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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: [mg56794] Re: ZTarnsform[Sin[4 n],n,z] OK, but ZTransform[Sin[5 n],n,z,] hangs?
• From: "Mariusz Jankowski" <mjankowski at usm.maine.edu>
• Date: Fri, 6 May 2005 03:00:05 -0400 (EDT)
• Organization: University of Southern Maine
• References: <d5cth5$mbe$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Steve, yes, indeed strange. must be some unfortunate limitation (Error?) in
an internal evaluation. Possibly algebraic explosion. The same problem
occurs for other Integers and reals, nothing special about '5'. Other
manifestations of problems abound:

ZTransform[ Sin[2 Pi n], n, z] -> 0 (* ok*)

ZTransform[ Sin[8 Pi n], n, z]  (* had to abort *)

What is also strange to me is the returned result for 

ZTransform[ Sin[ 1.5 n], n, z]

which comes back in terms of a rational representation for 1.5. I may be
wrong, but I do not recall Mathematica returning an exact result given an
approximate input?

Mariusz








>>> steve<nma124 at hotmail.com> 05/05/05 6:45 AM >>>
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