def test_harmonic():
n = Symbol("n")
assert harmonic(n, 0) == n
assert harmonic(n, 1) == harmonic(n)
assert harmonic(0, 1) == 0
assert harmonic(1, 1) == 1
assert harmonic(2, 1) == Rational(3, 2)
assert harmonic(3, 1) == Rational(11, 6)
assert harmonic(4, 1) == Rational(25, 12)
assert harmonic(0, 2) == 0
assert harmonic(1, 2) == 1
assert harmonic(2, 2) == Rational(5, 4)
assert harmonic(3, 2) == Rational(49, 36)
assert harmonic(4, 2) == Rational(205, 144)
assert harmonic(0, 3) == 0
assert harmonic(1, 3) == 1
assert harmonic(2, 3) == Rational(9, 8)
assert harmonic(3, 3) == Rational(251, 216)
assert harmonic(4, 3) == Rational(2035, 1728)
assert harmonic(oo, -1) == S.NaN
assert harmonic(oo, 0) == oo
assert harmonic(oo, S.Half) == oo
assert harmonic(oo, 1) == oo
assert harmonic(oo, 2) == (pi**2)/6
assert harmonic(oo, 3) == zeta(3)
def test_harmonic():
n = Symbol("n")
m = Symbol("m")
assert harmonic(n, 0) == n
assert harmonic(n).evalf() == harmonic(n)
assert harmonic(n, 1) == harmonic(n)
assert harmonic(1, n).evalf() == harmonic(1, n)
assert harmonic(0, 1) == 0
assert harmonic(1, 1) == 1
assert harmonic(2, 1) == Rational(3, 2)
assert harmonic(3, 1) == Rational(11, 6)
assert harmonic(4, 1) == Rational(25, 12)
assert harmonic(0, 2) == 0
assert harmonic(1, 2) == 1
assert harmonic(2, 2) == Rational(5, 4)
assert harmonic(3, 2) == Rational(49, 36)
assert harmonic(4, 2) == Rational(205, 144)
assert harmonic(0, 3) == 0
assert harmonic(1, 3) == 1
assert harmonic(2, 3) == Rational(9, 8)
assert harmonic(3, 3) == Rational(251, 216)
assert harmonic(4, 3) == Rational(2035, 1728)
assert harmonic(oo, -1) == S.NaN
assert harmonic(oo, 0) == oo
assert harmonic(oo, S.Half) == oo
assert harmonic(oo, 1) == oo
assert harmonic(oo, 2) == (pi**2) / 6
assert harmonic(oo, 3) == zeta(3)
assert harmonic(0, m) == 0
def test_tangent_sequence():
a = tangent_sequence(20)
for n, b in enumerate(a):
if n == 0:
assert b == 1
else:
f = (-16)**(n + 1) - (-4)**(n + 1)
assert b == f * zeta(-1 - 2 * n)
def test_CXX17CodePrinter():
assert CXX17CodePrinter().doprint(beta(x, y)) == 'std::beta(x, y)'
assert CXX17CodePrinter().doprint(Ei(x)) == 'std::expint(x)'
assert CXX17CodePrinter().doprint(zeta(x)) == 'std::riemann_zeta(x)'
# Automatic rewrite
assert CXX17CodePrinter().doprint(frac(x)) == 'x - std::floor(x)'
assert CXX17CodePrinter().doprint(
riemann_xi(x)
) == '(1.0/2.0)*std::pow(M_PI, -1.0/2.0*x)*x*(x - 1)*std::tgamma((1.0/2.0)*x)*std::riemann_zeta(x)'
def test_harmonic():
n = Symbol("n")
m = Symbol("m")
assert harmonic(n, 0) == n
assert harmonic(n).evalf() == harmonic(n)
assert harmonic(n, 1) == harmonic(n)
assert harmonic(1, n).evalf() == harmonic(1, n)
assert harmonic(0, 1) == 0
assert harmonic(1, 1) == 1
assert harmonic(2, 1) == Rational(3, 2)
assert harmonic(3, 1) == Rational(11, 6)
assert harmonic(4, 1) == Rational(25, 12)
assert harmonic(0, 2) == 0
assert harmonic(1, 2) == 1
assert harmonic(2, 2) == Rational(5, 4)
assert harmonic(3, 2) == Rational(49, 36)
assert harmonic(4, 2) == Rational(205, 144)
assert harmonic(0, 3) == 0
assert harmonic(1, 3) == 1
assert harmonic(2, 3) == Rational(9, 8)
assert harmonic(3, 3) == Rational(251, 216)
assert harmonic(4, 3) == Rational(2035, 1728)
assert harmonic(oo, -1) is S.NaN
assert harmonic(oo, 0) is oo
assert harmonic(oo, S.Half) is oo
assert harmonic(oo, 1) is oo
assert harmonic(oo, 2) == (pi**2) / 6
assert harmonic(oo, 3) == zeta(3)
assert harmonic(oo, Dummy(negative=True)) is S.NaN
ip = Dummy(integer=True, positive=True)
if (1 / ip <= 1) is True: #---------------------------------+
assert None, 'delete this if-block and the next line' #|
ip = Dummy(even=True, positive=True) #--------------------+
assert harmonic(oo, 1 / ip) is oo
assert harmonic(oo, 1 + ip) is zeta(1 + ip)
assert harmonic(0, m) == 0
def test_zeta_printing_issue_14820():
assert octave_code(zeta(x)) == 'zeta(x)'
assert octave_code(zeta(
x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
def test_harmonic_limit_fail():
n = Symbol("n")
m = Symbol("m")
# For m > 1:
assert limit(harmonic(n, m), n, oo) == zeta(m)
def test_harmonic_limit_fail():
n = Symbol("n")
m = Symbol("m")
# For m > 1:
assert limit(harmonic(n, m), n, oo) == zeta(m)
def test_CXX17CodePrinter():
assert CXX17CodePrinter().doprint(beta(x, y)) == "std::beta(x, y)"
assert CXX17CodePrinter().doprint(Ei(x)) == "std::expint(x)"
assert CXX17CodePrinter().doprint(zeta(x)) == "std::riemann_zeta(x)"
def test_zeta_printing_issue_14820():
assert octave_code(zeta(x)) == 'zeta(x)'
assert octave_code(zeta(x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
def test_CXX17CodePrinter():
assert CXX17CodePrinter().doprint(beta(x, y)) == 'std::beta(x, y)'
assert CXX17CodePrinter().doprint(Ei(x)) == 'std::expint(x)'
assert CXX17CodePrinter().doprint(zeta(x)) == 'std::riemann_zeta(x)'
