http://projecteuler.net/problem=101
#euler 101
# let's use numpy for our linear algebra matrix operations
import math
from numpy import *
# we'll use the array data structure for vectors, matrix
# multiplication, and inverses
#tenth polynomial generating function (and the test cube function)
def polyTerm(n):
return int(1 - n + n*n - math.pow(n,3) + math.pow(n,4) - math.pow(n,5) + math.pow(n,6) - math.pow(n,7) + math.pow(n,8) - math.pow(n,9) + math.pow(n,10))
def cubethis(n):
return n*n*n
poly = {}
for i in range(1, 11):
poly[i] = polyTerm(i)
cube = {}
for i in range(1, 11):
cube[i] = cubethis(i)
def matr(n): # returns square matrix nxn
output = []
for i in range(n): # i is rows
temp = [int(math.pow(x+1, i)) for x in range(n)]
output.append(temp)
a = array(output).transpose()
return a
def opCalc(n, sequence): # takes n from 2 to length of sequence
if n == 1:
return sequence[1]
else:
m = matr(n)
mI = linalg.inv(m)
v = array([sequence[x] for x in range(1, n+1)])
d = dot(mI, v)
p = n+1
pS = [int(math.pow(p, e)) for e in range(n)]
return sum(d*pS)
answer = 0
for i in range(1, 11):
temp = opCalc(i,poly)
print i, temp
answer += temp
print "the answer is ", int(answer)
