diff: variable must not be a number; found: | bug??

   Date: Mon, 18 Nov 2013 09:37:05 -0500
   From: Evan Cooch <evan.cooch at gmail.com>

   Using 5.31.2 under Win 7. Am having major problems trying to figure out 
   why diff is choking on something. Here is a MWE:

   base : 
   matrix([f1*gam,f2*gam,f3*gam,0,0],[0,0,0,S*eps1,0],[0,0,0,0,S*eps2],[f1*(1-gam),f2*(1-gam),f3*(1-gam),0,0],[0,0,0,S*(1-eps1),S*(1-eps2)]);
   cp_base : charpoly(base,lambda);

   Then, I want to implicitly differentiate the characteristic polynomial 
   for f1 wrt to lambda. To do this, I use

   depends(lambda,f1);
   deriv : diff(cp_base,f1);
   lls_f1: solve(deriv,'diff(lambda,f1));


   So far, everything works as it should -- the implicit derivative is 
   exactly what is yielded by other CAS (e.g., Maple).

   The problem is when I try to subst in values for the different 
   parameters (e.g., gam, or f1...). I want to numerically evaluate the 
   derivative. When I try

   lls_f1 : 
   subst([f3=18,f2=12,f1=8,gam=0.0725,S=0.4,eps1=0.1,eps2=0.02,lambda=1.065], 
   lls_f1);

   Maxima returns the following error:

   diff: variable must not be a number; found: 8

Maxima/diff is telling you that when it subst's f1=8 into lls_f1, it
finds diff(blah,8), which is non-sensical.

You want something like 

at(lls_f1,[f1=8]);


   Insights? Suggestions?

There are lots of previous threads on this topic, see for e.g.

http://comments.gmane.org/gmane.comp.mathematics.maxima.general/35582

Leo