From: fateman@gmail.com   
      
   There's more than just "size" to determine if the result of an integration is   
   optimal. Indeed, size might be misleading.    
   Consider the two results for integration of x^n wrt x.   
      
   r1= x^(n+1)/(n+1)   
      
   and   
   r2= (x^(n+1)-1)/(n+1)   
      
   Clearly r2 has more characters, and by some measure is more complex.   
      
   r1-r2   is 1/(n+1), a constant wrt x.  so we should realize both answers are   
   correct "within a constant".   
      
   Arguably r2 is better because the limit of r2 as n approaches -1  is ln(x).   
   The limit as r1 approaches -1 is indeterminate.   
      
   Looking at a very small sample of the Rubi tests, it seems that other measures   
   of optimality might be missed.  For example, an answer that has a structure of   
   a series in sin(x), sin(2*x), sin(3*x) .... vs powers of sin(x), cos(x)...   
      
   Another aspect is whether the integration program has as its responsiblity the   
   reduction of the answer -- or is the user likely to apply a simplification   
   program  (say, to canonicalize rational functions, expand polynomials or   
   factor them, apply    
   trigonometric simplifications, etc.)   
      
   I can imagine a situation in which one program returns an answer that includes   
   an integral of sin(x)/x  [thereby failing the Rubi test]  where another   
   returns Si(x),  the sine integral, defined as the integral of sin(x)/x.  Which   
   looks mostly like a    
   nomenclature issue.  There is also the possibility that  (I see this in   
   Maxima), the result is expressed  in another form entirely, e.g. via   
   Incomplete Gamma functions.  I suppose that it depends on what your favorite   
   numerical library contains, Si,    
   Gamma, Hypergeometric functions etc.   
      
   If it is not already considered, perhaps the simplification issue can be   
   separated out somewhat.  For instance, the Rubi testing might consider a   
   result R from Maxima to be too complicated.  What about trigsimp(R), or   
   ratsimp(R)  or for that matter,    
   ratsimp(trigsimp(R))?  There are a number of additional plausible routines.   
   I don't see an easy way of handling the possibilities though.     
   In fact, given g = diff ( integrate(f,x),x),  if the programs are correct, we   
   know that f and g are equivalent.  Yet  computing simplify(f-g) to get 0, for   
   some simplification program,  may be quite difficult.   
      
   This testing of Rubi is valuable --- I  look forward to Rubi 5 for Maxima,    
   the system I most often use.   
   RJF   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)