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Re: ZTarnsform[Sin[4 n],n,z] OK, but ZTransform[Sin[5 n],n,z,] hangs?

• To: mathgroup at smc.vnet.net
• Subject: [mg56804] Re: [mg56772] ZTarnsform[Sin[4 n],n,z] OK, but ZTransform[Sin[5 n],n,z,] hangs?
• From: Devendra Kapadia <dkapadia at wolfram.com>
• Date: Fri, 6 May 2005 03:00:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On Thu, 5 May 2005, steve wrote:

> Hello;
> This is Mathematica 5.1 on windows.
> 
> This is a strange one.
> 
> When I start Mathematica and type
> 
> ZTarnsform[Sin[4 n],n,z]
> 
> Then I get the answer.
> 
> but if replace '4' by '5' above, I see Mathematica starts
> to consume huge amount of memory untill the PC hangs running
> out of virtual RAM.
> 
> ZTarnsform[Sin[5 n],n,z]   <---- hangs
> ZTarnsform[Sin[4 n],n,z]   <---- ok
> 
> any one has any idea what is going on? is this some subtle
> mathemtical thing I am overlooking that is causing this?
> what is so special about '5' here? 
> 
> thanks,
> Steve
> 
Hello Steve,

Thank you for reporting this problem with ZTransform in Mathematica 5.

This appears to have been caused by a hang in Limit (which is used by 
ZTransform for convergence testing), when we use Sin[5 n] instead of
Sin[4 n] in ZTransform, in Mathematica 5.

As a workaround, you could try applying TrigToExp in the example that 
hangs, as shown below. 

================================================================
In[1]:= $Version

Out[1]= 5.1 for Linux (February 20, 2005)

In[2]:= ZTransform[TrigToExp[Sin[5 n]], n, z] // Together//InputForm

Out[2]//InputForm=
((I/2)*(-1 + E^(10*I))*z)/(-E^(5*I) + z + E^(10*I)*z - E^(5*I)*z^2)

================================================================

 
Sorry for the inconvenience caused by this problem.

Sincerely,

Devendra Kapadia.
Wolfram Research, Inc.