Hi Jonathan,
I would agree with you if what I was asking was arbitrary precision math. But
this is not what I am asking for, what I am asking for is that integer true
division should result in a Fraction. The difference is huge: arbitrary
precision math is costly, and while arbitrarily precise, that "arbitrary" does
not include "exact". Fractions, on the other hand, are exact.
The speed argument also does not hold: whenever you do actual math on the
fractions, they will be seemlessly converted to floats. Anybody doing anything
speed will use something like numpy anyways, and there is no discussion there,
numpy uses floats, and I am not proposing to change that.
To illustrate what I am talking about, see how it looks like in reality (yes,
this is the actual Python interpreter with my changes, not artificially
generated stuff):
>>> from math import sin, sqrt
>>> sin(1/2)
0.479425538604203
>>> sqrt(1/4)
0.5
>>> (1/2)**2
1/4
>>> (1/4)**(1/2)
0.5
>>> (1/2)**-2
4
Now you can ask, if everything is converted to floats anyways, where is the
benefit? The benefit is when you use symbolic math (or, indeed, arbitrary
precision math like the Decimal example I already mentioned):
>>> from sympy import symbols, sqrt, sin
>>> x = symbols("x")
>>> sin(1/2)
sin(1/2)
>>> 1/2 + x
x + 1/2
>>> 2/3 * x
2*x/3
>>> sqrt(1/4)
1/2
So, my argument is, this change will benefit many people, and be of only a
small disadvantage to others. That disadvantage is that yes, there will be
places where it does not work, so libraries need to get fixed. But this is the
case with every Python update. Once it will be working, there will be no
disadvantage anymore.
Cheers
Martin
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