From: vanjac12@... (Van Jacques)
Date: 2003-12-12T22:27:04+09:00
Subject: Re: prog for g.c.d. of 2 integers

Florian Pflug writes

> a,b=b,a%b while (b != 0)
> a.abs

This works well, and either a or b (or both) can be < 0.
I note that a%b < 0 if b < 0, but it's still OK.
g.c.d. are postive though, so a.abs is the g.c.d.
after the while statement has executed.

My text says that a > b, but (I think) that is so that
the Euclidean algorithm, r_i = r_(i-2) % r_(i-1), for
i >=2, can include a = r_0 and b = r_1 and then say that
r_0 > r_1 > ... > r_n > 0 must terminate with the g.c.d r_n.
(r_n | r_(n-1) or r_(n-1) % r_n = 0.)

Josef 'Jupp' SCHUGT writes;

>> Topics from mathematics make good practice programs, IMO.

>I don't agree with that. When starting with mathematics the most
>important task of programming has already taken place: The modelling
>of the problem in an abstract way.

This is a good point. In a ruby tutorial by Camerra (sp?),
his example of an addressbook is a good non-math example.

As a physicisct and amateur mathematician I have done many
math programs, whence comes my prejudice.
I will probably continue to do these kinds of problems,
since they help me learn abstract algebra, groups, and
number theory, but I will try to think up some other kinds
of problems, like the addressbook. (Or the song player I
saw somewhere.)

Both your solutions look fine to me.

m / gcd(m, n) * n -- I assume, as in C, equal precedence ops.

are left associative. I would write

m*n/gcd(m,n)  .

Van