Sqrt problems

• To: mathgroup at smc.vnet.net
• Subject: [mg19504] Sqrt problems
• From: Rita Bijlsma <R.Bijlsma at iri.tudelft.nl>
• Date: Sat, 28 Aug 1999 15:53:22 -0400
• Organization: Interfaculty Reactor Institute of Delft
• Sender: owner-wri-mathgroup at wolfram.com

```Hi All,

I'm working with the textual version of mathematica 2.2 on VMS
and I have some questions related to Sqrt

PowerExpand[%15]

2   2            4    4   4
1   n  Pi    Sqrt[4 Dq  + n  Pi ]
- - ------ + --------------------
2       2               2
4 Dq            4 Dq

- How do I get mathematica to give me:

2   2             4   4
1   n  Pi         1   n  Pi
- - ------ + Sqrt[- + ------]
2       2         4        4
4 Dq              16 Dq

(  Or even better, with  Power[(n Pi)/(2 Dq), ..] in it, but
forget         that)

- So I would like something like PowerExpandAll[]

- I would like to tell PowerExpand which of the variables
are real and positive, just like the way ComplexExpand works,
is this available in later versions of Mathematica?

I tried to give && Dq > 0 as one of a set of equations but
this was not allowed and && Dq == Abs(Dq) introduces transcendental
functions that made the set unsolvable.

- Is there some way to add a condition like x > 0 to a set of
equations?

I noticed that simplify may sometimes not
work on the equation form, but does on the corresponding
simple expression form.

- How can I get mathematica to perform the PowerExpand on
the equation (and rule) forms?

Mathematica's answer to a set of equations was:

Sqrt[1 - 2 Fr] n Pi
---------------------------------
Sqrt[Fr] Sqrt[-4 + 4 Fr]

- How can I get mathematica to give it like this:

1
Sqrt[-2 + ------] n Pi
1 - Fr
-----------------------
2 Sqrt[Fr]

   The form given by mathematica is very ugly as the arguments of
the       Sqrt are normally negative. It is not affected by PowerExpand.
The input equations did not have the offending Sqrt seperately,
so mathematica really changed it into this form.
As mathematica is unwilling to perform Sqrt[x y] = Sqrt[x] Sqrt[y]
unless PowerExpand is used, the above should not have happend,
I think.

- Could I have done something to prevent it?

Thanks for all and any help!,
Rita

---
.-. || Drs. Rita Bijlsma                 tel: +31-15-2787109
/   \|| IRI dept of Radiation Physics     fax: +31-15-2786422
|   ||| Delft University of Technology  email: rita at iri.tudelft.nl
|   |||_The Netherlands ______________ http://www.iri.tudelft.nl/~rita

```

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