antispam@math.uni.wroc.pl schrieb:   
   >   
   > clicliclic@freenet.de wrote:   
   > >   
   > > A state-of-the-art implementation of a Risch integrator   
   > >   
   > > )version   
   > >   
   > > Value = "FriCAS 1.3.0 compiled at Thu Sep  1 17:01:37 UTC 2016"   
   > >   
   > > responds to   
   > >   
   > > integrate((1 + x)/((1 + x + x^2)*(a + b*x^3)^(1/3)), x)   
   > >   
   > > with   
   > >   
   > > >> Error detected within library code:   
   > >    catdef: division by zero   
   > >   
   > > In his "Symbolic Integration Tutorial", Bronstein appears to believe in   
   > > the existence of a workable integration algorithm for algebraic   
   > > integrands involving a simple radical extension. Didn't he know what he   
   > > was talking about?   
   >   
   > Writing paper he ceratainly knew what is is writing.  But writing   
   > code he apparently assumed that he will be lucky.  Or to put it   
   > differetly: code he wrote is enough to "demostrate" that algorithm   
   > works.  But there remain "uninteresting" programming probles to   
   > resolve.  To the point: his code uses random integers.  If   
   > substituting those integers into one of denominators gives zero,   
   > then you will see this error.  Correct algorithm would retry   
   > with different values.  But his code just gives error.  Recent   
   > changes to FriCAS lead to change in random choice and for   
   > some integrals (like this one) the problem became very visible.   
   >   
   > One can try to hide the problem using more randomness.  Or   
   > one can do "uninteresting" programming and properly implement   
   > retry.   
   >   
   > BTW: This is FriCAS bug and proper place to report this is   
   > FriCAS mailing list or Sourceforge bugtracke.  And this   
   > problem was was already reported (after relase of 1.3.0).   
   >   
      
   Oh, I thought I was the first to try this particular variation of a   
   familar cube-root integrand. But to implement a loop over different   
   pseudo-random numbers should be easy, and its omission may be a mere   
   oversight. I will submit this integrand again to the next version.   
      
   Another thing has me wondering. Your antiderivatives of rational   
   functions can be discontinuous because the ATAN part is not always   
   rewritten to involve polynomial arguments only, as proposed by Rioboo.   
   For example, FriCAS 1.3.0 computes (expressed in Derive notation)   
      
   INT((2560*x^3 - 400*x^2 - 576*x - 84)/(320*x^4 + 80*x^3 - 12*x^2   
    + 24*x + 9), x) = 2*LN(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9)   
    + 2*SQRT(11)*ATAN(SQRT(11)*(10*x + 3)/(80*x^2 + 10*x - 9))   
      
   This is surprising especially since Bronstein provides pseudocode of   
   Rioboo's algorithm in his book (Ch. 2.8).   
      
   Martin.   
      
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