clicliclic@freenet.de  wrote:   
   >   
   > "Nasser M. Abbasi" schrieb:   
   > >   
   > > On 3/9/2020 12:20 PM, clicliclic@freenet.de wrote:   
   > > >   
   > > > antispam@math.uni.wroc.pl schrieb:   
   > > >>   
   > > >> [Fri]CAS is an advanced computer algebra system. Its capabilities   
   > > >> range from calculus (integration and differentiation) to abstract   
   > > >> algebra. It can plot functions and has integrated help system.   
   > > >>   
   > > >> [...]   
   > > >>   
   > > >> Notable changes (compared to version 1.3.5):   
   > > >>   
   > > >> - Small improvements to integrator and limits   
   > > >>   
   > > >> - Generalized a few domains and packages   
   > > >>   
   > > >> - Two new convolutions for quantum probability   
   > > >>   
   > > >> - Main FriCAS environment variable is now called FRICAS and main   
   > > >>    executable is called FRICASsys   
   > > >>   
   > > >> Bug fixes, in particular:   
   > > >>   
   > > >> - Better error detection for numeric elementary functions   
   > > >>   
   > > >> - Fixed TeX output of formal derivatives   
   > > >>   
   > > >> - Fixed input form of formal derivatives   
   > > >>   
   > > >   
   > > > Perhaps the new version needs to be broken in like a new pair of   
   > > > shoes? Here are some tough Risch integration exercises involving   
   > > > cube roots:   
   > > >   
   > > >    integrate((x + 3)/((x - 1)^2*(x^2 - 1)^(1/3)), x)   
   > > >   
   > > >    integrate((x + 1)/((x + 3)*(2*x + 1)*(x^2 + 1)^(1/3)), x)   
   > > >   
   > > >    integrate((x + 1)/((x - 1)*(2*x + 1)*(3*x^2 - 1)^(1/3)), x)   
   > > >   
   > >   
   > >   FriCAS Computer Algebra System   
   > >    Version: FriCAS 1.3.6   
   > > Timestamp: Mon 09 Mar 2020 12:35:03 PM CDT   
   > >   
   > > ii:=integrate((x + 3)/((x - 1)^2*(x^2 - 1)^(1/3)), x);   
   > >   
   > >     ((-3)*((x^2+(-1))^(1/3))^2)/(2*x^2+(-4)*x+2)   
   > >   
   > > setSimplifyDenomsFlag(true)   
   > > ii:=integrate((x + 1)/((x + 3)*(2*x + 1)*(x^2 + 1)^(1/3)), x);   
   > >   
   > >     >> Error detected within library code:   
   > >     integrate: implementation incomplete (residue poly has multiple   
   non-linear factors)   
   > >   
   > > ii:=integrate((x + 1)/((x - 1)*(2*x + 1)*(3*x^2 - 1)^(1/3)), x);   
   > >   
   > >     >> Error detected within library code:   
   > >     integrate: implementation incomplete (residue poly has multiple   
   non-linear factors)   
   > >   
   >   
   > The last two evaluations are not wrong, but they are certainly   
   > suboptimal :(. I suspect that Rubi can do better!   
      
   There are many things in FriCAS that could be improved.  This   
   release contains relatively small improvements to integrator.   
   I am preparing bigger changes, but finishing them will take   
   time.  Concering those integrals, there are several possibilities   
   to handle them.  Changing variable eliminates degree 3 root   
   and gives square root of degree 3 polynomial.  On similar   
   (maybe the same) examples it changes integral that FriCAS   
   can not handle to one that gives result.  It is also possible   
   that other improvement will sove the problem: the integrals   
   exhibit strange singularity, I plan to use method which   
   is less sensitive to singularits.   
      
   And of course, having no better method one could use Rubi   
   way: add lookup table and retrive precomputed answer from   
   the table.   
      
   --   
                                 Waldek Hebisch   
      
   --- SoupGate-Win32 v1.05   
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