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)