Python RootOf.epsilon_eq示例

示例#1

文件： test_rootoftools.py 项目： lucasvinhas/sympy

def test_RootOf_evalf():
    real = RootOf(x**3 + x + 3, 0).evalf(n=20)

    assert real.epsilon_eq(Float("-1.2134116627622296341"))

    re, im = RootOf(x**3 + x + 3, 1).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(-Float("1.45061224918844152650"))

    re, im = RootOf(x**3 + x + 3, 2).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(Float("1.45061224918844152650"))

示例#2

文件： test_rootoftools.py 项目： BDGLunde/sympy

def test_RootOf_evalf():
    real = RootOf(x**3 + x + 3, 0).evalf(n=20)

    assert real.epsilon_eq(Float("-1.2134116627622296341"))

    re, im = RootOf(x**3 + x + 3, 1).evalf(n=20).as_real_imag()

    assert re.epsilon_eq( Float("0.60670583138111481707"))
    assert im.epsilon_eq(-Float("1.45061224918844152650"))

    re, im = RootOf(x**3 + x + 3, 2).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(Float("1.45061224918844152650"))

示例#3

文件： test_rootoftools.py 项目： Bercio/sympy

def test_RootOf_evalf():
    real = RootOf(x**3 + x + 3, 0).evalf(n=20)

    assert real.epsilon_eq(Float("-1.2134116627622296341"))

    re, im = RootOf(x**3 + x + 3, 1).evalf(n=20).as_real_imag()

    assert re.epsilon_eq( Float("0.60670583138111481707"))
    assert im.epsilon_eq(-Float("1.45061224918844152650"))

    re, im = RootOf(x**3 + x + 3, 2).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(Float("1.45061224918844152650"))

    p = legendre_poly(4, x, polys=True)
    roots = [str(r.n(17)) for r in p.real_roots()]
    assert roots == [
            "-0.86113631159405258",
            "-0.33998104358485626",
             "0.33998104358485626",
             "0.86113631159405258",
             ]

    re = RootOf(x**5 - 5*x + 12, 0).evalf(n=20)
    assert re.epsilon_eq(Float("-1.84208596619025438271"))

    re, im = RootOf(x**5 - 5*x + 12, 1).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("-1.709561043370328882010"))

    re, im = RootOf(x**5 - 5*x + 12, 2).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("+1.709561043370328882010"))

    re, im = RootOf(x**5 - 5*x + 12, 3).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("-0.719798681483861386681"))

    re, im = RootOf(x**5 - 5*x + 12, 4).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("+0.719798681483861386681"))

示例#4

文件： test_rootoftools.py 项目： wuxi20/Pythonista

def test_RootOf_evalf():
    real = RootOf(x**3 + x + 3, 0).evalf(n=20)

    assert real.epsilon_eq(Float("-1.2134116627622296341"))

    re, im = RootOf(x**3 + x + 3, 1).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(-Float("1.45061224918844152650"))

    re, im = RootOf(x**3 + x + 3, 2).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(Float("1.45061224918844152650"))

    p = legendre_poly(4, x, polys=True)
    roots = [str(r.n(17)) for r in p.real_roots()]
    assert roots == [
        "-0.86113631159405258",
        "-0.33998104358485626",
        "0.33998104358485626",
        "0.86113631159405258",
    ]

    re = RootOf(x**5 - 5 * x + 12, 0).evalf(n=20)
    assert re.epsilon_eq(Float("-1.84208596619025438271"))

    re, im = RootOf(x**5 - 5 * x + 12, 1).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("-1.709561043370328882010"))

    re, im = RootOf(x**5 - 5 * x + 12, 2).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("+1.709561043370328882010"))

    re, im = RootOf(x**5 - 5 * x + 12, 3).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("-0.719798681483861386681"))

    re, im = RootOf(x**5 - 5 * x + 12, 4).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("+0.719798681483861386681"))

示例#5

def test_RootOf_evalf():
    real = RootOf(x**3 + x + 3, 0).evalf(n=20)

    assert real.epsilon_eq(Float("-1.2134116627622296341"))

    re, im = RootOf(x**3 + x + 3, 1).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(-Float("1.45061224918844152650"))

    re, im = RootOf(x**3 + x + 3, 2).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(Float("1.45061224918844152650"))

    p = legendre_poly(4, x, polys=True)
    roots = [str(r.n(17)) for r in p.real_roots()]
    assert roots == [
        "-0.86113631159405258",
        "-0.33998104358485626",
        "0.33998104358485626",
        "0.86113631159405258",
    ]

    re = RootOf(x**5 - 5 * x + 12, 0).evalf(n=20)
    assert re.epsilon_eq(Float("-1.84208596619025438271"))

    re, im = RootOf(x**5 - 5 * x + 12, 1).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("-1.709561043370328882010"))

    re, im = RootOf(x**5 - 5 * x + 12, 2).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("+1.709561043370328882010"))

    re, im = RootOf(x**5 - 5 * x + 12, 3).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("-0.719798681483861386681"))

    re, im = RootOf(x**5 - 5 * x + 12, 4).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("+0.719798681483861386681"))

