(RuntimeWarning):
        xx1, yy1, pp1 = s1.get_data()
        assert not np.isnan(yy1).any()
        xx2, yy2, pp2 = s2.get_data()
        assert np.isnan(yy2).any()

    with warns(
            UserWarning,
            match="NumPy is unable to evaluate with complex numbers some of",
            test_stacklevel=False,
        ):
        f = (x * u + x * I * v)**n
        r, i = re(f), im(f)
        s1 = Parametric2DLineSeries(r.subs(u, -2), i.subs(u, -2),
            (v, -2, 2), params={x: 1},
            adaptive=False, n1=1000, detect_poles=False)
        s2 = Parametric2DLineSeries(r.subs(u, -2), i.subs(u, -2),
            (v, -2, 2), params={x: 1},
            adaptive=False, n1=1000, detect_poles=True)
    with ignore_warnings(RuntimeWarning):
        xx1, yy1, pp1 = s1.get_data()
        assert not np.isnan(yy1).any()
        xx2, yy2, pp2 = s2.get_data()
        assert np.isnan(yy2).any()


def test_number_discretization_points():
    # verify that the different ways to set the number of discretization
    # points are consistent with each other.
    if not np:
        skip("numpy not installed.")

    x, y, z = symbols("x:z")

    for pt in [LineOver1DRangeSeries, Parametric2DLineSeries,
        Parametric3DLineSeries]:
        kw1 = _set_discretization_points({"n": 10}, pt)
        kw2 = _set_discretization_points({"n": [10, 20, 30]}, pt)
        kw3 = _set_discretization_points({"n1": 10}, pt)
        assert all(("n1" in kw) and kw["n1"] == 10 for kw in [kw1, kw2, kw3])

    for pt in [SurfaceOver2DRangeSeries, ContourSeries, ParametricSurfaceSeries,
        ImplicitSeries]:
        kw1 = _set_discretization_points({"n": 10}, pt)
        kw2 = _set_discretization_points({"n": [10, 20, 30]}, pt)
        kw3 = _set_discretization_points({"n1": 10, "n2": 20}, pt)
        assert kw1["n1"] == kw1["n2"] == 10
        assert all((kw["n1"] == 10) and (kw["n2"] == 20) for kw in [kw2, kw3])

    # verify that line-related series can deal with large float number of
    # discretization points
    LineOver1DRangeSeries(cos(x), (x, -5, 5), adaptive=False, n=1e04).get_data()


def test_list2dseries():
    if not np:
        skip("numpy not installed.")

    xx = np.linspace(-3, 3, 10)
    yy1 = np.cos(xx)
    yy2 = np.linspace(-3, 3, 20)

    # same number of elements: everything is fine
    s = List2DSeries(xx, yy1)
    assert not s.is_parametric
    # different number of elements: error
    raises(ValueError, lambda: List2DSeries(xx, yy2))

    # no color func: returns only x, y components and s in not parametric
    s = List2DSeries(xx, yy1)
    xxs, yys = s.get_data()
    assert np.allclose(xx, xxs)
    assert np.allclose(yy1, yys)
    assert not s.is_parametric


def test_interactive_vs_noninteractive():
    # verify that if a *Series class receives a `params` dictionary, it sets
    # is_interactive=True
    x, y, z, u, v = symbols("x, y, z, u, v")

    s = LineOver1DRangeSeries(cos(x), (x, -5, 5))
    assert not s.is_interactive
    s = LineOver1DRangeSeries(u * cos(x), (x, -5, 5), params={u: 1})
    assert s.is_interactive

    s = Parametric2DLineSeries(cos(x), sin(x), (x, -5, 5))
    assert not s.is_interactive
    s = Parametric2DLineSeries(u * cos(x), u * sin(x), (x, -5, 5),
        params={u: 1})
    assert s.is_interactive

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, -5, 5))
    assert not s.is_interactive
    s = Parametric3DLineSeries(u * cos(x), u * sin(x), x, (x, -5, 5),
        params={u: 1})
    assert s.is_interactive

    s = SurfaceOver2DRangeSeries(cos(x * y), (x, -5, 5), (y, -5, 5))
    assert not s.is_interactive
    s = SurfaceOver2DRangeSeries(u * cos(x * y), (x, -5, 5), (y, -5, 5),
        params={u: 1})
    assert s.is_interactive

    s = ContourSeries(cos(x * y), (x, -5, 5), (y, -5, 5))
    assert not s.is_interactive
    s = ContourSeries(u * cos(x * y), (x, -5, 5), (y, -5, 5),
        params={u: 1})
    assert s.is_interactive

    s = ParametricSurfaceSeries(u * cos(v), v * sin(u), u + v,
        (u, -5, 5), (v, -5, 5))
    assert not s.is_interactive
    s = ParametricSurfaceSeries(u * cos(v * x), v * sin(u), u + v,
        (u, -5, 5), (v, -5, 5), params={x: 1})
    assert s.is_interactive


def test_lin_log_scale():
    # Verify that data series create the correct spacing in the data.
    if not np:
        skip("numpy not installed.")

    x, y, z = symbols("x, y, z")

    s = LineOver1DRangeSeries(x, (x, 1, 10), adaptive=False, n=50,
        xscale="linear")
    xx, _ = s.get_data()
    assert np.isclose(xx[1] - xx[0], xx[-1] - xx[-2])

    s = LineOver1DRangeSeries(x, (x, 1, 10), adaptive=False, n=50,
        xscale="log")
    xx, _ = s.get_data()
    assert not np.isclose(xx[1] - xx[0], xx[-1] - xx[-2])

    s = Parametric2DLineSeries(
        cos(x), sin(x), (x, pi / 2, 1.5 * pi), adaptive=False, n=50,
        xscale="linear")
    _, _, param = s.get_data()
    assert np.isclose(param[1] - param[0], param[-1] - param[-2])

    s = Parametric2DLineSeries(
        cos(x), sin(x), (x, pi / 2, 1.5 * pi), adaptive=False, n=50,
        xscale="log")
    _, _, param = s.get_data()
    assert not np.isclose(param[1] - param[0], param[-1] - param[-2])

    s = Parametric3DLineSeries(
        cos(x), sin(x), x, (x, pi / 2, 1.5 * pi), adaptive=False, n=50,
        xscale="linear")
    _, _, _, param = s.get_data()
    assert np.isclose(param[1] - param[0], param[-1] - param[-2])

    s = Parametric3DLineSeries(
        cos(x), sin(x), x, (x, pi / 2, 1.5 * pi), adaptive=False, n=50,
        xscale="log")
    _, _, _, param = s.get_data()
    assert not np.isclose(param[1] - param[0], param[-1] - param[-2])

    s = SurfaceOver2DRangeSeries(
        cos(x ** 2 + y ** 2), (x, 1, 5), (y, 1, 5), n=10,
        xscale="linear", yscale="linear")
    xx, yy, _ = s.get_data()
    assert np.isclose(xx[0, 1] - xx[0, 0], xx[0, -1] - xx[0, -2])
    assert np.isclose(yy[1, 0] - yy[0, 0], yy[-1, 0] - yy[-2, 0])

    s = SurfaceOver2DRangeSeries(
        cos(x ** 2 + y ** 2), (x, 1, 5), (y, 1, 5), n=10,
        xscale="log", yscale="log")
    xx, yy, _ = s.get_data()
    assert not np.isclose(xx[0, 1] - xx[0, 0], xx[0, -1] - xx[0, -2])
    assert not np.isclose(yy[1, 0] - yy[0, 0], yy[-1, 0] - yy[-2, 0])

    s = ImplicitSeries(
        cos(x ** 2 + y ** 2) > 0, (x, 1, 5), (y, 1, 5),
        n1=10, n2=10, xscale="linear", yscale="linear", adaptive=False)
    xx, yy, _, _ = s.get_data()
    assert np.isclose(xx[0, 1] - xx[0, 0], xx[0, -1] - xx[0, -2])
    assert np.isclose(yy[1, 0] - yy[0, 0], yy[-1, 0] - yy[-2, 0])

    s = ImplicitSeries(
        cos(x ** 2 + y ** 2) > 0, (x, 1, 5), (y, 1, 5),
        n=10, xscale="log", yscale="log", adaptive=False)
    xx, yy, _, _ = s.get_data()
    assert not np.isclose(xx[0, 1] - xx[0, 0], xx[0, -1] - xx[0, -2])
    assert not np.isclose(yy[1, 0] - yy[0, 0], yy[-1, 0] - yy[-2, 0])


def test_rendering_kw():
    # verify that each series exposes the `rendering_kw` attribute
    if not np:
        skip("numpy not installed.")

    u, v, x, y, z = symbols("u, v, x:z")

    s = List2DSeries([1, 2, 3], [4, 5, 6])
    assert isinstance(s.rendering_kw, dict)

    s = LineOver1DRangeSeries(1, (x, -5, 5))
    assert isinstance(s.rendering_kw, dict)

    s = Parametric2DLineSeries(sin(x), cos(x), (x, 0, pi))
    assert isinstance(s.rendering_kw, dict)

