Re: Simplify Question
- To: mathgroup at smc.vnet.net
- Subject: [mg41808] Re: Simplify Question
- From: "Dana DeLouis" <delouis at bellsouth.net>
- Date: Fri, 6 Jun 2003 09:50:39 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Thanks Jens-Peer. I learned something new from studying your example.
Unfortunately, I get 3 Sqrt functions.
(FullSimplify[#1, x > 0, ComplexityFunction ->
(If[Head[#1] === Rational, 1, 0] & )] & )[Sqrt[2]/Sqrt[1 + 1/x]]
(Sqrt[2]*Sqrt[x])/Sqrt[1 + x]
I guess Mathematica gives a high priority to the exact number of Sqrt[2] and
factors it out.
Here, without making any assumptions on "a", the equation fully simplifies
to the simple Sqrt[a/b].
FullSimplify[Sqrt[a]/Sqrt[b], b > 0]
Sqrt[a/b]
However, if you replace "a" with a number, then it returns a function with 2
Sqrt functions instead of Sqrt[2/b].
FullSimplify[Sqrt[2]/Sqrt[b], b > 0]
Sqrt[2]/Sqrt[b]
The only way I came close was with the following...
FullSimplify[Sqrt[2]/Sqrt[1 + 1/x], x > 0,
ComplexityFunction -> (Count[{#1}, _Power, 2] & )]
Sqrt[2 - 2/(1 + x)]
Then, if I select everything inside the Sqrt function, and hit the Simplify
button, then I get a function with only 1 sqrt function.
Sqrt[(2*x)/(1 + x)]
This was the form I was looking for.
I tried all variations using the option "TransformationFunctions", but I had
no luck with this either.
Well, no big deal I guess. Now that I am aware of this limitation, I will
try to use variables instead of numbers in the future.
Look forward to the next version.
Thanks again.
--
Dana DeLouis
Windows XP
Mathematica $VersionNumber -> 4.2
delouis at bellsouth.net
"Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote in message
news:bb73d6$b7f$1 at smc.vnet.net...
> Hi,
>
> do you like the output of
>
> Sqrt[2]/Sqrt[1 + 1/x] //
> FullSimplify[#, x > 0,
> ComplexityFunction -> (If[Head[#] === Rational, 1, 0] &)] &
>
> more ??
>
> Regards
> Jens
>
> >
> > Hello. Could someone offer an explanation or a solution on the
following? I am trying to simplify an equation that has a Sqrt in both the
numerator and denominator. I would like to have just one Sqrt function.
> >
> > Sqrt[2]/Sqrt[1 + 1/x]
> > Returns...
> > Sqrt[2]/Sqrt[1 + 1/x]
>> I am looking for the following form: (1 Sqrt function)
>> Sqrt[(2*x)/(1 + x)]
<<snip>>