Differential operators

• To: mathgroup at smc.vnet.net
• Subject: [mg2166] Differential operators
• From: sherod at boussinesq.Colorado.EDU (Scott Herod)
• Date: Wed, 11 Oct 1995 01:58:52 -0400
• Organization: University of Colorado at Boulder

```I was trying to write a small piece of code to play with computing
commutators of vector fields.  I wanted something like

vector = x D[#, x] + y D[#, y] &;

etc.  Unfortunately I noticed the following annoying behavior.

----------------------------------------------
Mathematica 2.2 for Solaris
License valid through 28 Nov 1995.
-- Open Look graphics initialized --

In[1]:= vector = D[#, x] &

Out[1]= D[#1, x] &

In[2]:= Simplify[vector]

Out[2]= 0 &

In[3]:= vector = Dt[#, x] &

Out[3]= Dt[#1, x] &

In[4]:= Simplify[vector]

Out[4]= 0 &

-----------------------------------------------

I know that I could write my own derivative operator but it would be nice
to use the built in version.  Suggestions?  Notice that vector does work
correctly.

-----------------------------------------------
In[5]:= vector

Out[5]= Dt[#1, x] &

In[6]:= vector[f]

Out[6]= Dt[f, x]
----------------------------------------------

Scott A. Herod
Applied Mathematics