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 2 * pi))
    assert isinstance(s.rendering_kw, dict)

    s = SurfaceOver2DRangeSeries(x + y, (x, -2, 2), (y, -3, 3))
    assert isinstance(s.rendering_kw, dict)

    s = ContourSeries(x + y, (x, -2, 2), (y, -3, 3))
    assert isinstance(s.rendering_kw, dict)

    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1))
    assert isinstance(s.rendering_kw, dict)


def test_data_shape():
    # Verify that the series produces the correct data shape when the input
    # expression is a number.
    if not np:
        skip("numpy not installed.")

    u, x, y, z = symbols("u, x:z")

    # scalar expression: it should return a numpy ones array
    s = LineOver1DRangeSeries(1, (x, -5, 5))
    xx, yy = s.get_data()
    assert len(xx) == len(yy)
    assert np.all(yy == 1)

    s = LineOver1DRangeSeries(1, (x, -5, 5), adaptive=False, n=10)
    xx, yy = s.get_data()
    assert len(xx) == len(yy) == 10
    assert np.all(yy == 1)

    s = Parametric2DLineSeries(sin(x), 1, (x, 0, pi))
    xx, yy, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(param))
    assert np.all(yy == 1)

    s = Parametric2DLineSeries(1, sin(x), (x, 0, pi))
    xx, yy, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(param))
    assert np.all(xx == 1)

    s = Parametric2DLineSeries(sin(x), 1, (x, 0, pi), adaptive=False)
    xx, yy, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(param))
    assert np.all(yy == 1)

    s = Parametric2DLineSeries(1, sin(x), (x, 0, pi), adaptive=False)
    xx, yy, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(param))
    assert np.all(xx == 1)

    s = Parametric3DLineSeries(cos(x), sin(x), 1, (x, 0, 2 * pi))
    xx, yy, zz, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(zz)) and (len(xx) == len(param))
    assert np.all(zz == 1)

    s = Parametric3DLineSeries(cos(x), 1, x, (x, 0, 2 * pi))
    xx, yy, zz, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(zz)) and (len(xx) == len(param))
    assert np.all(yy == 1)

    s = Parametric3DLineSeries(1, sin(x), x, (x, 0, 2 * pi))
    xx, yy, zz, param = s.get_data()
    assert (len(xx) == len(yy)) and (len(xx) == len(zz)) and (len(xx) == len(param))
    assert np.all(xx == 1)

    s = SurfaceOver2DRangeSeries(1, (x, -2, 2), (y, -3, 3))
    xx, yy, zz = s.get_data()
    assert (xx.shape == yy.shape) and (xx.shape == zz.shape)
    assert np.all(zz == 1)

    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1))
    xx, yy, zz, uu, vv = s.get_data()
    assert xx.shape == yy.shape == zz.shape == uu.shape == vv.shape
    assert np.all(xx == 1)

    s = ParametricSurfaceSeries(1, 1, y, (x, 0, 1), (y, 0, 1))
    xx, yy, zz, uu, vv = s.get_data()
    assert xx.shape == yy.shape == zz.shape == uu.shape == vv.shape
    assert np.all(yy == 1)

    s = ParametricSurfaceSeries(x, 1, 1, (x, 0, 1), (y, 0, 1))
    xx, yy, zz, uu, vv = s.get_data()
    assert xx.shape == yy.shape == zz.shape == uu.shape == vv.shape
    assert np.all(zz == 1)


def test_only_integers():
    if not np:
        skip("numpy not installed.")

    x, y, u, v = symbols("x, y, u, v")

    s = LineOver1DRangeSeries(sin(x), (x, -5.5, 4.5), "",
        adaptive=False, only_integers=True)
    xx, _ = s.get_data()
    assert len(xx) == 10
    assert xx[0] == -5 and xx[-1] == 4

    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2 * pi), "",
        adaptive=False, only_integers=True)
    _, _, p = s.get_data()
    assert len(p) == 7
    assert p[0] == 0 and p[-1] == 6

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 2 * pi), "",
        adaptive=False, only_integers=True)
    _, _, _, p = s.get_data()
    assert len(p) == 7
    assert p[0] == 0 and p[-1] == 6

    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -5.5, 5.5),
        (y, -3.5, 3.5), "",
        adaptive=False, only_integers=True)
    xx, yy, _ = s.get_data()
    assert xx.shape == yy.shape == (7, 11)
    assert np.allclose(xx[:, 0] - (-5) * np.ones(7), 0)
    assert np.allclose(xx[0, :] - np.linspace(-5, 5, 11), 0)
    assert np.allclose(yy[:, 0] - np.linspace(-3, 3, 7), 0)
    assert np.allclose(yy[0, :] - (-3) * np.ones(11), 0)

    r = 2 + sin(7 * u + 5 * v)
    expr = (
        r * cos(u) * sin(v),
        r * sin(u) * sin(v),
        r * cos(v)
    )
    s = ParametricSurfaceSeries(*expr, (u, 0, 2 * pi), (v, 0, pi), "",
        adaptive=False, only_integers=True)
    xx, yy, zz, uu, vv = s.get_data()
    assert xx.shape == yy.shape == zz.shape == uu.shape == vv.shape == (4, 7)

    # only_integers also works with scalar expressions
    s = LineOver1DRangeSeries(1, (x, -5.5, 4.5), "",
        adaptive=False, only_integers=True)
    xx, _ = s.get_data()
    assert len(xx) == 10
    assert xx[0] == -5 and xx[-1] == 4

    s = Parametric2DLineSeries(cos(x), 1, (x, 0, 2 * pi), "",
        adaptive=False, only_integers=True)
    _, _, p = s.get_data()
    assert len(p) == 7
    assert p[0] == 0 and p[-1] == 6

    s = SurfaceOver2DRangeSeries(1, (x, -5.5, 5.5), (y, -3.5, 3.5), "",
        adaptive=False, only_integers=True)
    xx, yy, _ = s.get_data()
    assert xx.shape == yy.shape == (7, 11)
    assert np.allclose(xx[:, 0] - (-5) * np.ones(7), 0)
    assert np.allclose(xx[0, :] - np.linspace(-5, 5, 11), 0)
    assert np.allclose(yy[:, 0] - np.linspace(-3, 3, 7), 0)
    assert np.allclose(yy[0, :] - (-3) * np.ones(11), 0)

    r = 2 + sin(7 * u + 5 * v)
    expr = (
        r * cos(u) * sin(v),
        1,
        r * cos(v)
    )
    s = ParametricSurfaceSeries(*expr, (u, 0, 2 * pi), (v, 0, pi), "",
        adaptive=False, only_integers=True)
    xx, yy, zz, uu, vv = s.get_data()
    assert xx.shape == yy.shape == zz.shape == uu.shape == vv.shape == (4, 7)


def test_is_point_is_filled():
    # verify that `is_point` and `is_filled` are attributes and that they
    # they receive the correct values
    if not np:
        skip("numpy not installed.")

    x, u = symbols("x, u")

    s = LineOver1DRangeSeries(cos(x), (x, -5, 5), "",
        is_point=False, is_filled=True)
    assert (not s.is_point) and s.is_filled
    s = LineOver1DRangeSeries(cos(x), (x, -5, 5), "",
        is_point=True, is_filled=False)
    assert s.is_point and (not s.is_filled)

    s = List2DSeries([0, 1, 2], [3, 4, 5],
        is_point=False, is_filled=True)
    assert (not s.is_point) and s.is_filled
    s = List2DSeries([0, 1, 2], [3, 4, 5],
        is_point=True, is_filled=False)
    assert s.is_point and (not s.is_filled)

    s = Parametric2DLineSeries(cos(x), sin(x), (x, -5, 5),
        is_point=False, is_filled=True)
    assert (not s.is_point) and s.is_filled
    s = Parametric2DLineSeries(cos(x), sin(x), (x, -5, 5),
        is_point=True, is_filled=False)
    assert s.is_point and (not s.is_filled)

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, -5, 5),
        is_point=False, is_filled=True)
    assert (not s.is_point) and s.is_filled
    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, -5, 5),
        is_point=True, is_filled=False)
    assert s.is_point and (not s.is_filled)


def test_is_filled_2d():
    # verify that the is_filled attribute is exposed by the following series
    x, y = symbols("x, y")

    expr = cos(x**2 + y**2)
    ranges = (x, -2, 2), (y, -2, 2)

    s = ContourSeries(expr, *ranges)
    assert s.is_filled
    s = ContourSeries(expr, *ranges, is_filled=True)
    assert s.is_filled
    s = ContourSeries(expr, *ranges, is_filled=False)
    assert not s.is_filled


def test_steps():
    if not np:
        skip("numpy not installed.")

