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Fractions in python returning ridiculously big numbers

I have Python code to solve some recursion and I want it to return some fractions.

The problem is that my code returns ridiculous fractions (which are correct) but they are not the smallest fractions possible, I know it since I can just solve the formula by hand.

Here's my code:

from __future__ import division
import sys
from fractions import Fraction
def t(n):
    if n==0:
        return 0
    else:
        return 1/(4-t(n-1))

print(Fraction(t(int(sys.argv[1]))))

If you run this code with python fraction.py 2 you should have 4/15 but here's what I get:

4803839602528529/18014398509481984

which is numerically correct I think, when I just calculate it i get 0.26666666666666666 (maybe both fractions are different at x digits from 0).

What is the problem here?

Solution

  • Convert to Fraction objects before you do the math, not after:

    def t(n):
    n = Fraction(n)
    if n==0:
        return n
    else:
        return 1/(4-t(n-1))

    If you do the math before converting to a Fraction, the math gets done as floating point math, giving you an imprecise result which then you convert to an imprecise Fraction.

    If you convert first, then the math gets done as fraction math and things stay precise.