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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)
*References*: <9uq8cg$ada$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Peter,
The correct answer, assuming t>0, which is what PowerExpand assumes, is 1/t.
We can trace this from the definition
z^p = Exp[p(Log[Abs[z]] + Arg[z] I)]
(notethat Log is here working on real nunbers and Arg gives the principal
value, in (-Pi,Pi] )
as follows
Exp[3/2( Log[Abs[-1/t]]+ I Arg[-1/t])] *Exp[1/2 (Log[Abs[-t]]+ I
Arg[-t])]
Exp[3/2( Log[1/t]+ I Pi)] Exp[1/2 (Log[t]+ I Pi)]
Exp[3/2( -Log[t]+ I Pi)] Exp[1/2 (Log[t]+ I Pi)]
Exp[3/2( -Log[t])]*Exp[3/2I Pi] *Exp[1/2 Log[t]]*Exp[ 1/2I Pi]
Exp[3/2( -Log[t])+1/2 Log[t]]*Exp[3/2I Pi+1/2 I Pi]
Exp[ -Log[t]]*Exp[2I Pi]
1/t*1
1/t
Check this against
Simplify[(-1/t)^(3/2) Sqrt[-t],t>0]
1/t
Also
Simplify[(-1/t)^(3/2) Sqrt[-t],t<0]
-(1/t)
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Peter" <ptrsn2001 at yahoo.com> wrote in message
news:9uq8cg$ada$1 at smc.vnet.net...
> 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[1]:= PowerExpand[(-1/t)^(3/2) Sqrt[-t]]
>
> 1
> Out[1]= -
> t
> ---------------------------------
> The correct answer is -1/t, of course.
>
> Thanks,
> Peter
>
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