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.
->
->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
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

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* Paul A. Rubin                                  Phone: (517) 432-3509   *
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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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