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MathGroup Archive 2000

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Re: Flat, OneIdentity attributes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21632] Re: Flat, OneIdentity attributes
  • From: "Drago Ganic" <drago.ganic at in2.hr>
  • Date: Tue, 18 Jan 2000 02:35:18 -0500 (EST)
  • References: <85u3e7$d5j@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Ted !
 
The Mathematica Book section 2.3.7 says
 
 "However, in the case where x_ matches a single argument in a flat function, the question comes up as to whether the object it matches is really just the argument a itself, or f[a]. Mathematica chooses the first of these cases if the function carries the attribute OneIdentity, and chooses the second case otherwise. "  <<=========
 
 In our case f[2] is transformed to f [ f[2] ] 
 
 
 When you use 
 
 In ->        f[2] /. f[n_] :> n+10
 Out ->    10+ f[2]
 
you can see it clear. 
 
 
 For the input      
 
     f[2] /. f[n_Integer] :> n+10
     f[2]
 
 we don't have a match, because the _head_ of the argument is f and not Integer (the argument is f [2]). 
 
 Try
 
     f[2] /. f[n_f] :> n+10
     10 + f[2]
 
 Exactly this problem is eliminated with OneIdentity.
 
 Hope, I helped.
 
 Greetings from Croatia,
 Drago Ganic
 
"Ersek, Ted R" <ErsekTR at navair.navy.mil> wrote in message news:85u3e7$d5j at smc.vnet.net...
> For the most part I understand how Flat and OneIdentity are related and I
> demonstrate this using Version 4 in the examples below.
> 
> In the first example (f) has the attributes Flat and OneIdentity. 
> The pattern matcher treats f[a,2,3] as f[a,f[2,3]] then uses the 
> replacement rule and {1,{2,3}} is returned.
> 
> In[1]:=
> ClearAll[f];
> Attributes[f]={Flat,OneIdentity};
> f[1,2,3]//.f[a_,b_]:>{a,b}
> 
> Out[3]=
> {1,{2,3}}
> 
> ---------------------------------------------------
> In the next example the only attribute (f) has is Flat.
> In this case the pattern matcher treats f[1,2,3] as 
> f[f[1],f[f[2],f[3]]] then uses the replacement rule and 
> {f[1],{f[2],f[3]}} is returned.
> 
> 
> In[4]:=
> ClearAll[f];
> Attributes[f]={Flat};
> f[1,2,3]//.f[a_,b_]:>{a,b}
> 
> Out[6]=
> {f[1],{f[2],f[3]}}
> 
> OneIdentity the pattern matcher doesn't wrap (f) around a single argument
> when it tries different ways of nesting (f).
> 
> --------------------------------
> In the next example (f) has the attributes Flat, OneIdentity and the rule is
> used.
> 
> In[7]:=
> ClearAll[f]
> Attributes[f]={Flat,OneIdentity};
> f[2]/.f[n_Integer]:>n+10
> 
> Out[9]=
> 12
> 
> --------------------------------
> For reasons I can't understand the rule isn't used in the next example. Can
> anyone explain why?
> 
> In[10]:=
> ClearAll[f]
> Attributes[f]={Flat};
> f[2]/.f[n_Integer]:>n+10
> 
> Out[12]=
> f[2]
> 
> ---------------------------------------------
> Regards,
> Ted Ersek
> 
> For Mathematica tips, tricks see 
> http://www.dot.net.au/~elisha/ersek/Tricks.html
> 



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