Hi Jurjen,
On Sun, Apr 20, 2008 at 12:13:22PM +0200, Jurjen N.E. Bos wrote:
>
> Op 19-apr-2008, om 18:58 heeft [EMAIL PROTECTED] het
> volgende geschreven:
> > Issue 93: Square root denesting
> > http://code.google.com/p/sympy/issues/detail?id=93
> >
> > Comment #11 by kirill.smelkov:
> > At present we have sqrtdenest written by David:
> >
> > In [1]: sqrtdenest(sqrt(14+4*sqrt(6)))
> > Out[1]:
> > ⎽⎽⎽ ⎽⎽⎽
> > ╲╱ 2 + 2*╲╱ 3
> >
> >
> > Jurjen, David, All,
> >
> > What is the state of this issue?
> Interesting you ask. There is a "sqrtdenest" function, which
> implements an article that has a nice theoretical approach to
> denesting, but omits a few important details.
> I've been struggling with the theory, and I am a few weeks from a
> brand new implementation that is more understandable, more flexible,
> and faster.
> The short idea is:
> If you denest sqrt(a+b), a and/or b has sqrts in it,
> you first denest sqrt(a**2-b**2), and if that denests to d,
> write sqrt(a+b) as sqrt((a+d)/2)+-sqrt((a-d)/2)
> the sign is equal to the sign of b.
> The interesting challenges are:
> - split the expression below the sqrt into the proper a and b (I am
> quite far with that, while the original article lacks about all
> information on how to do this)
> - find the sign of b (sometimes not so easy, but I'll work this out,
> I guess)
> - extrapolate for expressions that are not Numbers (work in progress).
> - Jurjen
Thanks for your reply - it is indeed interesting :)
How do you think, could you please prepare a patch with your new
implementation for sqrtdenest?
--
Всего хорошего, Кирилл.
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