"Nasser M. Abbasi" schrieb:   
   >   
   > On 2/22/2018 1:24 PM, clicliclic@freenet.de wrote:   
   > >   
   > > "Nasser M. Abbasi" schrieb:   
   > >>   
   > >> On 2/22/2018 7:57 AM, clicliclic@freenet.de wrote:   
   > >>>   
   > >>> "Nasser M. Abbasi" schrieb:   
   > >>>>   
   > >>>> How high a number "n" can your cas integrate this?   
   > >>>>   
   > >>>>           1/((1 + x^n)*(1 + x^2))   
   > >>>>   
   > >>>> Fricas 1.3.2 and Rubi 4.14.7 go up to n=18. Then after that, they   
   > >>>> return unevaluated.   
   > >>>>   
   > >>>> Mathematica gives an answer for higher than 18, but the result   
   > >>>> after 18 is in terms of Root objects. I tried up to n=100.   
   > >>>>   
   > >>>> Maple also can go higher than n=18, and it also gives results   
   > >>>> in terms of RootOf. Tried up to n=200. So to remove these Roots,   
   > >>>> one has to evaluate the answer numerically.  I assume this is why   
   > >>>> Rubi and Fricas stop at n=18.   
   > >>>>   
   > >>>> Any insight why 18 is the limit here? Is it due to some   
   > >>>> factorization done, which after n=18 produces polynomials that   
   > >>>> can't be solved exactly for higher order?   
   > >>>>   
   > >>   
   > >> [...]   
   > >>   
   > >> Sorry, let me clarify things again. FriCAS hangs at n=29.   
   > >> I have it running for one hr now at n=29. Will leave it   
   > >> running and will check on it after I come back from school.   
   > >>   
   > >> Here is what I found:   
   > >> ======================   
   > >> Rubi:  Up to n=18 OK, then unevaluated after n=18.   
   > >> Maple: Up to n=18 OK, then uses ROOT objects for n>18. Tried to 200   
   > >> Mathematica: Up to n=18 OK, then uses ROOT objects for n>18. Tried   
   > >> to 100 FriCAS: Up to n=28 OK, then "hangs" or still trying.....   
   > >>   
   > >> So the winner so far is FriCAS on this test, it does it   
   > >> for n=28, with no root objects. root objects can only be   
   > >> evaluated numerically to get rid of them.   
   > >>   
   > >   
   >   
   > > I am glad to learn that the super-massive FriCAS bug has vanished   
   > > at a second glance! In fact, I see no problem here at all. While it   
   > > remains uncertain how long the computation for n=29 takes, this is   
   > > likely to happen for some power anyway ...   
   > >   
   >   
   > Yes, sorry, I must have mixed it up with 1/((1 + x^n)*(1 + x^2))   
   > for `n` being symbolic (no numerical value). In this call,   
   > all CAS systems return unevaluated.   
   >   
   > I like to also report that Fricas finally gave answer for n=29.   
   > many pages long. But it did not hang.   
   >   
   > good job Fricas.   
   >   
      
   It may be appropriate here to recall another integrand for which   
   something basic went wrong inside FriCAS:   
      
   integrate(1/((p*sqrt(1 - x^2) - 1)*sqrt(p*sqrt(1 - x^2) - x^2)), x)   
      
   which used to exit with:   
      
   >> Error detected within library code:   
      Denominator not equal to 1   
      
   If this integral is found to be non-elementary, as I expect it to, it   
   should simply be returned unevaluated.   
      
   Martin.   
      
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