       Re: PowerExpand in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg31868] Re: PowerExpand in mathematica
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sat, 8 Dec 2001 05:51:44 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Peter,
The correct answer, assuming t>0, which is what PowerExpand assumes, is 1/t.
We can trace this from the definition
z^p = Exp[p(Log[Abs[z]] + Arg[z] I)]
(notethat Log is here working on real nunbers and Arg gives the principal
value, in (-Pi,Pi] )
as follows

Exp[3/2( Log[Abs[-1/t]]+ I Arg[-1/t])] *Exp[1/2 (Log[Abs[-t]]+ I
Arg[-t])]

Exp[3/2( Log[1/t]+ I Pi)] Exp[1/2 (Log[t]+ I Pi)]

Exp[3/2( -Log[t]+ I Pi)] Exp[1/2 (Log[t]+ I Pi)]

Exp[3/2( -Log[t])]*Exp[3/2I Pi] *Exp[1/2 Log[t]]*Exp[ 1/2I Pi]

Exp[3/2( -Log[t])+1/2 Log[t]]*Exp[3/2I Pi+1/2  I Pi]

Exp[ -Log[t]]*Exp[2I Pi]

1/t*1
1/t

Check this against

Simplify[(-1/t)^(3/2) Sqrt[-t],t>0]

1/t
Also

Simplify[(-1/t)^(3/2) Sqrt[-t],t<0]

-(1/t)

--
Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Peter" <ptrsn2001 at yahoo.com> wrote in message
> Hi,
>
> Is this a known bug, feature? Or I am doing something wrong?
> -------------------------------
> Mathematica 4.0 for Linux
> Copyright 1988-1999 Wolfram Research, Inc.
>  -- Motif graphics initialized --
>
> In:= PowerExpand[(-1/t)^(3/2) Sqrt[-t]]
>
>         1
> Out= -
>         t
> ---------------------------------
> The correct answer is -1/t, of course.
>
> Thanks,
> Peter
>

```

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