    x, u = symbols("x, u")

    def do_test(s1, s2):
        if (not s1.is_parametric) and s1.is_2Dline:
            xx1, _ = s1.get_data()
            xx2, _ = s2.get_data()
        elif s1.is_parametric and s1.is_2Dline:
            xx1, _, _ = s1.get_data()
            xx2, _, _ = s2.get_data()
        elif (not s1.is_parametric) and s1.is_3Dline:
            xx1, _, _ = s1.get_data()
            xx2, _, _ = s2.get_data()
        else:
            xx1, _, _, _ = s1.get_data()
            xx2, _, _, _ = s2.get_data()
        assert len(xx1) != len(xx2)

    s1 = LineOver1DRangeSeries(cos(x), (x, -5, 5), "",
        adaptive=False, n=40, steps=False)
    s2 = LineOver1DRangeSeries(cos(x), (x, -5, 5), "",
        adaptive=False, n=40, steps=True)
    do_test(s1, s2)

    s1 = List2DSeries([0, 1, 2], [3, 4, 5], steps=False)
    s2 = List2DSeries([0, 1, 2], [3, 4, 5], steps=True)
    do_test(s1, s2)

    s1 = Parametric2DLineSeries(cos(x), sin(x), (x, -5, 5),
        adaptive=False, n=40, steps=False)
    s2 = Parametric2DLineSeries(cos(x), sin(x), (x, -5, 5),
        adaptive=False, n=40, steps=True)
    do_test(s1, s2)

    s1 = Parametric3DLineSeries(cos(x), sin(x), x, (x, -5, 5),
        adaptive=False, n=40, steps=False)
    s2 = Parametric3DLineSeries(cos(x), sin(x), x, (x, -5, 5),
        adaptive=False, n=40, steps=True)
    do_test(s1, s2)


def test_interactive_data():
    # verify that InteractiveSeries produces the same numerical data as their
    # corresponding non-interactive series.
    if not np:
        skip("numpy not installed.")

    u, x, y, z = symbols("u, x:z")

    def do_test(data1, data2):
        assert len(data1) == len(data2)
        for d1, d2 in zip(data1, data2):
            assert np.allclose(d1, d2)

    s1 = LineOver1DRangeSeries(u * cos(x), (x, -5, 5), params={u: 1}, n=50)
    s2 = LineOver1DRangeSeries(cos(x), (x, -5, 5), adaptive=False, n=50)
    do_test(s1.get_data(), s2.get_data())

    s1 = Parametric2DLineSeries(
        u * cos(x), u * sin(x), (x, -5, 5), params={u: 1}, n=50)
    s2 = Parametric2DLineSeries(cos(x), sin(x), (x, -5, 5),
        adaptive=False, n=50)
    do_test(s1.get_data(), s2.get_data())

    s1 = Parametric3DLineSeries(
        u * cos(x), u * sin(x), u * x, (x, -5, 5),
        params={u: 1}, n=50)
    s2 = Parametric3DLineSeries(cos(x), sin(x), x, (x, -5, 5),
        adaptive=False, n=50)
    do_test(s1.get_data(), s2.get_data())

    s1 = SurfaceOver2DRangeSeries(
        u * cos(x ** 2 + y ** 2), (x, -3, 3), (y, -3, 3),
        params={u: 1}, n1=50, n2=50,)
    s2 = SurfaceOver2DRangeSeries(
        cos(x ** 2 + y ** 2), (x, -3, 3), (y, -3, 3),
        adaptive=False, n1=50, n2=50)
    do_test(s1.get_data(), s2.get_data())

    s1 = ParametricSurfaceSeries(
        u * cos(x + y), sin(x + y), x - y, (x, -3, 3), (y, -3, 3),
        params={u: 1}, n1=50, n2=50,)
    s2 = ParametricSurfaceSeries(
        cos(x + y), sin(x + y), x - y, (x, -3, 3), (y, -3, 3),
        adaptive=False, n1=50, n2=50,)
    do_test(s1.get_data(), s2.get_data())

    # real part of a complex function evaluated over a real line with numpy
    expr = re((z ** 2 + 1) / (z ** 2 - 1))
    s1 = LineOver1DRangeSeries(u * expr, (z, -3, 3), adaptive=False, n=50,
        modules=None, params={u: 1})
    s2 = LineOver1DRangeSeries(expr, (z, -3, 3), adaptive=False, n=50,
        modules=None)
    do_test(s1.get_data(), s2.get_data())

    # real part of a complex function evaluated over a real line with mpmath
    expr = re((z ** 2 + 1) / (z ** 2 - 1))
    s1 = LineOver1DRangeSeries(u * expr, (z, -3, 3), n=50, modules="mpmath",
        params={u: 1})
    s2 = LineOver1DRangeSeries(expr, (z, -3, 3),
        adaptive=False, n=50, modules="mpmath")
    do_test(s1.get_data(), s2.get_data())


def test_list2dseries_interactive():
    if not np:
        skip("numpy not installed.")

    x, y, u = symbols("x, y, u")

    s = List2DSeries([1, 2, 3], [1, 2, 3])
    assert not s.is_interactive

    # symbolic expressions as coordinates, but no ``params``
    raises(ValueError, lambda: List2DSeries([cos(x)], [sin(x)]))

    # too few parameters
    raises(ValueError,
        lambda: List2DSeries([cos(x), y], [sin(x), 2], params={u: 1}))

    s = List2DSeries([cos(x)], [sin(x)], params={x: 1})
    assert s.is_interactive

    s = List2DSeries([x, 2, 3, 4], [4, 3, 2, x], params={x: 3})
    xx, yy = s.get_data()
    assert np.allclose(xx, [3, 2, 3, 4])
    assert np.allclose(yy, [4, 3, 2, 3])
    assert not s.is_parametric

    # numeric lists + params is present -> interactive series and
    # lists are converted to Tuple.
    s = List2DSeries([1, 2, 3], [1, 2, 3], params={x: 1})
    assert s.is_interactive
    assert isinstance(s.list_x, Tuple)
    assert isinstance(s.list_y, Tuple)


def test_mpmath():
    # test that the argument of complex functions evaluated with mpmath
    # might be different than the one computed with Numpy (different
    # behaviour at branch cuts)
    if not np:
        skip("numpy not installed.")

    z, u = symbols("z, u")

    s1 = LineOver1DRangeSeries(im(sqrt(-z)), (z, 1e-03, 5),
        adaptive=True, modules=None, force_real_eval=True)
    s2 = LineOver1DRangeSeries(im(sqrt(-z)), (z, 1e-03, 5),
        adaptive=True, modules="mpmath", force_real_eval=True)
    xx1, yy1 = s1.get_data()
    xx2, yy2 = s2.get_data()
    assert np.all(yy1 < 0)
    assert np.all(yy2 > 0)

    s1 = LineOver1DRangeSeries(im(sqrt(-z)), (z, -5, 5),
        adaptive=False, n=20, modules=None, force_real_eval=True)
    s2 = LineOver1DRangeSeries(im(sqrt(-z)), (z, -5, 5),
        adaptive=False, n=20, modules="mpmath", force_real_eval=True)
    xx1, yy1 = s1.get_data()
    xx2, yy2 = s2.get_data()
    assert np.allclose(xx1, xx2)
    assert not np.allclose(yy1, yy2)


def test_str():
    u, x, y, z = symbols("u, x:z")

    s = LineOver1DRangeSeries(cos(x), (x, -4, 3))
    assert str(s) == "cartesian line: cos(x) for x over (-4.0, 3.0)"

    d = {"return": "real"}
    s = LineOver1DRangeSeries(cos(x), (x, -4, 3), **d)
    assert str(s) == "cartesian line: re(cos(x)) for x over (-4.0, 3.0)"

    d = {"return": "imag"}
    s = LineOver1DRangeSeries(cos(x), (x, -4, 3), **d)
    assert str(s) == "cartesian line: im(cos(x)) for x over (-4.0, 3.0)"

    d = {"return": "abs"}
    s = LineOver1DRangeSeries(cos(x), (x, -4, 3), **d)
    assert str(s) == "cartesian line: abs(cos(x)) for x over (-4.0, 3.0)"

    d = {"return": "arg"}
    s = LineOver1DRangeSeries(cos(x), (x, -4, 3), **d)
    assert str(s) == "cartesian line: arg(cos(x)) for x over (-4.0, 3.0)"

    s = LineOver1DRangeSeries(cos(u * x), (x, -4, 3), params={u: 1})
    assert str(s) == "interactive cartesian line: cos(u*x) for x over (-4.0, 3.0) and parameters (u,)"

    s = LineOver1DRangeSeries(cos(u * x), (x, -u, 3*y), params={u: 1, y: 1})
    assert str(s) == "interactive cartesian line: cos(u*x) for x over (-u, 3*y) and parameters (u, y)"

    s = Parametric2DLineSeries(cos(x), sin(x), (x, -4, 3))
    assert str(s) == "parametric cartesian line: (cos(x), sin(x)) for x over (-4.0, 3.0)"

    s = Parametric2DLineSeries(cos(u * x), sin(x), (x, -4, 3), params={u: 1})
    assert str(s) == "interactive parametric cartesian line: (cos(u*x), sin(x)) for x over (-4.0, 3.0) and parameters (u,)"

    s = Parametric2DLineSeries(cos(u * x), sin(x), (x, -u, 3*y), params={u: 1, y:1})
    assert str(s) == "interactive parametric cartesian line: (cos(u*x), sin(x)) for x over (-u, 3*y) and parameters (u, y)"

