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Re: [Axiom-developer] sbcl and Axiom

From: root
Subject: Re: [Axiom-developer] sbcl and Axiom
Date: Wed, 26 Jul 2006 21:19:57 -0400

> Axiom needs to be able to do higher-order expressions like:
> >    x := p^n * 3*p^m + 2
> >    y := q^r * 6*q^s - 3
> > what is the j'th term of x*y? Well, since the we don't know the
> > exponents (n, m, r, or s) we have to construct a function that
> > will return the k'th component of x, the i'th component of y and
> > a final function that gives the result of x*y as a function of
> > the component functions. f(x(k),y(i)). Nobody does this yet to
> > my knowledge.
> I need to check but I think work related to this as been show at last ISSAC
> ?

Actually, it was. But the scheme given there is overly complicated in
my opinion. He measures the distance between the various entries and
computes a graph over the matrix.

In Axiom you could simply construct lists to represent the input so:

   [ a_1 ... a_n   ]
   [ a_2 .   a_n+1 ]
   [ .    .  .     ]
   [ .     . .     ]
   [ a_m ... a_n+m ]

could simply be represented as a list of lists with the dots as
list elements:

   ( ( a_1 ldots a_n ) (a_2 ldots a_n+1) hdots

kinds of a data structure. Then you could compute any given
element dynamically. It seems like an easier approach.


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