[q-lang-users] Q as a Computer Algebra System

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

Hello Anthony,

I too first became interested in 'Q' because of mathematics. I am
fairly new to Q too.

Q is not, in my view, a typical functional language. If you're
interested in learning functional languages, you should also take a
look at some others. It would probably be instructive to try Standard
ML <http://www.smlnj.org/>. There are many other interesting
functional languages. However, I think you will really enjoy using Q.
It's one of the languages that I most enjoy using.

Beware that Q may not always behave quite as you expect at first. For
example, if you enter the simple program consisting of just the
rewrite rule:
    X+X = 2*X;
and the giving Q some expressions to reduce:
    ==> A+A+B
    2*A+B
    ==> A+B+B
    A+B+B
the final response from Q may not be what you expect.

A+B+B, which is (A+B)+B due to the left-associativity of (+), was not
reduced, as this does not match the given rule.
With the additional rule
    Y+X+X = Y+2*X;
you will now get the responses from the Q system
    ==> A+B+B
    A+2*B
    ==> A+A+B+B+C+C+D+D
    2*A+2*B+2*C+2*D

To quote Albert Graef's informative reply to one of my questions:
'Yes, it's surprisingly hard to do apparently basic stuff like this,
because it involves "rewriting modulo AC" (AC =
associativity/commutativity). The conventional way to deal with this
is to transform the original terms into a "sum of products" normal
form and represent that as a list which is lexicographically ordered
according to the involved symbols. It's not really that hard to do but
it indeed involves additional rules on a kind of meta-level, so there
is no straightforward solution with just a few equations.'

I was at first disappointed with Q not being the simple computer
algebra system I hoped it would be. But then that's not what it's
intended to be. Once you get used to it, you find that Q does seem to
do the "right thing". Those involved with developing Q take great care
to keep Q a sensible and consistent language. (See for example the
helpful reply from John Cowan in a discussion
<http://sourceforge.net/mailarchive/message.php?msg_id=19294969> of
type tests, in the lead up to the release of Q7.2)

Not many languages that I know are so well thought out, but I think
that Q is. And Q has fairly comprehensive libraries, together with
comprehensive programming tools, such as the debugger.

When I want to do some maths, I now usually reach for Q. But I tend to
write code for the specific type of mathematical object I'm currently
interested in. I imagine that to write a fairly comprehensive symbolic
computer algebra system would be a job of comparable complexity in any
language, Q, C++, ML, Python, or any other "general purpose" language.

By the way, if anyone does know of a good free / open source symbolic
computer algebra system or programming language, please let me know.
Mathematica is unbelievably expensive, and I don't need anything that
powerful or comprehensive.

I hope these comments (and opinions) are helpful,
Rob.

On 15/08/06, Anthony <ad...@ke...> wrote:
>
> Just a general question...Q is my first experience
> with a functional language.  What would it take to
> write a Mathematica clone in Q?
>
> I don't mean a full-Mathematica clone, but something
> that would emulate the kernel mode, circa 1988--an
> unlimited integer, numeric, graphical, and symbolic
> program with an easy syntax.
>
> For example x + 8  will generate internally a
> Plus[x,8] production, and 1+x^2+(y+z)^2 generates
>
> Plus[1, Power[x,2], Power[Plus[y,z],2]]
>
> What I'd like to do is just write a small Q program
> that parses a line of input according to the rules of
> Mathematica.  No need to evaluate the functions...just
> want to build a syntax checker at first.
>
> Or maybe I am dreaming...