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Re: A Simplify that really simplifies?

> In the specific case of a^2+2 a b +b^2 +x, I'm not sure that
> simplifying this expression is a mathematically well-defined
> operation.  It's not clear, for example, what this operation
> would do with (x^2 + 2 x) or (a^2 + 2 a b + b^2 + 2 a c + c^2).
> If the operation isn't well-defined, and there isn't a good set
> of heuristics for deciding what to do in ambiguous cases, then
> it is quite impossible to implement it in Mathematica or any
> other computer program.

This may be true in a mathematical sense but in everydays work it 
is very annoying to see how an expression could be simplified but having
no idea how to tell the computer. I'm constantly loosing the time
I saved, by using Mma for e.g. an integration, by reducing the expressions
from one page to two lines. Of course reducing expressions (this is perhaps
a better definition: measure the amount of space it takes to write the 
expression unsing a normal size pencil:-) is no straightforward operation.
It is more like sculpturing, the outcome depends on the skills and tools
of the craftsman. So what we need is a variety of flexible (heuristic) tools 
(transformationrules, operations) which can be applied to subexpressions and not
one black box called Simplify (yes I know there are already a lot of other functions too but there are similar problems).

> Still, a package to implement such a collection of partial factoring
> heuristics might be useful in some situations.

And if you add some improved facilities for formatting TeX Output
(keeping certain expressions together and line breaking), combine it
with an interactive mouse-based Hyper-Text notebook (or a sort of
spreadsheet containg definitions, equations and data in different but
realted cells) for X-Windows which produces Tex-output ready for
publication but keeping all transformations and operations in mind,
this, together with an easy link to my Fortran programs/subroutines and
favourite libraries, would be perfect. -- OK. I'm just dreaming.

Heino Falcke

and I used them all 

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