def test_sincos_rewrite_sqrt():
for p in [1, 3, 5, 17]:
for t in [1, 8]:
n = t*p
for i in range(1, (n + 1)//2 + 1):
if 1 == gcd(i, n):
x = i*pi/n
s1 = sin(x).rewrite(sqrt)
c1 = cos(x).rewrite(sqrt)
assert not s1.has(cos, sin), f'fails for {i:d}*pi/{n:d}'
assert not c1.has(cos, sin), f'fails for {i:d}*pi/{n:d}'
assert 1e-3 > abs(sin(x.evalf(5)) - s1.evalf(2)), f'fails for {i:d}*pi/{n:d}'
assert 1e-3 > abs(cos(x.evalf(5)) - c1.evalf(2)), f'fails for {i:d}*pi/{n:d}'
def test_tancot_rewrite_sqrt():
for p in [1, 3, 5, 17]:
for t in [1, 8]:
n = t*p
for i in range(1, (n + 1)//2 + 1):
if 1 == gcd(i, n):
x = i*pi/n
if 2*i != n and 3*i != 2*n:
t1 = tan(x).rewrite(sqrt)
assert not t1.has(cot, tan), f'fails for {i:d}*pi/{n:d}'
assert 1e-3 > abs( tan(x.evalf(7)) - t1.evalf(4) ), f'fails for {i:d}*pi/{n:d}'
if i != 0 and i != n:
c1 = cot(x).rewrite(sqrt)
assert not c1.has(cot, tan), f'fails for {i:d}*pi/{n:d}'
assert 1e-3 > abs( cot(x.evalf(7)) - c1.evalf(4) ), f'fails for {i:d}*pi/{n:d}'
def t(m, n):
x = Integer(m) / n
r = polygamma(0, x)
if r.has(polygamma):
return False
return abs(polygamma(0, x.evalf()).evalf(strict=False) -
r.evalf()).evalf(strict=False) < 1e-10
def test_evalf_bugs():
assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10)
assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10)
assert NS('log(1+1/10**50)', 20) == '1.0000000000000000000e-50'
assert NS('log(10**100,10)', 10) == '100.0000000'
assert NS('log(2)', 10) == '0.6931471806'
assert NS(
'(sin(x)-x)/x**3', 15, subs={x: '1/10**50'}) == '-0.166666666666667'
assert NS(sin(1) + Rational(
1, 10**100)*I, 15) == '0.841470984807897 + 1.00000000000000e-100*I'
assert x.evalf() == x
assert NS((1 + I)**2*I, 6) == '-2.00000'
d = {n: (
-1)**Rational(6, 7), y: (-1)**Rational(4, 7), x: (-1)**Rational(2, 7)}
assert NS((x*(1 + y*(1 + n))).subs(d).evalf(), 6) == '0.346011 + 0.433884*I'
assert NS(((-I - sqrt(2)*I)**2).evalf()) == '-5.82842712474619'
assert NS((1 + I)**2*I, 15) == '-2.00000000000000'
# issue sympy/sympy#4758 (1/2):
assert NS(Float(pi.evalf(69), 100) - pi) == '-4.43863937855894e-71'
assert NS(pi.evalf(69) - pi) == '-0.e-71'
