Re: [q-lang-users] newbie question

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

Hello Álvaro,

> I'm taking a look at this programming language and I'm trying to
> figure out some of its uses. I've read about equations in this
> programming language and pattern rewriting. I find it really
> interesting.
>
> I would like to ask a very simple question. Is it possible to use this
> language for solving symbolic equations? if so, could you give me a
> quick example with two linear equations?

I myself first got interested in Q whilst looking to do some symbolic
mathematics.

I think the first thing to say is that Q is *not* a CAS (computer
algebra system). There are very many out there. Amongst the free
and/or open source tools, I would recommend taking a look at Axiom
<http://wiki.axiom-developer.org/> and wxMaxima
<http://wxmaxima.sourceforge.net/wiki/index.php/Main_Page>. Axiom is
the most comprehensive and sophisticated CAS that I've encountered,
but has quite a steep learning curve; its type system is
extraordinary. wxMaxima, on the other hand, is a very easy tool to get
started with. I'd highly recommend taking a look at both.

That said, Q, too is a very useful tool with which to do some
mathematics. I spent some time working with (univariate, numerical)
polynomials, particularly those with rational coefficients, and that
resulted in the creation of Q's rational number and polynomial
libraries (now distributed with Q).

Q has very useful features for working symbolically, such as the quote
operator (a single ' prefix), and the string / quoted-expression
conversion functions strq and valq.

Q (or Pure) would both be perfectly suitable languages in which to
write a CAS, but are not in themselves CASs. To represent mathematical
expressions and other objects, you really need a more sophisticated
set of data structures than just the parse trees. For example, it
might be appropriate to store expressions modulo associativity, or to
reduce an expression internally to some specific normal form.

To manipulate an expression in Q, you will need to explicitly handle
associativity and commutativity in all possible contexts. For example,
notice that (B+C) is not a sub-expression of (A+B+C), as the latter is
((A+B)+C).

If you're specifically interested in solving linear equations, then
what you need is probably a matrix library.

I hope you remain interested in Q. Please also take a look at Qpad
(Windows only), Qcalc (not available for Windows yet) and Pure (an
alpha(?) version of a replacement for Q).


Regards,
Rob.

Rob Hubbard