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, -4, 3))
    assert str(s) == "3D parametric cartesian line: (cos(x), sin(x), x) for x over (-4.0, 3.0)"

    s = Parametric3DLineSeries(cos(u*x), sin(x), x, (x, -4, 3), params={u: 1})
    assert str(s) == "interactive 3D parametric cartesian line: (cos(u*x), sin(x), x) for x over (-4.0, 3.0) and parameters (u,)"

    s = Parametric3DLineSeries(cos(u*x), sin(x), x, (x, -u, 3*y), params={u: 1, y: 1})
    assert str(s) == "interactive 3D parametric cartesian line: (cos(u*x), sin(x), x) for x over (-u, 3*y) and parameters (u, y)"

    s = SurfaceOver2DRangeSeries(cos(x * y), (x, -4, 3), (y, -2, 5))
    assert str(s) == "cartesian surface: cos(x*y) for x over (-4.0, 3.0) and y over (-2.0, 5.0)"

    s = SurfaceOver2DRangeSeries(cos(u * x * y), (x, -4, 3), (y, -2, 5), params={u: 1})
    assert str(s) == "interactive cartesian surface: cos(u*x*y) for x over (-4.0, 3.0) and y over (-2.0, 5.0) and parameters (u,)"

    s = SurfaceOver2DRangeSeries(cos(u * x * y), (x, -4*u, 3), (y, -2, 5*u), params={u: 1})
    assert str(s) == "interactive cartesian surface: cos(u*x*y) for x over (-4*u, 3.0) and y over (-2.0, 5*u) and parameters (u,)"

    s = ContourSeries(cos(x * y), (x, -4, 3), (y, -2, 5))
    assert str(s) == "contour: cos(x*y) for x over (-4.0, 3.0) and y over (-2.0, 5.0)"

    s = ContourSeries(cos(u * x * y), (x, -4, 3), (y, -2, 5), params={u: 1})
    assert str(s) == "interactive contour: cos(u*x*y) for x over (-4.0, 3.0) and y over (-2.0, 5.0) and parameters (u,)"

    s = ParametricSurfaceSeries(cos(x * y), sin(x * y), x * y,
        (x, -4, 3), (y, -2, 5))
    assert str(s) == "parametric cartesian surface: (cos(x*y), sin(x*y), x*y) for x over (-4.0, 3.0) and y over (-2.0, 5.0)"

    s = ParametricSurfaceSeries(cos(u * x * y), sin(x * y), x * y,
        (x, -4, 3), (y, -2, 5), params={u: 1})
    assert str(s) == "interactive parametric cartesian surface: (cos(u*x*y), sin(x*y), x*y) for x over (-4.0, 3.0) and y over (-2.0, 5.0) and parameters (u,)"

    s = ImplicitSeries(x < y, (x, -5, 4), (y, -3, 2))
    assert str(s) == "Implicit expression: x < y for x over (-5.0, 4.0) and y over (-3.0, 2.0)"


def test_use_cm():
    # verify that the `use_cm` attribute is implemented.
    if not np:
        skip("numpy not installed.")

    u, x, y, z = symbols("u, x:z")

    s = List2DSeries([1, 2, 3, 4], [5, 6, 7, 8], use_cm=True)
    assert s.use_cm
    s = List2DSeries([1, 2, 3, 4], [5, 6, 7, 8], use_cm=False)
    assert not s.use_cm

    s = Parametric2DLineSeries(cos(x), sin(x), (x, -4, 3), use_cm=True)
    assert s.use_cm
    s = Parametric2DLineSeries(cos(x), sin(x), (x, -4, 3), use_cm=False)
    assert not s.use_cm

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, -4, 3),
        use_cm=True)
    assert s.use_cm
    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, -4, 3),
        use_cm=False)
    assert not s.use_cm

    s = SurfaceOver2DRangeSeries(cos(x * y), (x, -4, 3), (y, -2, 5),
        use_cm=True)
    assert s.use_cm
    s = SurfaceOver2DRangeSeries(cos(x * y), (x, -4, 3), (y, -2, 5),
        use_cm=False)
    assert not s.use_cm

    s = ParametricSurfaceSeries(cos(x * y), sin(x * y), x * y,
        (x, -4, 3), (y, -2, 5), use_cm=True)
    assert s.use_cm
    s = ParametricSurfaceSeries(cos(x * y), sin(x * y), x * y,
        (x, -4, 3), (y, -2, 5), use_cm=False)
    assert not s.use_cm


def test_surface_use_cm():
    # verify that SurfaceOver2DRangeSeries and ParametricSurfaceSeries get
    # the same value for use_cm

    x, y, u, v = symbols("x, y, u, v")

    # they read the same value from default settings
    s1 = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2))
    s2 = ParametricSurfaceSeries(u * cos(v), u * sin(v), u,
        (u, 0, 1), (v, 0 , 2*pi))
    assert s1.use_cm == s2.use_cm

    # they get the same value
    s1 = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        use_cm=False)
    s2 = ParametricSurfaceSeries(u * cos(v), u * sin(v), u,
        (u, 0, 1), (v, 0 , 2*pi), use_cm=False)
    assert s1.use_cm == s2.use_cm

    # they get the same value
    s1 = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        use_cm=True)
    s2 = ParametricSurfaceSeries(u * cos(v), u * sin(v), u,
        (u, 0, 1), (v, 0 , 2*pi), use_cm=True)
    assert s1.use_cm == s2.use_cm


def test_sums():
    # test that data series are able to deal with sums
    if not np:
        skip("numpy not installed.")

    x, y, u = symbols("x, y, u")

    def do_test(data1, data2):
        assert len(data1) == len(data2)
        for d1, d2 in zip(data1, data2):
            assert np.allclose(d1, d2)

    s = LineOver1DRangeSeries(Sum(1 / x ** y, (x, 1, 1000)), (y, 2, 10),
        adaptive=False, only_integers=True)
    xx, yy = s.get_data()

    s1 = LineOver1DRangeSeries(Sum(1 / x, (x, 1, y)), (y, 2, 10),
        adaptive=False, only_integers=True)
    xx1, yy1 = s1.get_data()

    s2 = LineOver1DRangeSeries(Sum(u / x, (x, 1, y)), (y, 2, 10),
        params={u: 1}, only_integers=True)
    xx2, yy2 = s2.get_data()
    xx1 = xx1.astype(float)
    xx2 = xx2.astype(float)
    do_test([xx1, yy1], [xx2, yy2])

    s = LineOver1DRangeSeries(Sum(1 / x, (x, 1, y)), (y, 2, 10),
        adaptive=True)
    with warns(
        UserWarning,
        match="The evaluation with NumPy/SciPy failed",
        test_stacklevel=False,
    ):
        raises(TypeError, lambda: s.get_data())


def test_apply_transforms():
    # verify that transformation functions get applied to the output
    # of data series
    if not np:
        skip("numpy not installed.")

    x, y, z, u, v = symbols("x:z, u, v")

    s1 = LineOver1DRangeSeries(cos(x), (x, -2*pi, 2*pi), adaptive=False, n=10)
    s2 = LineOver1DRangeSeries(cos(x), (x, -2*pi, 2*pi), adaptive=False, n=10,
        tx=np.rad2deg)
    s3 = LineOver1DRangeSeries(cos(x), (x, -2*pi, 2*pi), adaptive=False, n=10,
        ty=np.rad2deg)
    s4 = LineOver1DRangeSeries(cos(x), (x, -2*pi, 2*pi), adaptive=False, n=10,
        tx=np.rad2deg, ty=np.rad2deg)

    x1, y1 = s1.get_data()
    x2, y2 = s2.get_data()
    x3, y3 = s3.get_data()
    x4, y4 = s4.get_data()
    assert np.isclose(x1[0], -2*np.pi) and np.isclose(x1[-1], 2*np.pi)
    assert (y1.min() < -0.9) and (y1.max() > 0.9)
    assert np.isclose(x2[0], -360) and np.isclose(x2[-1], 360)
    assert (y2.min() < -0.9) and (y2.max() > 0.9)
    assert np.isclose(x3[0], -2*np.pi) and np.isclose(x3[-1], 2*np.pi)
    assert (y3.min() < -52) and (y3.max() > 52)
    assert np.isclose(x4[0], -360) and np.isclose(x4[-1], 360)
    assert (y4.min() < -52) and (y4.max() > 52)

