def gauss_to_string(l, m, numeric=False):
"""Return string representation of the generalized gaussian::
_____ 2
m / 1 l! l+3/2 -a r l m
g (x,y,z) = / ----- --------- (4 a) e r Y (x,y,z)
l \/ 4 pi (2l + 1)! l
numeric=True/False indicates whether the normalization constant should
be written as a number or an algebraic expression.
"""
norm, xyzs = Y_collect(l, m)
ng = Q(2**(2*l+3) * factorial(l), 2 * factorial(2 * l + 1))
norm.multiply(ng)
string = to_string(l, xyzs)
string = (' * ' + string) * (string != '1')
if numeric:
snorm = repr(eval(repr(norm.norm)))
else:
snorm = repr(norm.norm)
string = 'sqrt(a**%s*%s)/pi'%(2*l+3, snorm) + string
string += ' * exp(-a*r2)'
return string
def gauss_to_string(l, m, numeric=False):
"""Return string representation of the generalized gaussian::
_____ 2
m / 1 l! l+3/2 -a r l m
g (x,y,z) = / ----- --------- (4 a) e r Y (x,y,z)
l \/ 4 pi (2l + 1)! l
numeric=True/False indicates whether the normalization constant should
be written as a number or an algebraic expression.
"""
norm, xyzs = Y_collect(l, m)
ng = Q(2**(2 * l + 3) * factorial(l), 2 * factorial(2 * l + 1))
norm.multiply(ng)
string = to_string(l, xyzs)
string = (' * ' + string) * (string != '1')
if numeric:
snorm = repr(eval(repr(norm.norm)))
else:
snorm = repr(norm.norm)
string = 'sqrt(a**%s*%s)/pi' % (2 * l + 3, snorm) + string
string += ' * exp(-a*r2)'
return string
def get(n):
# n! / ((n/2 !) * (n/2 !)) = (n * (n-1) * (n-2) * (n-3) .... ((n/2)+1)) / ((n/2)!)
# ------------------ t ---------------------
t = 1
for i in range(n, int(n / 2), -1):
t *= i
return int(t / factorial(int(n / 2)))
def __init__(self, l, m):
m = abs(m)
if m == 0:
self.norm = Q(2 * l + 1, 4)
else:
self.norm = Q((2 * l + 1) * factorial(l - m), 2 * factorial(l + m))
def perm(l, n):
if len(l) <= 1:
return l
fct = factorial(len(l) - 1)
q, r = n / fct, n % fct
return [l[q]] + perm(l[:q] + l[q + 1 :], r)
from tools import factorial print sum([ int(n) for n in str(factorial(100))])
import tools
limit = tools.factorial(9)*7
i = 10
results = []
while i<=limit:
s = str(i)
if i < tools.factorial(9) and ('9' in s):
i += 1
continue
if i < tools.factorial(8) and ('8' in s):
i += 1
continue
if i < tools.factorial(7) and ('7' in s):
i += 1
continue
summa = 0
for x in [int(c) for c in s]:
summa += tools.factorial(x)
if summa > i:
break
if summa == i:
results.append(i)
print sum(results)
i += 1
print sum(results)
import tools
results = 0
for n in range(23, 101):
nf = tools.factorial(n)
if nf <= 1000000:
continue
for r in range(2, n + 1):
rf = tools.factorial(r)
if nf / rf <= 1000000:
continue
if nf / rf / tools.factorial(n - r) > 1000000:
results += 1
print results
def __init__(self, l, m):
m = abs(m)
if m == 0:
self.norm = Q(2 * l + 1, 4)
else:
self.norm = Q((2 * l + 1) * factorial(l - m), 2 * factorial(l + m))
from tools import factorial
#Precalculate factorials of 0..9
FACTORIAL = {}
for i in range(0, 10):
FACTORIAL[str(i)] = factorial(i)
UPPER_BOUND = 7 * FACTORIAL['9'] + 1
s = 0
for i in xrange(10, UPPER_BOUND, 1):
if sum(FACTORIAL[c] for c in str(i)) == i:
s += i
print s
def factsum(x): s = 0 while x: s += tools.factorial(x%10) x /= 10 return s
def pe020():
"""# Find the digit-sum of '100!'"""
from tools import factorial, digitSum
return digitSum(factorial(100))