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Re: root cubic

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From:
Ralph Mellor
Date:
July 9, 2020 17:28
Subject:
Re: root cubic
Message ID:
CAPLR5Sf6H8SGGCxyTO8zyKX0t7m0x5_RZ2wM8e39NLBXqB2YMA@mail.gmail.com
You have several useful answers.

I want to summarize what they saButy, and add a couple resources.

* You probably meant 9 ** <1/2>.
  Which will display 3.
  But it's a Num. It's not the right type if you care about accuracy.

* A solution to get rationals right is built into Raku.
  See https://medium.com/@raiph_mellor/fixed-point-is-still-an-approximation-727c6facdbff
  But it won't work for `**` because it coerces to Num if the RHS is rational.

* The full solution to getting math right is symbolic math.
  For Raku that means https://github.com/raydiak/Math-Symbolic
  Note that it includes features for roots.
  Note that we would all love to hear it works for you for
      equivalents of 9 ** <1/2> and/or 27 ** <1/3>
  In particular, not that the result *seems* right,
      but that it is the right type. (Int or Rat).

Hth.

On Thu, Jul 9, 2020 at 5:11 PM Tobias Boege <tobs@taboege.de> wrote:
>
> On Thu, 09 Jul 2020, Aureliano Guedes wrote:
> > Hi all,
> >
> > A quick question.
> >
> > This is expected?
> >
> > raku -e 'say 9 ** (1/3)'
> > 2.080083823051904
> >
> >
> > Why do I'm asking this?
> > I know about the computational floating problem and I also know that the
> > Raku deal with rational whenever it is possible and store numbers as
> > expressions (actually I don't know if there are more details). That's why
> > 0.2 + 0.1 == 0.3 in Raku returns True whilst in other languages like
> > Python, Perl5, and Ruby return False.
> >
> > Then, I was just playing around and I'd like to check if it is expected.
> >
>
> I for one expected it. The equation 0.1 + 0.2 == 0.3 uses the Rat type in
> Raku, which stores rational numbers as exact fractions of numerator and
> denominator, avoiding the floating point inaccuracies you mention, and
> hence making equality comparisons trustworthy.
>
> The number 9 ** (1/3) is not rational and in general exponentiation with a
> fractional power might not produce a rational number, so exact representation
> via Rat is out of the question. Therefore Rakudo does the computation with
> Num, which are inexact floating point values again.
>
> Now, there are effective ways to represent algebraic numbers like 9 ** (1/3)
> in such a way that you can do arithmetic with them, but I'm not aware of any
> implementation of that available to Raku. For someone with enough tuits,
> I think this [1] can serve as a sort of high-level manual for creating such
> a module. In terms of ready-made non-Raku packages, I only know of CGAL [2],
> which provides a clean and even (template-)parametric interface to real
> algebraic numbers. In fact, I might have a try at NativeCall'ing it this
> evening.
>
> Best,
> Tobias
>
> [1] https://math.stackexchange.com/a/3144516
> [2] https://www.cgal.org/
>
> --
> "There's an old saying: Don't change anything... ever!" -- Mr. Monk

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