How to simplify ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) + (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2 to 2?

[Humberto Bortolossi]

Hi!

Is there a way to make Maxima simplify the expression

((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
(2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2

to 2?

Thanks in advance, Humberto.
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[andrej.vodopivec]

On 11/14/06, Humberto Bortolossi <humberto.bortolossi@...> wrote:
> Hi!
>
> Is there a way to make Maxima simplify the expression
>
> ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
> (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2
>
> to 2?

(%i1) load(sqdnst)$
(%i2) ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
(2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2$
(%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
(%o3) 2

HTH,
Andrej
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[Nicolas Pettiaux-2]

2006/11/14, Andrej Vodopivec <andrej.vodopivec@...>:

> On 11/14/06, Humberto Bortolossi <humberto.bortolossi@...> wrote:
> > Hi!
> >
> > Is there a way to make Maxima simplify the expression
> >
> > ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
> > (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2
> >
> > to 2?
>
> (%i1) load(sqdnst)$
> (%i2) ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
> (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2$
> (%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
> (%o3) 2

thanks.

Now we know maxima can do it ... but the user have to deal with

1/ know to load that precise module. How can they find it ?
2/ know how to ask maxima to use it as the expression
> (%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
does not appear as a simple one to me.

How could I (and my student) have come to this ?

Thanks,

Nicolas
--
Nicolas Pettiaux - email: nicolas.pettiaux@...
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[andrej.vodopivec]

> Now we know maxima can do it ... but the user have to deal with
>
> 1/ know to load that precise module. How can they find it ?
> 2/ know how to ask maxima to use it as the expression
> > (%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
> does not appear as a simple one to me.
>
> How could I (and my student) have come to this ?

Well I overcomplicated it. It can be done simpler with

(%i1) load(sqdnst)$
(%i2) ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
(2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2$
(%i3) ratsimp(sqrtdenest(%));
(%o3) 2

So all you need to know is that the problem in the expression are
nested roots and that maxima has a function for dealing with them in
sqdnst package.

Andrej
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