Sympy - Rationalize all numeric values in expression? (Like Mathematica's Rationalize[])

Question

Is there a simple method to (attempt to) rationalize all numeric values in an expression within a given delta, much like Rationalize[] in Mathematica?

An example in Mathematica:

In[25]:= Rationalize[0.5 x^2 - 3.333333 x, 10^-4]
Out[25]= x^2/2-(10 x)/3

I see the nsimplify() function, but that seems like overkill.

Answer 1

I don't see how nsimplify is over kill. nsimplify does exactly what you want, because you can pass it a SymPy expression, and it will rationalize the terms in the expression

>>> print nsimplify(0.5*x**2 - 3.333333*x, tolerance=0.001, rational=True)
x**2/2 - 3333333*x/1000000

(the tolerance keyword doesn't seem to work, which I guess is a bug).

Answer 2

You can use Fraction.from_float:

>>> from fractions import Fraction
>>> Fraction.from_float(0.5)
Fraction(1, 2)

Even though it seems less smart than Mathematica:

>>> Fraction.from_float(3.33333333)
Fraction(7505999371444827, 2251799813685248)

It actually simply convert the float to its exact rational representation(so numbers that cannot be written exactly as floats wont be converted "correctly").

You can get more "human-readable" limiting the denominator:

>>> Fraction.from_float(3.333333333).limit_denominator(10)
Fraction(10, 3)

Even though it is trickier to understand which limit you should put to get the "correct" fraction, and it may happen that it is still impossible to obtain it due to the float representation.

If you have to stay with sympy than I don't think you can avoid using nsimplify, which seems written exactly for such purposes.

edit: from python2.7+ you can simply call Fraction(0.5) instead of using the from_float method.