> I think it is a lot of work, though.
John, you have a gift for understatement.
----- Original Message -----
From: John Randall <[EMAIL PROTECTED]>
Date: Friday, December 8, 2006 6:30 am
Subject: Re: [Jgeneral] exp(y). sin(y) and accuracy.
> Roger Hui wrote:
> > Actually, symbolic computations can be done as
> > yet another datatype and the only cost ("sacrifice")
> > would be implementation effort that could be
> > expended in other areas. You can look at f&.g and
> > f b. _1 for indications of what can be done with
> > symbolics in J.
>
> I understand and appreciate what can be done symbolically in J
> (and I
> am constantly amazed at the scope of b._1). The type of issue I am
> talking about involves the way in which symbolic languages are
> normally implemented:
>
> (a) Having a large number of data types to represent expressions, and
> being able to convert between them. For example, rational function
> may be represented most appropriately as a quotient of fully factored
> polynomials or in partial fractions, depending on context.
>
> (b) Maintaining a unique instance of the simplification of every
> expression. This is necessary to cope with the intermediate
> expression swell that otherwise dogs symbolic computation.
>
> (c) Using a large collection of simplification rules. This is needed
> if you want to get textbook solutions to college-level math problems.
>
> For example, Maple will give the exact solution to the initial value
> problem y''-2y=x exp(x), y(0)=1, y'(0)=2 by entering it in essentially
> this form.
>
> > dsolve({diff(y(x),x,x)-2*y(x)=x*exp(x),y(0)=1,D(y)(0)=2});
> y(x) =
>
> / 1/2 \ / 1/2\
> 1/2 |5 2 | 1/2 | 5 2 |
> exp(2 x) |------ + 3/2| + exp(-2 x) |3/2 - ------| - (2
> + x) exp(x)
> \ 4 / \ 4 /
>
> However, this capability has a huge price: the infrastructure
> described above, which is applied to every expression. Symbolic
> calculation at this level of generality is very useful, but in quite
> limited contexts. If it can be parcelled off so that it does not
> affect non-symbolic computation, that would be great. I think it
> is a
> lot of work, though.
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