I think the basic issue with methods that try to find a small form for an
expression of many terms is that the only effective methods known (or
possible, perhaps) involve a search in a space of exponential size.
There are other issues too, such as recognizing the collapse of certain
combinations of trigonometric or hypergeometric or algebraic expressions,
the rearrangement of polynomial expressions in terms of their roots or
factors, and probably other issues that do not appear strictly in the
algebra, but come from the application domain, grouping terms by some
external meaning. An example might be substituting E for m*c^2 in some
expressions.
There is also the concern that rearrangement will change the value of an
expression if it is to be evaluated in floating-point. That is, expressions
such as ((x-1)+y)+1 may be rather different from x+y.
So all of this exploration is OK with me, but I think we have to be careful
about claiming to have "the solution" unless we have also addressed the big
picture.
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-
> bounces at math.utexas.edu] On Behalf Of ZINTEL Gerhard
> Sent: Wednesday, January 10, 2007 4:57 AM
> To: Stavros Macrakis
> Cc: maxima at math.utexas.edu
> Subject: Re: [Maxima] How to make results more compact
>
>
>
> > > The following should do steps 1, 2,3 the rest by hand.
> >
> > You can use "optimize" for the rest:
> >
> > optimize ( c*(f*(i+h+g)+e*(i+h+g)+d*(i+h+g))+b*(f*(i+h+g)+
> > e*(i+h+g)+d*(i+h+g))+a*(f*(i+h+g)+e*(i+h+g)+d*(i+h+g)) ) =>
> >
> > block([%1,%2],
> > %1:i+h+g,
> > %2:f*%1+e*%1+d*%1,
> > c*%2+b*%2+a*%2)
> >
> > Note that optimize does *not* find subexpressions like a+b in a+b+c.
>
> Obviously I'm a bit stubborn, but in my mind optimized should give:
> block([%1,%2],
> %1:i+h+g,
> %2:%1*(f+e+d),
> %2*(c+b+a)
>
> I know, it's all very well to say that but it's surely hard to code it.
>
> Thank you very much for your help!
> Gerhard
>
>
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