    xx = np.linspace(-2*np.pi, 2*np.pi, 10)
    yy = np.cos(xx)
    s1 = List2DSeries(xx, yy)
    s2 = List2DSeries(xx, yy, tx=np.rad2deg, ty=np.rad2deg)
    x1, y1 = s1.get_data()
    x2, y2 = s2.get_data()
    assert np.isclose(x1[0], -2*np.pi) and np.isclose(x1[-1], 2*np.pi)
    assert (y1.min() < -0.9) and (y1.max() > 0.9)
    assert np.isclose(x2[0], -360) and np.isclose(x2[-1], 360)
    assert (y2.min() < -52) and (y2.max() > 52)

    s1 = Parametric2DLineSeries(
        sin(x), cos(x), (x, -pi, pi), adaptive=False, n=10)
    s2 = Parametric2DLineSeries(
        sin(x), cos(x), (x, -pi, pi), adaptive=False, n=10,
        tx=np.rad2deg, ty=np.rad2deg, tp=np.rad2deg)
    x1, y1, a1 = s1.get_data()
    x2, y2, a2 = s2.get_data()
    assert np.allclose(x1, np.deg2rad(x2))
    assert np.allclose(y1, np.deg2rad(y2))
    assert np.allclose(a1, np.deg2rad(a2))

    s1 =  Parametric3DLineSeries(
        sin(x), cos(x), x, (x, -pi, pi), adaptive=False, n=10)
    s2 = Parametric3DLineSeries(
        sin(x), cos(x), x, (x, -pi, pi), adaptive=False, n=10, tp=np.rad2deg)
    x1, y1, z1, a1 = s1.get_data()
    x2, y2, z2, a2 = s2.get_data()
    assert np.allclose(x1, x2)
    assert np.allclose(y1, y2)
    assert np.allclose(z1, z2)
    assert np.allclose(a1, np.deg2rad(a2))

    s1 = SurfaceOver2DRangeSeries(
        cos(x**2 + y**2), (x, -2*pi, 2*pi), (y, -2*pi, 2*pi),
        adaptive=False, n1=10, n2=10)
    s2 = SurfaceOver2DRangeSeries(
        cos(x**2 + y**2), (x, -2*pi, 2*pi), (y, -2*pi, 2*pi),
        adaptive=False, n1=10, n2=10,
        tx=np.rad2deg, ty=lambda x: 2*x, tz=lambda x: 3*x)
    x1, y1, z1 = s1.get_data()
    x2, y2, z2 = s2.get_data()
    assert np.allclose(x1, np.deg2rad(x2))
    assert np.allclose(y1, y2 / 2)
    assert np.allclose(z1, z2 / 3)

    s1 = ParametricSurfaceSeries(
        u + v, u - v, u * v, (u, 0, 2*pi), (v, 0, pi),
        adaptive=False, n1=10, n2=10)
    s2 = ParametricSurfaceSeries(
        u + v, u - v, u * v, (u, 0, 2*pi), (v, 0, pi),
        adaptive=False, n1=10, n2=10,
        tx=np.rad2deg, ty=lambda x: 2*x, tz=lambda x: 3*x)
    x1, y1, z1, u1, v1 = s1.get_data()
    x2, y2, z2, u2, v2 = s2.get_data()
    assert np.allclose(x1, np.deg2rad(x2))
    assert np.allclose(y1, y2 / 2)
    assert np.allclose(z1, z2 / 3)
    assert np.allclose(u1, u2)
    assert np.allclose(v1, v2)


def test_series_labels():
    # verify that series return the correct label, depending on the plot
    # type and input arguments. If the user set custom label on a data series,
    # it should returned un-modified.
    if not np:
        skip("numpy not installed.")

    x, y, z, u, v = symbols("x, y, z, u, v")
    wrapper = "$%s$"

    expr = cos(x)
    s1 = LineOver1DRangeSeries(expr, (x, -2, 2), None)
    s2 = LineOver1DRangeSeries(expr, (x, -2, 2), "test")
    assert s1.get_label(False) == str(expr)
    assert s1.get_label(True) == wrapper % latex(expr)
    assert s2.get_label(False) == "test"
    assert s2.get_label(True) == "test"

    s1 = List2DSeries([0, 1, 2, 3], [0, 1, 2, 3], "test")
    assert s1.get_label(False) == "test"
    assert s1.get_label(True) == "test"

    expr = (cos(x), sin(x))
    s1 = Parametric2DLineSeries(*expr, (x, -2, 2), None, use_cm=True)
    s2 = Parametric2DLineSeries(*expr, (x, -2, 2), "test", use_cm=True)
    s3 = Parametric2DLineSeries(*expr, (x, -2, 2), None, use_cm=False)
    s4 = Parametric2DLineSeries(*expr, (x, -2, 2), "test", use_cm=False)
    assert s1.get_label(False) == "x"
    assert s1.get_label(True) == wrapper % "x"
    assert s2.get_label(False) == "test"
    assert s2.get_label(True) == "test"
    assert s3.get_label(False) == str(expr)
    assert s3.get_label(True) == wrapper % latex(expr)
    assert s4.get_label(False) == "test"
    assert s4.get_label(True) == "test"

    expr = (cos(x), sin(x), x)
    s1 = Parametric3DLineSeries(*expr, (x, -2, 2), None, use_cm=True)
    s2 = Parametric3DLineSeries(*expr, (x, -2, 2), "test", use_cm=True)
    s3 = Parametric3DLineSeries(*expr, (x, -2, 2), None, use_cm=False)
    s4 = Parametric3DLineSeries(*expr, (x, -2, 2), "test", use_cm=False)
    assert s1.get_label(False) == "x"
    assert s1.get_label(True) == wrapper % "x"
    assert s2.get_label(False) == "test"
    assert s2.get_label(True) == "test"
    assert s3.get_label(False) == str(expr)
    assert s3.get_label(True) == wrapper % latex(expr)
    assert s4.get_label(False) == "test"
    assert s4.get_label(True) == "test"

    expr = cos(x**2 + y**2)
    s1 = SurfaceOver2DRangeSeries(expr, (x, -2, 2), (y, -2, 2), None)
    s2 = SurfaceOver2DRangeSeries(expr, (x, -2, 2), (y, -2, 2), "test")
    assert s1.get_label(False) == str(expr)
    assert s1.get_label(True) == wrapper % latex(expr)
    assert s2.get_label(False) == "test"
    assert s2.get_label(True) == "test"

    expr = (cos(x - y), sin(x + y), x - y)
    s1 = ParametricSurfaceSeries(*expr, (x, -2, 2), (y, -2, 2), None)
    s2 = ParametricSurfaceSeries(*expr, (x, -2, 2), (y, -2, 2), "test")
    assert s1.get_label(False) == str(expr)
    assert s1.get_label(True) == wrapper % latex(expr)
    assert s2.get_label(False) == "test"
    assert s2.get_label(True) == "test"

    expr = Eq(cos(x - y), 0)
    s1 = ImplicitSeries(expr, (x, -10, 10), (y, -10, 10), None)
    s2 = ImplicitSeries(expr, (x, -10, 10), (y, -10, 10), "test")
    assert s1.get_label(False) == str(expr)
    assert s1.get_label(True) == wrapper % latex(expr)
    assert s2.get_label(False) == "test"
    assert s2.get_label(True) == "test"


def test_is_polar_2d_parametric():
    # verify that Parametric2DLineSeries isable to apply polar discretization,
    # which is used when polar_plot is executed with polar_axis=True
    if not np:
        skip("numpy not installed.")

    t, u = symbols("t u")

    # NOTE: a sufficiently big n must be provided, or else tests
    # are going to fail
    # No colormap
    f = sin(4 * t)
    s1 = Parametric2DLineSeries(f * cos(t), f * sin(t), (t, 0, 2*pi),
        adaptive=False, n=10, is_polar=False, use_cm=False)
    x1, y1, p1 = s1.get_data()
    s2 = Parametric2DLineSeries(f * cos(t), f * sin(t), (t, 0, 2*pi),
        adaptive=False, n=10, is_polar=True, use_cm=False)
    th, r, p2 = s2.get_data()
    assert (not np.allclose(x1, th)) and (not np.allclose(y1, r))
    assert np.allclose(p1, p2)

    # With colormap
    s3 = Parametric2DLineSeries(f * cos(t), f * sin(t), (t, 0, 2*pi),
        adaptive=False, n=10, is_polar=False, color_func=lambda t: 2*t)
    x3, y3, p3 = s3.get_data()
    s4 = Parametric2DLineSeries(f * cos(t), f * sin(t), (t, 0, 2*pi),
        adaptive=False, n=10, is_polar=True, color_func=lambda t: 2*t)
    th4, r4, p4 = s4.get_data()
    assert np.allclose(p3, p4) and (not np.allclose(p1, p3))
    assert np.allclose(x3, x1) and np.allclose(y3, y1)
    assert np.allclose(th4, th) and np.allclose(r4, r)


def test_is_polar_3d():
    # verify that SurfaceOver2DRangeSeries is able to apply
    # polar discretization
    if not np:
        skip("numpy not installed.")

