def pellSolution(pNumber):
"""return the solution of Pell equation x*x - pNumber*y*y = 1"""
l = continuedFraction(pNumber, pNumber * 2)
# print l
t = fraction(l)
P, Q = t[0], t[1]
for i in range(len(P)):
pi, qi = P[i], Q[i]
# print pi,qi
if pi * pi - pNumber * qi * qi == 1:
return [pi, qi]
def fractionPeriod(pN): '''return the period of continued Fraction of squareRoot(n)''' squareRoot = int(math.floor(math.sqrt(pN))) length = 10 *squareRoot l = continuedFraction(pN, length)[1:] # print l k = 0 nonSatisfy = True while nonSatisfy: k+=1 nonSatisfy = False for t in range(0,10): if (t+2)* k < length: if not nonSatisfy and l[t*k:(t+1)*k]!= l[(t+1)*k:(t+2)*k]: # print l[t*k:(t+1)*k], l[(t+1)*k:(t+2)*k] nonSatisfy = True return k
from functions import gcd, continuedFraction import math def properFraction(pNume,pDeno): '''pNume: numerator, pDeno: Denominator return [z,x,y] such that pNume/pDeno =z + x/y and gcd(x,y) = 1''' t = gcd(pDeno,pNume) z = pNume / pDeno x,y = (pNume - z*pDeno)/t, pDeno/t return [z,x,y] print properFraction(20,15) print continuedFraction(13,10) def fractionPeriod(pN): '''return the period of continued Fraction of squareRoot(n)''' squareRoot = int(math.floor(math.sqrt(pN))) length = 10 *squareRoot l = continuedFraction(pN, length)[1:] # print l k = 0 nonSatisfy = True while nonSatisfy: k+=1 nonSatisfy = False for t in range(0,10): if (t+2)* k < length: if not nonSatisfy and l[t*k:(t+1)*k]!= l[(t+1)*k:(t+2)*k]: