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Comment by learnstats2 | Hacker News Reader

"I’m also not aware of any calculator (or programming language) that currently works this way." [represent fractions exactly wherever reasonable to do so]

This is surprising to me!

Casio scientific calculators definitely do this, and have done for many years now. And Casio (it appears) also represents pi and square roots exactly/symbolicly, wherever it's reasonable to do so.

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I know that in Python, you can do:

    >>> import fractions
    >>> from fractions import Fraction as F
    >>> F(3, 17) * F(12, 5) + F(56, 99)
    Fraction(8324, 8415)
    >>> F(3, 17) * F(12, 5) + F(56, 99) / 3 + 2 * 4
    Fraction(217412, 25245)

However, if you use a float or a complex with it, the fraction get resolved:

    >>> F(217412, 25245) + 0.1
    8.712081600316894
    >>> F(217412, 25245) + 1j
    (8.612081600316895+1j)

You also have some constants:

    >>> import math
    >>> math.pi
    3.141592653589793
    >>> math.e
    2.718281828459045

But they are not just symbol, there is a precision-limited value behind it. Although the value seems to match the precision NASA considers to be enough for trajectories of spacecrafts like Voyager: https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimal...

Raku Perl 6 uses rationals by default for decimal literals. No imports necessary. You actually have to opt-in to floating point by using engineering notation.

https://docs.perl6.org/language/numerics#Rational

> "I’m also not aware of any calculator (or programming language) that currently works this way." [represent fractions exactly wherever reasonable to do so]

Author here. The paraphrase makes this sound wrong, but what I actually meant is that I don’t know of any calculator that uses rationals while the numerator and denominator can be represented as integer floating point doubles, and then falls back to a single floating point double if the numerator or denominator overflow.

I am aware of many systems that use arbitrary precision rationals, and I mentioned this in the post:

> Rational numbers where the numerator and denominator are allowed to grow arbitrarily large are used by computer algebra systems (CAS) like Mathematica and Maple (and also some high-end handheld graphing calculators).

Yeah, they just lack exposure to systems that do:

  :; sbcl
  This is SBCL 1.5.5, an implementation of ANSI Common Lisp.
  ...
  * (/ 1 3)
  1/3

To be fair that is a pretty recent addition to Lisp, only added in the late 1970s. They might not be keeping up with the latest stuff.

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