Albert Rich schrieb:   
   >   
   > [...]   
   >   
   > You comment that only 3 rules are required to reduce the exponents of   
   > nondegenerate integrands to [-1,0].  Unfortunately, their   
   > implementation in the real-world is not so simple.  Understandably,   
   > Mathematica's pattern matcher does not recognize expressions of the   
   > form A, A+B x  and  A+C x^2  as matching expressions of the form  A+B   
   > x+C x^2  (that is B and C cannot be 0 in order to match).  So the new   
   > Rubi has to have 3 rules for integrating each of the following forms:   
   >   
   >      (a+b x+c x^2)^p (d+e x+f x^2)^q   
   >      (a+b x+c x^2)^p (d+e x+f x^2)^q (A+B x)   
   >      (a+b x+c x^2)^p (d+e x+f x^2)^q (A+C x^2)   
   >      (a+b x+c x^2)^p (d+e x+f x^2)^q (A+B x+C x^2)   
   >   
   >      (a+b x+c x^2)^p (d+f x^2)^q   
   >      (a+b x+c x^2)^p (d+f x^2)^q (A+B x)   
   >      (a+b x+c x^2)^p (d+f x^2)^q (A+C x^2)   
   >      (a+b x+c x^2)^p (d+f x^2)^q (A+B x+C x^2)   
   >   
   >      (a+c x^2)^p (d+e x+f x^2)^q   
   >      (a+c x^2)^p (d+e x+f x^2)^q (A+B x)   
   >      (a+c x^2)^p (d+e x+f x^2)^q (A+C x^2)   
   >      (a+c x^2)^p (d+e x+f x^2)^q (A+B x+C x^2)   
   >   
   >      (a+c x^2)^p (d+f x^2)^q   
   >      (a+c x^2)^p (d+f x^2)^q (A+B x)   
   >      (a+c x^2)^p (d+f x^2)^q (A+C x^2)   
   >      (a+c x^2)^p (d+f x^2)^q (A+B x+C x^2)   
   >   
   > Clearly as the number of parameters to rules increases, the   
   > impracticality of using pattern matching to implement a rule-based   
   > system like Rubi 4 becomes obvious.  Happily however, using a   
   > decision-tree to implement a rule-based system like Rubi 5 avoids this   
   > fan-out problem.  This is because like your int22 function, a   
   > decision-tree's if-then-else function can accept arguments having a   
   > value of 0.   
   >   
   > So I need to resist the urge to add more knowledge to Rubi 4, and   
   > instead focus my efforts on getting Rubi 5 out-the-door...   
   >   
      
   16*3 = 48 rules; but distinguishing polynomials by degree only, this   
   would better be counted as 3*3 = 9 rules. It seems to be settled in your   
   mind by now that Rubi's pattern-matching activities should be quickly   
   forgotten once version 5 is out and stable. On that occasion, you may   
   thus even think of renaming Rubi and restarting at version 1 :).   
      
   Martin.   
      
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