Re: [q-lang-users] Complex numbers

[Rob H. <hub...@gm...>]

On 13/06/06, Albert Graef <Dr....@t-...> wrote:
> type Rat = private const rat P Q;
> public (over) P Q @ (/);
> P:Int over Q:Int = rat (P div D) (Q div D) where D = gcd P Q;
> unparse (rat P Q) = '(P over Q);

Should that go into rational.q, or is there a separate location for
the 'unparse' stuff?

> Also, I'm about to turn complex numbers into an algebraic type now. If
> anyone wants to complain, now is your last opportunity. ;-)

In the Rational code, the construction function rational takes a pair.
For 'deconstruction', I provide
    numerator
    denominator
and in the update I'm preparing, there's now a
    num_den
function returning the numerator and denominator in a pair.

It would be good if the Complex type could follow similarly, and for
both rectangular and polar coordinates as has been suggested.

So:
    public type Complex = private const cplx_rect X Y;

    //rectangular
    complex_rect (X, Y) = cplx_rect X Y; //takes a pair
    //polar
    complex_pol (R, Theta) = cplx_rect (R * cos Theta) (R * sin Theta);

    re (cplx_rect X Y) = X;
    im (cplx_rect X Y) = Y;
    rect (cplx_rect X Y) = (X, Y); //returns a pair

    abs (cplx_rect X Y) = sqrt (X^2 + Y^2);
    arg (cplx_rect X Y) = atan2 Y X;
    pol (cplx_rect X Y) = (abs (cplx_rect X Y), arg (cplx_rect X Y));

This means that, as rational and num_den are inverses; so are
complex_rect and rect, and complex_pol and pol.

I'm not sure about the naming, but I'd like to keep Rational as
consistent as possible with Complex. I'm happy to consider renaming my
symbols if desired (e.g. 'Rat' rather than 'Rational', 'num' rather
than 'numerator', swapping 'rational' with 'rat' to have the shorter
symbol public, num_den as something else,...).

Rob.