[Edu-sig] computer algebra

[kirby urner]

On Wed, Dec 10, 2008 at 6:47 PM, kirby urner <kirby.urner at gmail.com> wrote:

<< SNIP >>

> fractions.Fraction, on the other hand, barfs on anything but integers,
> isn't trying to be all divisions to all possible types, isn't
> pretending this is Mathematica or a generic CAS.
>
> Note that I'm not criticizing fractions.py in any way, am so far quite
> happy with it.  I'm simply drawing attention to some fine points.
>

OK, now I'm going to criticize a little.

I think the more natural and useful choice would be to continue
threads right here on edu-sig, regarding a Rational Number type, not
just this Fraction type.

The problem with Fraction is it's not actually much more than the
notion of Ratio (how many times one fits in the other), whereas the
Rational Number concept fits neatly in the sequence:  N < W < Z < Q <
R < C, where < could be replaced with the "subset" symbol.  Those be
Natural, Whole (Natural + 0), Integers, Rationals, Reals, and Complex
respectively, except the Real type is quite problematic, is treated
with Floats, Decimals and generators (iterable).

The thing about Rationals is they're a field, closed under + and *,
and therefore - and / (because of field properties).  So a Rational is
able to eat other Rationals for breakfast i.e. (1/3) / (3/1) makes
plenty of sense, and all integers are really just rationals in
disguise i.e. 0 = 0/1, 1 = 1/1 etc.

If Fraction could eat Fraction type objects, then we could have
continued fractions more easily, have other fun.

The silver lining here is fractions.py was actual named that, and not
rationals.py, which means we still have a hole to fill, a more generic
class, yet not too generic, not open to complex or matrix arguments,
just to rationals, integers a subtype.

Kirby