Subject: error in elliptic_e ? /simplification heuristics
From: Richard Fateman
Date: Fri, 18 Nov 2011 06:48:36 -0800
Mathematica has two commands, Simplify and FullSimplify, which attempt
to produce a simpler expression (measure of simplicity can be specified
by user) with various options. There is also something called
FunctionExpand, which may be worth looking at as well.
In case it is not obvious, these techniques can run up your computing
time substantially. In my limited experience with them, they are
generally useful only for expressions which are initially rather small,
to see if there is an expression that is even smaller. And even then,
they may not do the right thing. I was experimenting with Bessel
function identities. Some work, some don't.
A project for a student?
RJF
On 11/17/2011 9:51 PM, Robert Dodier wrote:
> On 11/17/11, Raymond Toy<toy.raymond at gmail.com> wrote:
>
>> I think elliptic_e(x,m) where x is a number (or %pi) should return the
>> messy expression that might be simplified. But I would hate it if
>> elliptic_e(x,m) always simplified to
>> elliptic_e(x-%pi*round(x/%pi),m)+2*round(x/%pi)*elliptic_ec(m) for symbolic
>> x and m. When x is a number (or %pi, %gamma, %e, etc.), maxima can do
>> something reasonable.
> Of course, we're under no obligation to produce a mess whenever it's possible.
> Not simplifying an expression is correct too. But if an expression simplifies,
> I hope it simplifies to something correct.
>
> The suggested policy for elliptic_e (simplify when x is a constant) seems
> reasonable, although I have to confess I really know very little about it.
>
> Something which is not really possible today, which seems like it would
> be useful, would be a simplification system in which it's easy to enable
> and disable simplifications (including built-in ones), and to see which
> simplifications are in effect. Then super-messy simplifications could be
> kept on the shelf, but easily enabled by a user who really wants them.
>
> best,
>
> Robert Dodier
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