    x, y, t = symbols("x, y, t")
    expr = (x**2 - 1)**2
    s1 = SurfaceOver2DRangeSeries(expr, (x, 0, 1.5), (y, 0, 2 * pi),
        n=10, adaptive=False, is_polar=False)
    s2 = SurfaceOver2DRangeSeries(expr, (x, 0, 1.5), (y, 0, 2 * pi),
        n=10, adaptive=False, is_polar=True)
    x1, y1, z1 = s1.get_data()
    x2, y2, z2 = s2.get_data()
    x22, y22 = x1 * np.cos(y1), x1 * np.sin(y1)
    assert np.allclose(x2, x22)
    assert np.allclose(y2, y22)


def test_color_func():
    # verify that eval_color_func produces the expected results in order to
    # maintain back compatibility with the old sympy.plotting module
    if not np:
        skip("numpy not installed.")

    x, y, z, u, v = symbols("x, y, z, u, v")

    # color func: returns x, y, color and s is parametric
    xx = np.linspace(-3, 3, 10)
    yy1 = np.cos(xx)
    s = List2DSeries(xx, yy1, color_func=lambda x, y: 2 * x, use_cm=True)
    xxs, yys, col = s.get_data()
    assert np.allclose(xx, xxs)
    assert np.allclose(yy1, yys)
    assert np.allclose(2 * xx, col)
    assert s.is_parametric

    s = List2DSeries(xx, yy1, color_func=lambda x, y: 2 * x, use_cm=False)
    assert len(s.get_data()) == 2
    assert not s.is_parametric

    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda t: t)
    xx, yy, col = s.get_data()
    assert (not np.allclose(xx, col)) and (not np.allclose(yy, col))
    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda x, y: x * y)
    xx, yy, col = s.get_data()
    assert np.allclose(col, xx * yy)
    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda x, y, t: x * y * t)
    xx, yy, col = s.get_data()
    assert np.allclose(col, xx * yy * np.linspace(0, 2*np.pi, 10))

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda t: t)
    xx, yy, zz, col = s.get_data()
    assert (not np.allclose(xx, col)) and (not np.allclose(yy, col))
    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda x, y, z: x * y * z)
    xx, yy, zz, col = s.get_data()
    assert np.allclose(col, xx * yy * zz)
    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda x, y, z, t: x * y * z * t)
    xx, yy, zz, col = s.get_data()
    assert np.allclose(col, xx * yy * zz * np.linspace(0, 2*np.pi, 10))

    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        adaptive=False, n1=10, n2=10, color_func=lambda x: x)
    xx, yy, zz = s.get_data()
    col = s.eval_color_func(xx, yy, zz)
    assert np.allclose(xx, col)
    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        adaptive=False, n1=10, n2=10, color_func=lambda x, y: x * y)
    xx, yy, zz = s.get_data()
    col = s.eval_color_func(xx, yy, zz)
    assert np.allclose(xx * yy, col)
    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        adaptive=False, n1=10, n2=10, color_func=lambda x, y, z: x * y * z)
    xx, yy, zz = s.get_data()
    col = s.eval_color_func(xx, yy, zz)
    assert np.allclose(xx * yy * zz, col)

    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1), adaptive=False,
        n1=10, n2=10, color_func=lambda u:u)
    xx, yy, zz, uu, vv = s.get_data()
    col = s.eval_color_func(xx, yy, zz, uu, vv)
    assert np.allclose(uu, col)
    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1), adaptive=False,
        n1=10, n2=10, color_func=lambda u, v: u * v)
    xx, yy, zz, uu, vv = s.get_data()
    col = s.eval_color_func(xx, yy, zz, uu, vv)
    assert np.allclose(uu * vv, col)
    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1), adaptive=False,
        n1=10, n2=10, color_func=lambda x, y, z: x * y * z)
    xx, yy, zz, uu, vv = s.get_data()
    col = s.eval_color_func(xx, yy, zz, uu, vv)
    assert np.allclose(xx * yy * zz, col)
    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1), adaptive=False,
        n1=10, n2=10, color_func=lambda x, y, z, u, v: x * y * z * u * v)
    xx, yy, zz, uu, vv = s.get_data()
    col = s.eval_color_func(xx, yy, zz, uu, vv)
    assert np.allclose(xx * yy * zz * uu * vv, col)

    # Interactive Series
    s = List2DSeries([0, 1, 2, x], [x, 2, 3, 4],
        color_func=lambda x, y: 2 * x, params={x: 1}, use_cm=True)
    xx, yy, col = s.get_data()
    assert np.allclose(xx, [0, 1, 2, 1])
    assert np.allclose(yy, [1, 2, 3, 4])
    assert np.allclose(2 * xx, col)
    assert s.is_parametric and s.use_cm

    s = List2DSeries([0, 1, 2, x], [x, 2, 3, 4],
        color_func=lambda x, y: 2 * x, params={x: 1}, use_cm=False)
    assert len(s.get_data()) == 2
    assert not s.is_parametric


def test_color_func_scalar_val():
    # verify that eval_color_func returns a numpy array even when color_func
    # evaluates to a scalar value
    if not np:
        skip("numpy not installed.")

    x, y = symbols("x, y")

    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda t: 1)
    xx, yy, col = s.get_data()
    assert np.allclose(col, np.ones(xx.shape))

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 2*pi),
        adaptive=False, n=10, color_func=lambda t: 1)
    xx, yy, zz, col = s.get_data()
    assert np.allclose(col, np.ones(xx.shape))

    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        adaptive=False, n1=10, n2=10, color_func=lambda x: 1)
    xx, yy, zz = s.get_data()
    assert np.allclose(s.eval_color_func(xx), np.ones(xx.shape))

    s = ParametricSurfaceSeries(1, x, y, (x, 0, 1), (y, 0, 1), adaptive=False,
        n1=10, n2=10, color_func=lambda u: 1)
    xx, yy, zz, uu, vv = s.get_data()
    col = s.eval_color_func(xx, yy, zz, uu, vv)
    assert np.allclose(col, np.ones(xx.shape))


def test_color_func_expression():
    # verify that color_func is able to deal with instances of Expr: they will
    # be lambdified with the same signature used for the main expression.
    if not np:
        skip("numpy not installed.")

    x, y = symbols("x, y")

    s1 = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        color_func=sin(x), adaptive=False, n=10, use_cm=True)
    s2 = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        color_func=lambda x: np.cos(x), adaptive=False, n=10, use_cm=True)
    # the following statement should not raise errors
    d1 = s1.get_data()
    assert callable(s1.color_func)
    d2 = s2.get_data()
    assert not np.allclose(d1[-1], d2[-1])

    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -pi, pi), (y, -pi, pi),
        color_func=sin(x**2 + y**2), adaptive=False, n1=5, n2=5)
    # the following statement should not raise errors
    s.get_data()
    assert callable(s.color_func)

    xx = [1, 2, 3, 4, 5]
    yy = [1, 2, 3, 4, 5]
    raises(TypeError,
        lambda : List2DSeries(xx, yy, use_cm=True, color_func=sin(x)))


def test_line_surface_color():
    # verify the back-compatibility with the old sympy.plotting module.
    # By setting line_color or surface_color to be a callable, it will set
    # the color_func attribute.

    x, y, z = symbols("x, y, z")

    s = LineOver1DRangeSeries(sin(x), (x, -5, 5), adaptive=False, n=10,
        line_color=lambda x: x)
    assert (s.line_color is None) and callable(s.color_func)

    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 2*pi),
        adaptive=False, n=10, line_color=lambda t: t)
    assert (s.line_color is None) and callable(s.color_func)

    s = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -2, 2), (y, -2, 2),
        n1=10, n2=10, surface_color=lambda x: x)
    assert (s.surface_color is None) and callable(s.color_func)


def test_complex_adaptive_false():
    # verify that series with adaptive=False is evaluated with discretized
    # ranges of type complex.
    if not np:
        skip("numpy not installed.")

    x, y, u = symbols("x y u")

    def do_test(data1, data2):
        assert len(data1) == len(data2)
        for d1, d2 in zip(data1, data2):
            assert np.allclose(d1, d2)

    expr1 = sqrt(x) * exp(-x**2)
    expr2 = sqrt(u * x) * exp(-x**2)
    s1 = LineOver1DRangeSeries(im(expr1), (x, -5, 5), adaptive=False, n=10)
    s2 = LineOver1DRangeSeries(im(expr2), (x, -5, 5),
        adaptive=False, n=10, params={u: 1})
    data1 = s1.get_data()
    data2 = s2.get_data()

    do_test(data1, data2)
    assert (not np.allclose(data1[1], 0)) and (not np.allclose(data2[1], 0))

    s1 = Parametric2DLineSeries(re(expr1), im(expr1), (x, -pi, pi),
        adaptive=False, n=10)
    s2 = Parametric2DLineSeries(re(expr2), im(expr2), (x, -pi, pi),
        adaptive=False, n=10, params={u: 1})
    data1 = s1.get_data()
    data2 = s2.get_data()
    do_test(data1, data2)
    assert (not np.allclose(data1[1], 0)) and (not np.allclose(data2[1], 0))

    s1 = SurfaceOver2DRangeSeries(im(expr1), (x, -5, 5), (y, -10, 10),
        adaptive=False, n1=30, n2=3)
    s2 = SurfaceOver2DRangeSeries(im(expr2), (x, -5, 5), (y, -10, 10),
        adaptive=False, n1=30, n2=3, params={u: 1})
    data1 = s1.get_data()
    data2 = s2.get_data()
    do_test(data1, data2)
    assert (not np.allclose(data1[1], 0)) and (not np.allclose(data2[1], 0))


def test_expr_is_lambda_function():
    # verify that when a numpy function is provided, the series will be able
    # to evaluate it. Also, label should be empty in order to prevent some
    # backend from crashing.
    if not np:
        skip("numpy not installed.")

