Jonathan Fine said
But here there is a cost. Arbitrary precision arithmetic (and roots) uses more memory and takes longer.
I think a wider (perhaps naive) interpretation of the idea could be, "can we defer certain lossy calculations until they have to be done?" Fraction may do eager arbitrary precision arithmetic (I don't know), but is it necessarily the case that integer division has to be eager? Could we have our cake and eat it, too? (Sorry for the dupe, Jonathan, I need to dig through my email configuration to learn why "reply" doesn't do what I think it should do.) On Fri, May 14, 2021 at 10:48 AM Jonathan Fine <jfine2358@gmail.com> wrote:
Martin wrote:
when dividing two integers, the result is a float, which means we
immediately lose precision. This is not good if you want to use code which supports higher precision.
I am of course in favour of keeping precision, if there is no cost. But here there is a cost. Arbitrary precision arithmetic (and roots) uses more memory and takes longer. Therefore, the system must allow the programmer to choice what's wanted (either explicitly or implicitly).
Python has been set up to make 1/3 evaluate to a float (an implicit choice), and have Fraction(1, 3) be a fraction (an explicit choice).
I don't think it fair to say that this decision is "not good". Rather, it's good for some use cases and not so good for others. On balance, I'm happy with that decision.
That said, as a pure mathematician who does integer calculations, I'd like numpy to have better capabilities for integer linear algebra.
I hope Martin that you agree with me, that this change would not be an improvement for everyone.
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