def test_RootOf_evalf_caching_bug():
r = RootOf(x**5 - 5 * x + 12, 1)
r.evalf()
a = r.interval
r = RootOf(x**5 - 5 * x + 12, 1)
r.evalf()
b = r.interval
assert a == b
def test_RootOf_evalf_caching_bug():
r = RootOf(x**5 - 5*x + 12, 1)
r.evalf()
a = r.interval
r = RootOf(x**5 - 5*x + 12, 1)
r.evalf()
b = r.interval
assert a == b
def test_RootOf_eval_rational():
p = legendre_poly(4, x, polys=True)
roots = [r.eval_rational(Rational(1, 10)**20) for r in p.real_roots()]
for r in roots:
assert isinstance(r, Rational)
# All we know is that the Rational instance will be at most 1/10^20 from
# the exact root. So if we evaluate to 17 digits, it must be exactly equal
# to:
roots = [str(r.evalf(17)) for r in roots]
assert roots == [
"-0.86113631159405258",
"-0.33998104358485626",
"0.33998104358485626",
"0.86113631159405258",
]
pytest.raises(NotImplementedError,
lambda: RootOf(x**3 + x + 3, 1).eval_rational(1e-3))
def test_RootOf_eval_rational():
p = legendre_poly(4, x, polys=True)
roots = [r.eval_rational(Rational(1, 10)**20) for r in p.real_roots()]
for r in roots:
assert isinstance(r, Rational)
# All we know is that the Rational instance will be at most 1/10^20 from
# the exact root. So if we evaluate to 17 digits, it must be exactly equal
# to:
roots = [str(r.evalf(17)) for r in roots]
assert roots == [
"-0.86113631159405258",
"-0.33998104358485626",
"0.33998104358485626",
"0.86113631159405258",
]
pytest.raises(NotImplementedError,
lambda: RootOf(x**3 + x + 3, 1).eval_rational(1e-3))
def test_RootOf_evalf():
real = RootOf(x**3 + x + 3, 0).evalf(20)
assert real.epsilon_eq(Float("-1.2134116627622296341"))
re, im = RootOf(x**3 + x + 3, 1).evalf(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(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.evalf(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(20)
assert re.epsilon_eq(Float("-1.84208596619025438271"))
re, im = RootOf(x**5 - 5 * x + 12, 1).evalf(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(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(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(20).as_real_imag()
assert re.epsilon_eq(Float("+1.272897223922499190910"))
assert im.epsilon_eq(Float("+0.719798681483861386681"))
# issue sympy/sympy#6393
assert str(RootOf(x**5 + 2 * x**4 + x**3 - 68719476736,
0).evalf(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).evalf(2).as_real_imag()
c, d = RootOf(eq, 2).evalf(2).as_real_imag()
assert a == c
assert b < d
assert b == -d
# issue sympy/sympy#6451
r = RootOf(legendre_poly(64, x), 7)
assert r.evalf(2) == r.evalf(100).evalf(2)
# issue sympy/sympy#8617
ans = [w[x].evalf(2) for w in solve(x**3 - x - 4)]
assert RootOf(exp(x)**3 - exp(x) - 4, 0).evalf(2) in ans
# issue sympy/sympy#9019
r0 = RootOf(x**2 + 1, 0, radicals=False)
r1 = RootOf(x**2 + 1, 1, radicals=False)
assert r0.evalf(4, chop=True) == -1.0 * I
assert r1.evalf(4, chop=True) == +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).evalf(3)) == '-0.976'
assert isinstance(RootOf(x**3 + y * x + 1, x, 0).evalf(2), RootOf)
assert RootOf(x**3 + I * x + 2,
0).evalf(7) == (Float('-1.260785326', dps=7) +
I * Float('0.2684419416', dps=7))
r = RootOf(x**2 - 4456178 * x + 60372201703370, 0, radicals=False)
assert r.evalf(2) == Float('2.2282e+6',
dps=2) - I * Float('7.4465e+6', dps=2)
def test_RootOf_evalf():
real = RootOf(x**3 + x + 3, 0).evalf(20)
assert real.epsilon_eq(Float("-1.2134116627622296341"))
re, im = RootOf(x**3 + x + 3, 1).evalf(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(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.evalf(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(20)
assert re.epsilon_eq(Float("-1.84208596619025438271"))
re, im = RootOf(x**5 - 5*x + 12, 1).evalf(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(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(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(20).as_real_imag()
assert re.epsilon_eq(Float("+1.272897223922499190910"))
assert im.epsilon_eq(Float("+0.719798681483861386681"))
# issue sympy/sympy#6393
assert str(RootOf(x**5 + 2*x**4 + x**3 - 68719476736, 0).evalf(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).evalf(2).as_real_imag()
c, d = RootOf(eq, 2).evalf(2).as_real_imag()
assert a == c
assert b < d
assert b == -d
# issue sympy/sympy#6451
r = RootOf(legendre_poly(64, x), 7)
assert r.evalf(2) == r.evalf(100).evalf(2)
# issue sympy/sympy#8617
ans = [w[x].evalf(2) for w in solve(x**3 - x - 4)]
assert RootOf(exp(x)**3 - exp(x) - 4, 0).evalf(2) in ans
# issue sympy/sympy#9019
r0 = RootOf(x**2 + 1, 0, radicals=False)
r1 = RootOf(x**2 + 1, 1, radicals=False)
assert r0.evalf(4, chop=True) == -1.0*I
assert r1.evalf(4, chop=True) == +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).evalf(3)) == '-0.976'
assert isinstance(RootOf(x**3 + y*x + 1, x, 0).evalf(2), RootOf)
assert RootOf(x**3 + I*x + 2, 0).evalf(7) == (Float('-1.260785326', dps=7) +
I*Float('0.2684419416', dps=7))
r = RootOf(x**2 - 4456178*x + 60372201703370, 0, radicals=False)
assert r.evalf(2) == Float('2.2282e+6', dps=2) - I*Float('7.4465e+6', dps=2)