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MathGroup Archive 1995

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Re: Operator Definition

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg993] Re: Operator Definition
  • From: rubin at msu.edu (Paul A. Rubin)
  • Date: Mon, 8 May 1995 03:18:22 -0400
  • Organization: Michigan State University

In article <3nv9j4$9g8 at news0.cybernetics.net>,
   pitts at mayo.EDU (Todd Pitts) wrote:
->I would like to define a shift operator similar to the derivative 
->for continuous time that is already built into Mma. i.e. 
->
->Shift[ how far ][ expression head ] [ variable(s) to which shift should 
be applied ]
->
->I would also like to have it enjoy a relationship to something called S 
sort of
->like D[] and Derivative[][][].  Any ideas on how to define it or where I 
could
->go to learn how to do it right?  I have the standard Mma reference book 
by
->Wolfram but haven't (as of yet) been able to extract the proper way to 
get 
->what I need.
->
->Thanks in Advance,
->Todd Pitts
->
Do you want to shift *all* the arguments of a function?  Assuming you're 
talking about shifting all arguments by adding a constant (as in a time 
shift), as opposed to rotating the order of the arguments, how about this 
definition?

   In[1]:=  Shift[lag_][f_][v__] := f[ Sequence @@ ((#+lag)& /@ {v}) ]
   In[2]:=  Shift[3][f][a, b, c]
   Out[2]=  f[3 + a, 3 + b, 3 + c]
   In[3]:=  Shift[-1][Exp][y]
   Out[3]=  E^(-1 + y)

Note that "v" in line 1 is followed by *two* underscores.

Paul


**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
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Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE


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