# issue sympy/sympy#4758 (2/2): With the bug present, this still only fails if the
# terms are in the order given here. This is not generally the case,
# because the order depends on the hashes of the terms.
assert NS(20 - 5008329267844*n**25 - 477638700*n**37 - 19*n,
subs={n: .01}) == '19.8100000000000'
assert NS(((x - 1)*((1 - x))**1000).n()
) == '(-x + 1.00000000000000)**1000*(x - 1.00000000000000)'
assert NS((-x).n()) == '-x'
assert NS((-2*x).n()) == '-2.00000000000000*x'
assert NS((-2*x*y).n()) == '-2.00000000000000*x*y'
assert cos(x).n(subs={x: 1+I}) == cos(x).subs(x, 1+I).n()
# issue sympy/sympy#6660. Also NaN != mpmath.nan
# In this order:
# 0*nan, 0/nan, 0*inf, 0/inf
# 0+nan, 0-nan, 0+inf, 0-inf
# >>> n = Some Number
# n*nan, n/nan, n*inf, n/inf
# n+nan, n-nan, n+inf, n-inf
assert (0*sin(oo)).n() == S.Zero
assert (0/sin(oo)).n() == S.Zero
assert (0*E**(oo)).n() == S.NaN
assert (0/E**(oo)).n() == S.Zero
assert (0+sin(oo)).n() == S.NaN
assert (0-sin(oo)).n() == S.NaN
assert (0+E**(oo)).n() == S.Infinity
assert (0-E**(oo)).n() == S.NegativeInfinity
assert (5*sin(oo)).n() == S.NaN
assert (5/sin(oo)).n() == S.NaN
assert (5*E**(oo)).n() == S.Infinity
assert (5/E**(oo)).n() == S.Zero
assert (5+sin(oo)).n() == S.NaN
assert (5-sin(oo)).n() == S.NaN
assert (5+E**(oo)).n() == S.Infinity
assert (5-E**(oo)).n() == S.NegativeInfinity
# issue sympy/sympy#7416
assert as_mpmath(0.0, 10, {'chop': True}) == 0
def test_subs():
assert NS('besseli(-x, y) - besseli(x, y)', subs={x: 3.5, y: 20.0}) == \
'-4.92535585957223e-10'
assert NS('Piecewise((x, x>0)) + Piecewise((1-x, x>0))', subs={x: 0.1}) == \
'1.00000000000000'
pytest.raises(TypeError, lambda: x.evalf(subs=(x, 1)))
def test_evalf_bugs():
assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10)
assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10)
assert NS('log(1+1/10**50)', 20) == '1.0000000000000000000e-50'
assert NS('log(10**100,10)', 10) == '100.0000000'
assert NS('log(2)', 10) == '0.6931471806'
assert NS(
'(sin(x)-x)/x**3', 15, subs={x: '1/10**50'}) == '-0.166666666666667'
assert NS(sin(1) + I/10**100, 15) == '0.841470984807897 + 1.00000000000000e-100*I'
assert x.evalf(strict=False) == x
assert NS((1 + I)**2*I, 6) == '-2.00000'
d = {n: (
-1)**Rational(6, 7), y: (-1)**Rational(4, 7), x: (-1)**Rational(2, 7)}
assert NS((x*(1 + y*(1 + n))).subs(d).evalf(), 6) == '0.346011 + 0.433884*I'
assert NS(((-I - sqrt(2)*I)**2).evalf(), strict=False) == '-5.82842712474619'
assert NS((1 + I)**2*I, 15) == '-2.00000000000000'
# issue sympy/sympy#4758 (1/2):
assert NS(Float(pi.evalf(69), 100) - pi) == '-4.43863937855894e-71'
assert NS(pi.evalf(69) - pi, strict=False) == '-0.e-71'
# issue sympy/sympy#4758 (2/2): With the bug present, this still only fails if the
# terms are in the order given here. This is not generally the case,
# because the order depends on the hashes of the terms.
assert NS(20 - 5008329267844*n**25 - 477638700*n**37 - 19*n,
subs={n: .01}, strict=False) == '19.8100000000000'
assert NS(((x - 1)*((1 - x))**1000).evalf(strict=False),
strict=False) == '(-x + 1.00000000000000)**1000*(x - 1.00000000000000)'
assert NS((-x).evalf(strict=False)) == '-x'
assert NS((-2*x).evalf(strict=False), strict=False) == '-2.00000000000000*x'
assert NS((-2*x*y).evalf(strict=False), strict=False) == '-2.00000000000000*x*y'
assert cos(x).evalf(subs={x: 1+I}) == cos(x).subs({x: 1 + I}).evalf()
# issue sympy/sympy#6660. Also NaN != mpmath.nan
# In this order:
# 0*nan, 0/nan, 0*inf, 0/inf
# 0+nan, 0-nan, 0+inf, 0-inf
# >>> n = Some Number
# n*nan, n/nan, n*inf, n/inf
# n+nan, n-nan, n+inf, n-inf
assert (0*sin(oo)).evalf() == 0
assert (0/sin(oo)).evalf() == 0
assert (0*E**oo).evalf() == nan
assert (0/E**oo).evalf() == 0
assert (0+sin(oo)).evalf() == nan
assert (0-sin(oo)).evalf() == nan
assert (0+E**oo).evalf() == +oo
assert (0-E**oo).evalf() == -oo
assert (5*sin(oo)).evalf() == nan
assert (5/sin(oo)).evalf() == nan
assert (5*E**oo).evalf() == oo
assert (5/E**oo).evalf() == 0
assert (5+sin(oo)).evalf() == nan
assert (5-sin(oo)).evalf() == nan
assert (5+E**oo).evalf() == +oo
assert (5-E**oo).evalf() == -oo
# issue sympy/sympy#7416
assert as_mpmath(0.0, 10, {'chop': True}) == 0
# issue sympy/sympy#5412
assert (oo*I).evalf() == oo*I
assert (oo + oo*I).evalf() == oo + oo*I
def test_subs():
assert NS('besseli(-x, y) - besseli(x, y)', subs={x: 3.5, y: 20.0}) == \
'-4.92535585957223e-10'
assert NS('Piecewise((x, x>0)) + Piecewise((1-x, x>0))', subs={x: 0.1}) == \
'1.00000000000000'
pytest.raises(TypeError, lambda: x.evalf(subs=(x, 1)))
