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Another problem with FunctionExpand

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27841] Another problem with FunctionExpand
  • From: Jack Goldberg <jackgold at math.lsa.umich.edu>
  • Date: Mon, 19 Mar 2001 17:51:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi;

Well here I go again.  In my previous posts on FunctionExpand,
Bob Hanlon suggested that using assumptions  Element[x,Reals] in 
this expression:  FunctionExpand[UnitStep[x^2],Element[x,Reals]] corrects
the embarrassment of having 

	FunctionExpand[UnitStep[x^2]] return UnitStep[-x]+UnitStep[x]

which is incorrect when x=0.  (Since UnitStep is defined only for real x,
such an assumption is logically redundant.)  However Element[x,Reals] does
not save 

	FunctionExpand[UnitStep[1-x^2],Element[x,Reals]]

This call returns -UnitStep[-1+x]+UnitStep[1+x] (which is incorrect at
x=1) on ver 4.0 using Unix and Mac operating systems.

I believe my list of 4 failures (some quit modest, I admit) of the
composition of FunctionExpand and UnitStep needs repair.  The overwhelming
response to my previous posts (1- it would have been zero except for Bob
Hanlon's lone voice) lead me to suspect that this repair has
low priority :-).  Oh well, you are warned!

ps.  Here is another "barn-burner :-) - 

	FunctionExpand[ f[x]*Discrete[x],Element[x,Reals] 

should return f[0]*Discrete[x].  It does not; f[x]*Discrete[x] is returned.  
 
Always peaking under the rug,

Jack




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