    # issue 6393
    assert str(RootOf(x**5 + 2 * x**4 + x**3 - 68719476736, 0).n(3)) == '147.'
    eq = (531441 * x**11 + 3857868 * x**10 + 13730229 * x**9 +
          32597882 * x**8 + 55077472 * x**7 + 60452000 * x**6 +
          32172064 * x**5 - 4383808 * x**4 - 11942912 * x**3 - 1506304 * x**2 +
          1453312 * x + 512)
    a, b = RootOf(eq, 1).n(2).as_real_imag()
    c, d = RootOf(eq, 2).n(2).as_real_imag()
    assert a == c
    assert b < d
    assert b == -d
    # issue 6451
    r = RootOf(legendre_poly(64, x), 7)
    assert r.n(2) == r.n(100).n(2)
    # issue 8617
    ans = [w.n(2) for w in solve(x**3 - x - 4)]
    assert RootOf(exp(x)**3 - exp(x) - 4, 0).n(2) in ans
    # issue 9019
    r0 = RootOf(x**2 + 1, 0, radicals=False)
    r1 = RootOf(x**2 + 1, 1, radicals=False)
    assert r0.n(4) == -1.0 * I
    assert r1.n(4) == 1.0 * I

    # make sure verification is used in case a max/min traps the "root"
    assert str(RootOf(4 * x**5 + 16 * x**3 + 12 * x**2 + 7,
                      0).n(3)) == '-0.976'

示例#6

文件： test_rootoftools.py 项目： rahvar/sympy

def test_RootOf_evalf():
    real = RootOf(x**3 + x + 3, 0).evalf(n=20)

    assert real.epsilon_eq(Float("-1.2134116627622296341"))

    re, im = RootOf(x**3 + x + 3, 1).evalf(n=20).as_real_imag()

    assert re.epsilon_eq( Float("0.60670583138111481707"))
    assert im.epsilon_eq(-Float("1.45061224918844152650"))

    re, im = RootOf(x**3 + x + 3, 2).evalf(n=20).as_real_imag()

    assert re.epsilon_eq(Float("0.60670583138111481707"))
    assert im.epsilon_eq(Float("1.45061224918844152650"))

    p = legendre_poly(4, x, polys=True)
    roots = [str(r.n(17)) for r in p.real_roots()]
    assert roots == [
            "-0.86113631159405258",
            "-0.33998104358485626",
             "0.33998104358485626",
             "0.86113631159405258",
             ]

    re = RootOf(x**5 - 5*x + 12, 0).evalf(n=20)
    assert re.epsilon_eq(Float("-1.84208596619025438271"))

    re, im = RootOf(x**5 - 5*x + 12, 1).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("-1.709561043370328882010"))

    re, im = RootOf(x**5 - 5*x + 12, 2).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("-0.351854240827371999559"))
    assert im.epsilon_eq(Float("+1.709561043370328882010"))

    re, im = RootOf(x**5 - 5*x + 12, 3).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("-0.719798681483861386681"))

    re, im = RootOf(x**5 - 5*x + 12, 4).evalf(n=20).as_real_imag()
    assert re.epsilon_eq(Float("+1.272897223922499190910"))
    assert im.epsilon_eq(Float("+0.719798681483861386681"))

    # issue 6393
    assert str(RootOf(x**5 + 2*x**4 + x**3 - 68719476736, 0).n(3)) == '147.'
    eq = (531441*x**11 + 3857868*x**10 + 13730229*x**9 + 32597882*x**8 +
        55077472*x**7 + 60452000*x**6 + 32172064*x**5 - 4383808*x**4 -
        11942912*x**3 - 1506304*x**2 + 1453312*x + 512)
    a, b = RootOf(eq, 1).n(2).as_real_imag()
    c, d = RootOf(eq, 2).n(2).as_real_imag()
    assert a == c
    assert b < d
    assert b == -d
    # issue 6451
    r = RootOf(legendre_poly(64, x), 7)
    assert r.n(2) == r.n(100).n(2)
    # issue 8617
    ans = [w.n(2) for w in solve(x**3 - x - 4)]
    assert RootOf(exp(x)**3 - exp(x) - 4, 0).n(2) in ans

    # make sure verification is used in case a max/min traps the "root"
    assert str(RootOf(4*x**5 + 16*x**3 + 12*x**2 + 7, 0).n(3)) == '-0.976'