    f = lambda x: np.cos(x)
    s1 = LineOver1DRangeSeries(f, ("x", -5, 5), adaptive=True, depth=3)
    s1.get_data()
    s2 = LineOver1DRangeSeries(f, ("x", -5, 5), adaptive=False, n=10)
    s2.get_data()
    assert s1.label == s2.label == ""

    fx = lambda x: np.cos(x)
    fy = lambda x: np.sin(x)
    s1 = Parametric2DLineSeries(fx, fy, ("x", 0, 2*pi),
        adaptive=True, adaptive_goal=0.1)
    s1.get_data()
    s2 = Parametric2DLineSeries(fx, fy, ("x", 0, 2*pi),
        adaptive=False, n=10)
    s2.get_data()
    assert s1.label == s2.label == ""

    fz = lambda x: x
    s1 = Parametric3DLineSeries(fx, fy, fz, ("x", 0, 2*pi),
        adaptive=True, adaptive_goal=0.1)
    s1.get_data()
    s2 = Parametric3DLineSeries(fx, fy, fz, ("x", 0, 2*pi),
        adaptive=False, n=10)
    s2.get_data()
    assert s1.label == s2.label == ""

    f = lambda x, y: np.cos(x**2 + y**2)
    s1 = SurfaceOver2DRangeSeries(f, ("a", -2, 2), ("b", -3, 3),
        adaptive=False, n1=10, n2=10)
    s1.get_data()
    s2 = ContourSeries(f, ("a", -2, 2), ("b", -3, 3),
        adaptive=False, n1=10, n2=10)
    s2.get_data()
    assert s1.label == s2.label == ""

    fx = lambda u, v: np.cos(u + v)
    fy = lambda u, v: np.sin(u - v)
    fz = lambda u, v: u * v
    s1 = ParametricSurfaceSeries(fx, fy, fz, ("u", 0, pi), ("v", 0, 2*pi),
        adaptive=False, n1=10, n2=10)
    s1.get_data()
    assert s1.label == ""

    raises(TypeError, lambda: List2DSeries(lambda t: t, lambda t: t))
    raises(TypeError, lambda : ImplicitSeries(lambda t: np.sin(t),
        ("x", -5, 5), ("y", -6, 6)))


def test_show_in_legend_lines():
    # verify that lines series correctly set the show_in_legend attribute
    x, u = symbols("x, u")

    s = LineOver1DRangeSeries(cos(x), (x, -2, 2), "test", show_in_legend=True)
    assert s.show_in_legend
    s = LineOver1DRangeSeries(cos(x), (x, -2, 2), "test", show_in_legend=False)
    assert not s.show_in_legend

    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 1), "test",
        show_in_legend=True)
    assert s.show_in_legend
    s = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 1), "test",
        show_in_legend=False)
    assert not s.show_in_legend

    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 1), "test",
        show_in_legend=True)
    assert s.show_in_legend
    s = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 1), "test",
        show_in_legend=False)
    assert not s.show_in_legend


@XFAIL
def test_particular_case_1_with_adaptive_true():
    # Verify that symbolic expressions and numerical lambda functions are
    # evaluated with the same algorithm.
    if not np:
        skip("numpy not installed.")

    # NOTE: xfail because sympy's adaptive algorithm is not deterministic

    def do_test(a, b):
        with warns(
            RuntimeWarning,
            match="invalid value encountered in scalar power",
            test_stacklevel=False,
        ):
            d1 = a.get_data()
            d2 = b.get_data()
            for t, v in zip(d1, d2):
                assert np.allclose(t, v)

    n = symbols("n")
    a = S(2) / 3
    epsilon = 0.01
    xn = (n**3 + n**2)**(S(1)/3) - (n**3 - n**2)**(S(1)/3)
    expr = Abs(xn - a) - epsilon
    math_func = lambdify([n], expr)
    s1 = LineOver1DRangeSeries(expr, (n, -10, 10), "",
        adaptive=True, depth=3)
    s2 = LineOver1DRangeSeries(math_func, ("n", -10, 10), "",
        adaptive=True, depth=3)
    do_test(s1, s2)


def test_particular_case_1_with_adaptive_false():
    # Verify that symbolic expressions and numerical lambda functions are
    # evaluated with the same algorithm. In particular, uniform evaluation
    # is going to use np.vectorize, which correctly evaluates the following
    # mathematical function.
    if not np:
        skip("numpy not installed.")

    def do_test(a, b):
        d1 = a.get_data()
        d2 = b.get_data()
        for t, v in zip(d1, d2):
            assert np.allclose(t, v)

    n = symbols("n")
    a = S(2) / 3
    epsilon = 0.01
    xn = (n**3 + n**2)**(S(1)/3) - (n**3 - n**2)**(S(1)/3)
    expr = Abs(xn - a) - epsilon
    math_func = lambdify([n], expr)

    s3 = LineOver1DRangeSeries(expr, (n, -10, 10), "",
        adaptive=False, n=10)
    s4 = LineOver1DRangeSeries(math_func, ("n", -10, 10), "",
        adaptive=False, n=10)
    do_test(s3, s4)


def test_complex_params_number_eval():
    # The main expression contains terms like sqrt(xi - 1), with
    # parameter (0 <= xi <= 1).
    # There shouldn't be any NaN values on the output.
    if not np:
        skip("numpy not installed.")

    xi, wn, x0, v0, t = symbols("xi, omega_n, x0, v0, t")
    x = Function("x")(t)
    eq = x.diff(t, 2) + 2 * xi * wn * x.diff(t) + wn**2 * x
    sol = dsolve(eq, x, ics={x.subs(t, 0): x0, x.diff(t).subs(t, 0): v0})
    params = {
        wn: 0.5,
        xi: 0.25,
        x0: 0.45,
        v0: 0.0
    }
    s = LineOver1DRangeSeries(sol.rhs, (t, 0, 100), adaptive=False, n=5,
        params=params)
    x, y = s.get_data()
    assert not np.isnan(x).any()
    assert not np.isnan(y).any()


    # Fourier Series of a sawtooth wave
    # The main expression contains a Sum with a symbolic upper range.
    # The lambdified code looks like:
    #       sum(blablabla for for n in range(1, m+1))
    # But range requires integer numbers, whereas per above example, the series
    # casts parameters to complex. Verify that the series is able to detect
    # upper bounds in summations and cast it to int in order to get successful
    # evaluation
    x, T, n, m = symbols("x, T, n, m")
    fs = S(1) / 2 - (1 / pi) * Sum(sin(2 * n * pi * x / T) / n, (n, 1, m))
    params = {
        T: 4.5,
        m: 5
    }
    s = LineOver1DRangeSeries(fs, (x, 0, 10), adaptive=False, n=5,
        params=params)
    x, y = s.get_data()
    assert not np.isnan(x).any()
    assert not np.isnan(y).any()


def test_complex_range_line_plot_1():
    # verify that univariate functions are evaluated with a complex
    # data range (with zero imaginary part). There shouldn't be any
    # NaN value in the output.
    if not np:
        skip("numpy not installed.")

    x, u = symbols("x, u")
    expr1 = im(sqrt(x) * exp(-x**2))
    expr2 = im(sqrt(u * x) * exp(-x**2))
    s1 = LineOver1DRangeSeries(expr1, (x, -10, 10), adaptive=True,
        adaptive_goal=0.1)
    s2 = LineOver1DRangeSeries(expr1, (x, -10, 10), adaptive=False, n=30)
    s3 = LineOver1DRangeSeries(expr2, (x, -10, 10), adaptive=False, n=30,
        params={u: 1})

    with ignore_warnings(RuntimeWarning):
        data1 = s1.get_data()
    data2 = s2.get_data()
    data3 = s3.get_data()

    assert not np.isnan(data1[1]).any()
    assert not np.isnan(data2[1]).any()
    assert not np.isnan(data3[1]).any()
    assert np.allclose(data2[0], data3[0]) and np.allclose(data2[1], data3[1])


@XFAIL
def test_complex_range_line_plot_2():
    # verify that univariate functions are evaluated with a complex
    # data range (with non-zero imaginary part). There shouldn't be any
    # NaN value in the output.
    if not np:
        skip("numpy not installed.")

