Re: Defining differential operators question

• To: mathgroup at smc.vnet.net
• Subject: [mg13850] Re: [mg13797] Defining differential operators question
• From: "Jurgen Tischer" <jtischer at col2.telecom.com.co>
• Date: Sun, 30 Aug 1998 03:35:37 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Tom,
this worked on my PC for your examples:

NewD[li_List,f_Symbol]:= Evaluate[li.
Table[Derivative[n][f][#],{n,0,Length[li]-1}]]&

Jurgen

-----Original Message-----
From: tgoetze at my-dejanews.com <tgoetze at my-dejanews.com> To:
mathgroup at smc.vnet.net
Subject: [mg13850] [mg13797] Defining differential operators question

>I would like to be able to define a family of differential operators
>that act on a function being passed in. For simplicity sake, I will
>assume that the functions being passed in are functions of one
>variable.
>
>Suppose that given a list L={a0,a1,a2,a3}, that the differential
>operator defined by L, acts on a function F by:
>
>a0*F + a1*F' + a2*F'' + a3*F'''
>
>My attempt was a package that looks like this:
>
>----------------------------Package Code----------------------------
>NewD::usage = "A differential operator defined by the list."
>
>Begin["Private`"]
>
>NewD[myList_List,f_Symbol]:=  Module[{},  If[myList[[1]] > 0,
>If[Length[myList] > 1, myList[[1]]*Identity +
>Sum[(myList[[i]])(Derivative[i-1][f]), {i,2,Length[myList]}],
>myList[[1]]*Identity],
>Sum[Times[myList[[i]],Derivative[i-1][f]],{i,2,Length[myList]}]  ]];
>End[] --------------------------End of Package
>code----------------------------
>
>Now this package seems to work for some simple cases, but for more
>complicated cases, it seems I get into a "nest" of pure functions that
>I can't seem to get Mathematica to evaluate.
>
>For example, here is a short kernel session illustrating the problem:
>
>------------------------Notebook Extract------------------------------
>Mathematica 3.0 for Microsoft Windows Copyright 1988-97 Wolfram
>Research, Inc.
> -- Terminal graphics initialized --
>
>In[1]:= <<"a:/diffop.m"
>
>Out[1]= Private`
>
>In[2]:= g[x_]:=x^3;
>
>In[3]:= NewD[{0,2,0,4},g]
>
>                          2
>Out[3]= 4 (6 & ) + 2 (3 #1  & )
>
>In[4]:= %[1]
>
>                           2
>Out[4]= (4 (6 & ) + 2 (3 #1  & ))[1]
>
>In[5]:= Through[%,Plus]
>
>                                2
>Out[5]= (4 (6 & ))[1] + (2 (3 #1  & ))[1]
>
>In[6]:= NewD[{1,1,1},g]
>
>                                    2 Out[6]= Identity + (6 #1 & ) + (3
>#1  & )
>
>In[7]:= %[1]
>
>                                     2 Out[7]= (Identity + (6 #1 & ) +
>(3 #1  & ))[1]
>
>In[8]:= Through[%,Plus]
>
>Out[8]= 10
>
>--------------------End of Notebook Extract-----------------------
>
>I want to be able to get %5 evaluated. Any suggestions? It looks like it
>might be a problem with the constant mulitple of a pure function. For
>example, what is 6 Identity as a pure function? I guess I want (6 #)&,
>but it's not clear how to do that. (I've tried (myList[[1]])& instead
>of myList[[1]]*Identity, but pure functions have Hold All, so it
>doesn't quite work).
>
>Thanks,
>
>Tom Goetze
>TomG at UltimateTech.com
>
>-----== Posted via Deja News, The Leader in Internet Discussion ==-----
>http://www.dejanews.com/rg_mkgrp.xp   Create Your Own Free Member Forum
>
>

```

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