def test_RootOf_evalf_caching_bug():
r = RootOf(x**5 - 5 * x + 12, 1)
r.n()
a = r._get_interval()
r = RootOf(x**5 - 5 * x + 12, 1)
r.n()
b = r._get_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.n(17)) for r in roots]
assert roots == [
"-0.86113631159405258",
"-0.33998104358485626",
"0.33998104358485626",
"0.86113631159405258",
]
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 sympy/sympy#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 sympy/sympy#6451
r = RootOf(legendre_poly(64, x), 7)
assert r.n(2) == r.n(100).n(2)
# issue sympy/sympy#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 sympy/sympy#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'
assert isinstance(RootOf(x**3 + y * x + 1, x, 0).n(2), RootOf)