From: nma@12000.org   
      
   On 8/31/2021 11:07 AM, clicliclic@freenet.de wrote:   
      
   >   
   > In his manuscript "A Simple Method for Computing Some Pseudo-Elliptic   
   > Integrals in Terms of Elementary Functions" (arXiv:2004.04910v2), Sam   
   > Blake found Maple's Trager method to solve 91.6% of his test suite of   
   > 190 algebraic integrals. So the 56.2% you obtained on a larger suite of   
   > 3154 algebraics are surprisingly few.   
   >   
   > When, in your last run of the full Rubi suite, Maple improved beyond   
   > FriCAS on the Timofeev integrals, that looked to me like a result of   
   > Maple automatically fielding Trager's method on purely algebraic   
   > integrands. But this interpretation may have been premature.   
   >   
   > The point may be settled by having Maple recompute the integrals with   
   > "method = Trager" instead of your implicit "method = _DEFAULT", or   
   > presumably much faster with "method = [_DEFAULT, Trager]".   
   >   
   > Martin.   
   >   
      
   What I can do is this. Run Maple with all its methods, using the   
   option "method=_RETURNVERBOSE" which tries all its methods and   
   then pick the result that passes but the with lowest leafsize.   
   When there is a  tie, will pick the first one.   
      
   For an example, I can change Maple test to do   
      
   sol:=int(x/(x^2-1)^(1/4),x,method=_RETURNVERBOSE)   
      
   Which gives   
      
   sol := ["gosper" = 2/3*(x - 1)*(x + 1)/(x^2 - 1)^(1/4),   
   "derivativedivides" = 2/3*(x^2 - 1)^(3/4),   
   "default" = 2/3*(x^2 - 1)^(3/4),   
   "trager" = 2/3*(x^2 - 1)^(3/4),   
   "meijerg" = 1/2*(-signum(x^2 - 1))^(1/4)*x^2*hypergeom([1/4, 1], [2],   
   x^2)/signum(x^2 - 1)^(1/4),   
   "risch" = 2/3*(x^2 - 1)^(3/4),   
   FAILS = ("lookup", "norman", "elliptic")]   
      
   If this sounds OK with everyone, I can do the above and re-run the   
      
        summer_2021/test_cases/9_Blake_problems   
      
   test and see if Maple result improves or not.   
      
   regards,   
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
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