def test_FunctionWrapper():
import sympy
sympy.var("n, m, theta, phi")
r = sympy.Ynm(n, m, theta, phi)
s = Integer(2) * r
assert isinstance(s, Mul)
assert isinstance(s.args[1]._sympy_(), sympy.Ynm)
def test_FunctionWrapper():
import sympy
n, m, theta, phi = sympy.symbols("n, m, theta, phi")
r = sympy.Ynm(n, m, theta, phi)
s = Integer(2) * r
assert isinstance(s, Mul)
assert isinstance(s.args[1]._sympy_(), sympy.Ynm)
x = symbols("x")
e = x + sympy.loggamma(x)
assert str(e) == "x + loggamma(x)"
assert isinstance(e, Add)
assert e + sympy.loggamma(x) == x + 2 * sympy.loggamma(x)
f = e.subs({x: 10})
assert f == 10 + log(362880)
f = e.subs({x: 2})
assert f == 2
f = e.subs({x: 100})
v = f.n(53, real=True)
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x)
assert f == 1 + sympy.polygamma(0, x)
def _get_cartfn(l, m):
"""Return the reference result in Cartesian coordinates with SymPy."""
# Take the complex spherical harmonics from SymPy and write in terms
# of simple trigoniometric functions.
ref = sp.Ynm(l, abs(m), theta, phi)
ref = ref.expand(func=True)
ref = ref.subs(sp.exp(sp.I * phi), sp.cos(phi) + sp.I * sp.sin(phi))
# Take the definition of real functions from Wikipedia, not from
# SymPy. The latter has an incompatible sign for the sin-like
# functions.
if m > 0:
ref = sp.re(ref) * sp.sqrt(2)
elif m < 0:
ref = sp.im(ref) * sp.sqrt(2)
# Undo the Condon-Shortley phase
ref *= (-sp.Integer(1))**abs(m)
# Convert to regular solid harmonics
ref = (sp.sqrt(4 * sp.pi / (2 * l + 1)) * ref * r**l).expand()
# From spherical to Cartesian coordinates
ref = ref.subs(sp.cos(phi), x / (r * sp.sin(theta)))
ref = ref.subs(sp.sin(phi), y / (r * sp.sin(theta)))
ref = ref.subs(sp.cos(theta), z / r)
ref = ref.subs(sp.sin(theta), sp.sqrt(x * x + y * y) / r)
ref = ref.subs(r, sp.sqrt(r2)).expand()
return sp.simplify(ref).expand()
def test_FunctionWrapper():
import sympy
n, m, theta, phi = sympy.symbols("n, m, theta, phi")
r = sympy.Ynm(n, m, theta, phi)
s = Integer(2) * r
assert isinstance(s, Mul)
assert isinstance(s.args[1]._sympy_(), sympy.Ynm)
x = symbols("x")
e = x + sympy.Mod(x, 2)
assert str(e) == "x + Mod(x, 2)"
assert isinstance(e, Add)
assert e + sympy.Mod(x, 2) == x + 2 * sympy.Mod(x, 2)
f = e.subs({x: 10})
assert f == 10
f = e.subs({x: 2})
assert f == 2
f = e.subs({x: 100})
v = f.n(53, real=True)
assert abs(float(v) - 100.00000000) < 1e-7