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Re: Dot[]->1

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  • Subject: Re: Dot[]->1
  • From: John Lee <lee at>
  • Date: Fri, 7 Aug 92 08:18:32 -0700

Michael Trott <trott at> writes:

>  On simplifying some large expressions via some rules I ended with
>  expressions of the following type:

>  Dot[]+Dot[x,y] .
>  In this expression I would like to replace the first part by 1. So I tried:

>  (Dot[] + Dot[x,y])/.{Dot[]->1}.

>  But the result was not what I expected (1+x.y), but rather

>  1 + 1.x.y   .

>  Can somebody tell me how to do my disired replacement and what happens
>  in the described example?

>  Actually I observed this behaviour first in expressions of the
>  above type with Dot --> NonCommutativeMultiply.

The reason for this behavior is that Dot has the Flat attribute, which
means that Dot[x,y] is equivalent to Dot[Dot[],x,y] for pattern matching
purposes.  The same goes for NonCommutativeMultiply. 

Here is an alternative pattern that does what you want:

  In[2]:= (Dot[] + Dot[x,y]) /. (x_Dot /; Length[x]==0) :> 1

  Out[2]= 1 + x . y

Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA

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