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MathGroup Archive 2000

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Re: ReplaceAll in Element[] Q

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25640] Re: [mg25599] ReplaceAll in Element[] Q
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Mon, 16 Oct 2000 03:04:57 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Indeed, this looks strange but actually are  a victim of an "optical
illusion". Observe:

In[1]:=
Element[{a,b},Reals]

Out[1]=
(a | b) \[Element] Reals
 
In other words,   Element[List[variables],Domain] is automatically converted
to Element[Alternatives[ variables],Domain]. These two forms are  equivalent
if entered as input, e.g.
 
In[2]:=
Element[{a,2},Reals]
 
Out[2]=
a \[Element] Reals
 
In[3]:=
Element[Alternatives[a,2],Reals]
 
Out[3]=
a \[Element] Reals
 
You can understand why these two approaches, using List and using
Alternatives, are equivalent if you look at the documentation for Element:
 
In[4]:=
?Element
 
Element[x, dom] asserts that x is an element of the domain
   dom. Element[{x1, x2, ... }, dom] asserts that all the xi
   are elements of dom. Element[patt, dom] asserts that any
   expression matching the pattern patt is an element of dom.
 
Since Alternatives[a,b] is a pattern, the last part of the above applies.
The statement Element[Alternatives[variables],dom] means that any expression
matching Alternatives[variables] is an element of Dom. But every variable in
variables matches Alternatives[variables]. Thus the statement amounts to
saying that all variables are in dom, which is the same as
Element[List[variables],dom].
 
 
on 00.10.11 4:50 PM, Arturas Acus at acus at itpa.lt wrote:
 
>
> Dear Group,
>
> Could anybody help me in understanding this
> obviously strange behaviour
>
> In[22]:=$Version
>
> Out[22]="4.0 for Linux (April 21, 1999)"
>
> In[23]:=ReplaceAll[Element[Alternatives[a, b], Reals], Alternatives -> List]
>
> Out[23]=(a | b) \[Element] Reals
>
> Why not replaced ??? Compare:
>
> In[24]:=ReplaceAll[El[Alternatives[a, b], Reals], Alternatives -> List]
>
> Out[24]=El[{a, b}, Reals]
> As expected
>
> Dr. Arturas Acus
> Institute of Theoretical
> Physics and Astronomy
> Gostauto 12, 2600,Vilnius
> Lithuania
>
>
> E-mail: acus at itpa.lt
> Fax: 370-2-225361
> Tel: 370-2-612906
>
 
--
Andrzej Kozlowski
Toyama International University
JAPAN
 
http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/
 
 


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