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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 9,870 of 10,432   
   clicliclic@freenet.de to clicliclic@freenet.de   
   Re: elementarily integrable or not?   
   17 Mar 18 19:31:26   
   
   clicliclic@freenet.de schrieb:   
   >   
   > "Nasser M. Abbasi" schrieb:   
   > >   
   > > On 3/16/2018 10:18 AM, clicliclic@freenet.de wrote:   
   > > >   
   > > > A different problem for a similar integrand:   
   > > >   
   > > > setSimplifyDenomsFlag(true)   
   > > >   
   > > > integrate((5*x-9*sqrt(6)+26)/((x^2-4*x-50)*sqrt(x^3-30*x-56)), x)   
   > > >   
   > > > on the FriCAS web interface currently results in:   
   > > >   
   > > >>> Error detected within library code:   
   > > >     catdef: division by zero   
   > > >   
   > > > The FriCAS )version command reports 1.3.2. Can earlier or later   
   > > > versions decide if this integral is elementary or not?   
   > > >   
   > >   
   > > Same thing on 1.3.3 on Linux:   
   > >   
   > > >fricas   
   > >                         FriCAS Computer Algebra System   
   > >                              Version: FriCAS 1.3.3   
   > >                     Timestamp: Tue Mar 13 22:58:43 CDT 2018   
   > > (1) -> setSimplifyDenomsFlag(true)   
   > >     (1)  false   
   > > (3) -> ii:=integrate((5*x-9*sqrt(6)+26)/((x^2-4*x-50)*sqrt(x^3-30*x-56)),   
   x)   
   > >   
   > >     >> Error detected within library code:   
   > >     catdef: division by zero   
   > >   
   >   
   > Thanks. "Is there any moderately-sized square-root pseudo-elliptic   
   > integral on which FriCAS is still known to fail?" I asked a while ago.   
   > The present integral would be one if it is integrable in elementary   
   > terms.   
   >   
      
   Here's a much more deadly failure:   
      
   setSimplifyDenomsFlag(true)   
      
   integrate((7*x + 6*sqrt(17*sqrt(2) + 23) + 9*sqrt(2) + 34)   
   /((x^2 + 2*x*(3*sqrt(sqrt(2) + 1) + 1) + 6*sqrt(58*sqrt(2) + 82)   
    - 18*sqrt(2) - 26)*sqrt(x^3 - 30*x - 56)), x)   
      
   is returned unevaluated on the web interface. But my oracle says that   
   the integand is pseudo-elliptic according to Goursat:   
      
   goursat3((7*x + 6*SQRT(17*SQRT(2) + 23) + 9*SQRT(2) + 34)   
   /(x^2 + 2*x*(3*SQRT(SQRT(2) + 1) + 1) + 6*SQRT(58*SQRT(2) + 82)   
    - 18*SQRT(2) - 26), x, -56, -30, 0, 1)   
      
   [false, false, false, true]   
      
   The last answer counts.   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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