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Re: Strange Behaviour of ReplaceAll with Subscript (A bug or what?)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113339] Re: Strange Behaviour of ReplaceAll with Subscript (A bug or what?)
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Sun, 24 Oct 2010 06:05:40 -0400 (EDT)
  • References: <i9ufjj$rjf$1@smc.vnet.net>

Thomas Dowling wrote:

> Hello,
>
> I have come across some strange behaviour with ReplaceAll when creating
> subscripted variables,
> which I am not able to explain.
>
> The Problem:
>
> I have lists like the following:
>
> list1 = Partition[Range[6], {3}]
>
> Out[5]={{1,2,3},{4,5,6}}
>
> list2 = Partition[Range[9], {3}]
> list3 = Partition[Range[12], {3}]
>
> I wish to convert to a list of indexed variables which I do as follows:
>
> replist={Subscript[a,x],Subscript[a,y],Subscript[a,z]};
>
> list1/.{x_,y_,z_}-> replist
>
> This produces the expected output
>
> {{Subscript[a, 1],Subscript[a, 2],Subscript[a, 3]},{Subscript[a,
> 4],Subscript[a, 5],Subscript[a, 6]}}
>
> The same applies to list3
>
> list3/.{x_,y_,z_}-> replist
>
> However, **list2** produces the following
>
> list2/.{x_,y_,z_}-> replist
>
> {Subscript[a, {1,2,3}],Subscript[a, {4,5,6}],Subscript[a, {7,8,9}]}
>
> No such problem arises with Power or with Times (but the same problem
> occurs with Superscript)
>
> list2/.{x_,y_,z_}-> {Power[a,x],Power[a,y],Power[a,z]}
>
> gives as output
> {{a,a^2,a^3},{a^4,a^5,a^6},{a^7,a^8,a^9}}
>
> A Workaround:
>
> There is an easy solution using Replace and specifying the level
>
> Replace[list2, {x_,y_,z_}-> replist, {1}]
>
> giving the expected output:
>
> {{Subscript[a, 1],Subscript[a, 2],Subscript[a, 3]},{Subscript[a,
> 4],Subscript[a, 5],Subscript[a, 6]},{Subscript[a, 7],Subscript[a,
> 8],Subscript[a, 9]}}
>
>
> The problem arises when the number of entries in the ReplaceAll list
> (ie,{x_,y_,z_}) is the same as the number of sublists in the target list
>
> (The same problem occurs with the following)
>
> Partition[Range[16], {4}]/.{w_,x_,y_,z_}->
> {Subscript[a,w],Subscript[a,x],Subscript[a,y],Subscript[a,z]}
>
> Is this a bug or is such behaviour expected (and if so, what am I missing?)
>
>
> Is thre a way of telling ReplaceAll what level to use (so that it ALWAYS
> produces the
> expected result)?
>
> The more general problem I have is that lists of this type are generated by
> a program, and everything is well unless the generated list happens to have
> 3 sublists.  I can fix things using Replace, but should I have predicted
> such a problem occurring?
>
> I would be interested in your thoughts, and in better workarounds (and in
> better approaches).
>
> Thanks
>
> Thomas Dowling
>
>

You can do the following

This function makes indices to lists like {1,3,5}

indList[v_?VectorQ]:=Subscript[a,#]&/@v

Apply it to nested lists:

indList[vl:{_?VectorQ ..}]:=Map[indList,vl,{1}]

Then you get:

In:= indList[list1]
Out={{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]},
     {Subscript[a,4],Subscript[a, 5], Subscript[a, 6]}}


In:=indList[list2]
Out={{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]},
     {Subscript[a, 4], Subscript[a, 5], Subscript[a, 6]},
     {Subscript[a, 7], Subscript[a, 8], Subscript[a, 9]}}

    
-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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