def test_composite_sums():
f = Rational(1, 2)*(7 - 6*n + Rational(1, 7)*n**3)
s = summation(f, (n, a, b))
assert not isinstance(s, Sum)
A = 0
for i in range(-3, 5):
A += f.subs(n, i)
B = s.subs(a, -3).subs(b, 4)
assert A == B
def test_composite_sums():
f = Rational(1, 2) * (7 - 6 * n + Rational(1, 7) * n**3)
s = summation(f, (n, a, b))
assert not isinstance(s, Sum)
A = 0
for i in range(-3, 5):
A += f.subs(n, i)
B = s.subs(a, -3).subs(b, 4)
assert A == B
def rge1L(N, BSMfermions=[], BSMscalars=[], num=False):
"""One loop RGE coefficient."""
a = Rational(-11, 3) * CA(N)
for rep in SMfermions + BSMfermions:
a += Rational(4, 3) * rep.wS2(N)
for rep in SMscalars + BSMscalars:
a += Rational(1, 3) * rep.wS2(N)
if num:
return float(a.subs({ng: 3, nh: 1}))
else:
return a
print alphavar, nvar, LaguerreP.subs(n, nvar).subs(alpha, alphavar).doit(), LaguerreP.subs(n, nvar).subs(
alpha, alphavar
).doit() == laguerre_poly(
nvar, x, alpha=alphavar
) # True
(LaguerreF.subs(n, n + 1) / LaguerreF).simplify() # (alpha + n + 1)/(-k + n + 1)
(LaguerreF.subs(k, k + 1) / LaguerreF).simplify() # x*(k - n)/((k + 1)*(alpha + k + 1))
LegendreF = Rat(1) / (Rat(2) ** n) * (binomial(n, k)) ** 2 * (x - Rat(1)) ** k * (x + Rat(1)) ** (n - k)
LegendreP = Sum(LegendreF, (k, 0, n))
for nvar in range(4):
legendre_poly(nvar, x) == LegendreP.subs(n, nvar).doit().expand() # True
(LegendreF.subs(n, n + 1) / LegendreF).simplify() # (n + 1)**2*(x + 1)/(2*(k - n - 1)**2)
(LegendreF.subs(k, k + 1) / LegendreF).simplify() # (k - n)**2*(x - 1)/((k + 1)**2*(x + 1))
JacobiF = (
Rat(1)
/ (Rat(2) ** n)
* binomial(n + alpha, n - k)
* binomial(n + beta, k)
* (x - Rat(1)) ** k
* (x + Rat(1)) ** (n - k)
)
JacobiP = Sum(JacobiF, (k, 0, n))
for alphvar in range(5):
for betvar in range(5):
for nvar in range(5):
jacobi_poly(nvar, alphvar, betvar, x) == JacobiP.subs(n, nvar).subs(alpha, alphvar).subs(
