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Re: "Transparency" with respect to differentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg74029] Re: "Transparency" with respect to differentiation
• From: Martin Schoenecker <ms_usenet at gmx.de>
• Date: Wed, 7 Mar 2007 03:06:00 -0500 (EST)
• Organization: Technische Universitaet Darmstadt
• References: <es909c$2c5$1@smc.vnet.net>

Regarding the object quat with the following properties

> quat[a_+b_]:=quat[a]+quat[b]
> quat/:D[quat[fun_],var__]:=quat[D[fun,var]]

The unwanted behaviour was that differenciation was carried out before 
distribution:

> In[8]:= D[quat[f[x] + g[x]], x]
> Out[8]= f'[x] quat'[f[x]] + g'[x] quat'[g[x]]

I found out with the help of the Mathematica Reference Guide, A.2.7 that 
  UpValues have a higher precedence than DownValues, which explains this 
behaviour.  Trying to give the needed rule explicitly results in


quat /: D[quat[(a_) + (b_)], var__] :=
   D[quat[a], var] + D[quat[b], var]

$Failed
TagSetDelayed::"tagpos":" .... too deep for an assigned rule to be found.

Now the question, reformulated, is:  how could I define the mentioned 
properties so that they would be carried out in the right order?

Thanks,
Martin