    # NOTE: xfail because sympy's adaptive algorithm is unable to deal with
    # complex number.

    x, u = symbols("x, u")

    # adaptive and uniform meshing should produce the same data.
    # because of the adaptive nature, just compare the first and last points
    # of both series.
    s1 = LineOver1DRangeSeries(abs(sqrt(x)), (x, -5-2j, 5-2j), adaptive=True)
    s2 = LineOver1DRangeSeries(abs(sqrt(x)), (x, -5-2j, 5-2j), adaptive=False,
        n=10)
    with warns(
            RuntimeWarning,
            match="invalid value encountered in sqrt",
            test_stacklevel=False,
        ):
        d1 = s1.get_data()
        d2 = s2.get_data()
        xx1 = [d1[0][0], d1[0][-1]]
        xx2 = [d2[0][0], d2[0][-1]]
        yy1 = [d1[1][0], d1[1][-1]]
        yy2 = [d2[1][0], d2[1][-1]]
        assert np.allclose(xx1, xx2)
        assert np.allclose(yy1, yy2)


def test_force_real_eval():
    # verify that force_real_eval=True produces inconsistent results when
    # compared with evaluation of complex domain.
    if not np:
        skip("numpy not installed.")

    x = symbols("x")

    expr = im(sqrt(x) * exp(-x**2))
    s1 = LineOver1DRangeSeries(expr, (x, -10, 10), adaptive=False, n=10,
        force_real_eval=False)
    s2 = LineOver1DRangeSeries(expr, (x, -10, 10), adaptive=False, n=10,
        force_real_eval=True)
    d1 = s1.get_data()
    with ignore_warnings(RuntimeWarning):
        d2 = s2.get_data()
    assert not np.allclose(d1[1], 0)
    assert np.allclose(d2[1], 0)


def test_contour_series_show_clabels():
    # verify that a contour series has the abiliy to set the visibility of
    # labels to contour lines

    x, y = symbols("x, y")
    s = ContourSeries(cos(x*y), (x, -2, 2), (y, -2, 2))
    assert s.show_clabels

    s = ContourSeries(cos(x*y), (x, -2, 2), (y, -2, 2), clabels=True)
    assert s.show_clabels

    s = ContourSeries(cos(x*y), (x, -2, 2), (y, -2, 2), clabels=False)
    assert not s.show_clabels


def test_LineOver1DRangeSeries_complex_range():
    # verify that LineOver1DRangeSeries can accept a complex range
    # if the imaginary part of the start and end values are the same

    x = symbols("x")

    LineOver1DRangeSeries(sqrt(x), (x, -10, 10))
    LineOver1DRangeSeries(sqrt(x), (x, -10-2j, 10-2j))
    raises(ValueError,
        lambda : LineOver1DRangeSeries(sqrt(x), (x, -10-2j, 10+2j)))


def test_symbolic_plotting_ranges():
    # verify that data series can use symbolic plotting ranges
    if not np:
        skip("numpy not installed.")

    x, y, z, a, b = symbols("x, y, z, a, b")

    def do_test(s1, s2, new_params):
        d1 = s1.get_data()
        d2 = s2.get_data()
        for u, v in zip(d1, d2):
            assert np.allclose(u, v)
        s2.params = new_params
        d2 = s2.get_data()
        for u, v in zip(d1, d2):
            assert not np.allclose(u, v)

    s1 = LineOver1DRangeSeries(sin(x), (x, 0, 1), adaptive=False, n=10)
    s2 = LineOver1DRangeSeries(sin(x), (x, a, b), params={a: 0, b: 1},
        adaptive=False, n=10)
    do_test(s1, s2, {a: 0.5, b: 1.5})

    # missing a parameter
    raises(ValueError,
        lambda : LineOver1DRangeSeries(sin(x), (x, a, b), params={a: 1}, n=10))

    s1 = Parametric2DLineSeries(cos(x), sin(x), (x, 0, 1), adaptive=False, n=10)
    s2 = Parametric2DLineSeries(cos(x), sin(x), (x, a, b), params={a: 0, b: 1},
        adaptive=False, n=10)
    do_test(s1, s2, {a: 0.5, b: 1.5})

    # missing a parameter
    raises(ValueError,
        lambda : Parametric2DLineSeries(cos(x), sin(x), (x, a, b),
            params={a: 0}, adaptive=False, n=10))

    s1 = Parametric3DLineSeries(cos(x), sin(x), x, (x, 0, 1),
        adaptive=False, n=10)
    s2 = Parametric3DLineSeries(cos(x), sin(x), x, (x, a, b),
        params={a: 0, b: 1}, adaptive=False, n=10)
    do_test(s1, s2, {a: 0.5, b: 1.5})

    # missing a parameter
    raises(ValueError,
        lambda : Parametric3DLineSeries(cos(x), sin(x), x, (x, a, b),
            params={a: 0}, adaptive=False, n=10))

    s1 = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -pi, pi), (y, -pi, pi),
        adaptive=False, n1=5, n2=5)
    s2 = SurfaceOver2DRangeSeries(cos(x**2 + y**2), (x, -pi * a, pi * a),
        (y, -pi * b, pi * b), params={a: 1, b: 1},
        adaptive=False, n1=5, n2=5)
    do_test(s1, s2, {a: 0.5, b: 1.5})

    # missing a parameter
    raises(ValueError,
        lambda : SurfaceOver2DRangeSeries(cos(x**2 + y**2),
        (x, -pi * a, pi * a), (y, -pi * b, pi * b), params={a: 1},
        adaptive=False, n1=5, n2=5))
    # one range symbol is included into another range's minimum or maximum val
    raises(ValueError,
        lambda : SurfaceOver2DRangeSeries(cos(x**2 + y**2),
        (x, -pi * a + y, pi * a), (y, -pi * b, pi * b), params={a: 1},
        adaptive=False, n1=5, n2=5))

    s1 = ParametricSurfaceSeries(
        cos(x - y), sin(x + y), x - y, (x, -2, 2), (y, -2, 2), n1=5, n2=5)
    s2 = ParametricSurfaceSeries(
        cos(x - y), sin(x + y), x - y, (x, -2 * a, 2), (y, -2, 2 * b),
        params={a: 1, b: 1}, n1=5, n2=5)
    do_test(s1, s2, {a: 0.5, b: 1.5})

    # missing a parameter
    raises(ValueError,
        lambda : ParametricSurfaceSeries(
        cos(x - y), sin(x + y), x - y, (x, -2 * a, 2), (y, -2, 2 * b),
        params={a: 1}, n1=5, n2=5))


def test_exclude_points():
    # verify that exclude works as expected
    if not np:
        skip("numpy not installed.")

    x = symbols("x")

    expr = (floor(x) + S.Half) / (1 - (x - S.Half)**2)

    with warns(
            UserWarning,
            match="NumPy is unable to evaluate with complex numbers some",
            test_stacklevel=False,
        ):
        s = LineOver1DRangeSeries(expr, (x, -3.5, 3.5), adaptive=False, n=100,
            exclude=list(range(-3, 4)))
        xx, yy = s.get_data()
        assert not np.isnan(xx).any()
        assert np.count_nonzero(np.isnan(yy)) == 7
        assert len(xx) > 100

    e1 = log(floor(x)) * cos(x)
    e2 = log(floor(x)) * sin(x)
    with warns(
            UserWarning,
            match="NumPy is unable to evaluate with complex numbers some",
            test_stacklevel=False,
        ):
        s = Parametric2DLineSeries(e1, e2, (x, 1, 12), adaptive=False, n=100,
            exclude=list(range(1, 13)))
        xx, yy, pp = s.get_data()
        assert not np.isnan(pp).any()
        assert np.count_nonzero(np.isnan(xx)) == 11
        assert np.count_nonzero(np.isnan(yy)) == 11
        assert len(xx) > 100


def test_unwrap():
    # verify that unwrap works as expected
    if not np:
        skip("numpy not installed.")

    x, y = symbols("x, y")
    expr = 1 / (x**3 + 2*x**2 + x)
    expr = arg(expr.subs(x, I*y*2*pi))
    s1 = LineOver1DRangeSeries(expr, (y, 1e-05, 1e05), xscale="log",
        adaptive=False, n=10, unwrap=False)
    s2 = LineOver1DRangeSeries(expr, (y, 1e-05, 1e05), xscale="log",
        adaptive=False, n=10, unwrap=True)
    s3 = LineOver1DRangeSeries(expr, (y, 1e-05, 1e05), xscale="log",
        adaptive=False, n=10, unwrap={"period": 4})
    x1, y1 = s1.get_data()
    x2, y2 = s2.get_data()
    x3, y3 = s3.get_data()
    assert np.allclose(x1, x2)
    # there must not be nan values in the results of these evaluations
    assert all(not np.isnan(t).any() for t in [y1, y2, y3])
    assert not np.allclose(y1, y2)
    assert not np.allclose(y1, y3)
    assert not np.allclose(y2, y3)