Rational numbers in Python

user_13461348 0
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I need to compute a recursive sequence of numbers. In the formula, I need to compute B(r) where B(x) is a polynomial with rational coefficients (i.e fractions) and r is a rational number. My code is

def B(x):
    return x**2-x+1/6

However, when I plug r in, I get a floating number, not a rational number. This is expected.

I have several polynomials like this and my formula involves addition/subtraction with these numbers. How can I return the final result as a rational number?

Thanks!

fractions python
2 Answers

As stated in the comments, the fractions module is really helpful.

from fractions import Fraction
def B(x):
    x = Fraction(x)
    return x**2-x + Fraction('1/6')

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Basically, x**2-x doesn't have division, it doesn't need to be a Fraction. Because 1/6 would become a floating point number, use Fraction('1/6'). I also could have used Fraction(1,6). Math with a Fraction input will return a Fraction. Putting x = Fraction(x) at the top allows for fractional inputs.

user_24155240

Since everyone keeps suggesting to use fractions.Fraction for some reason, I'm going to put this in here:

** FLOATS ARE RATIONAL **

As a matter of fact, the class numbers.Rational provides a default for the numerator/denominator of floats. You can use float.as_integer_ratio() to get the exact numerator/denominator representation.

Now of course, the reason for this is the limited precision of floats requires all irrationals are truncated to rationals. So if it is exact computations you are after, then yes, go with fractions.Fraction.

user_138256580
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