From: nma@12000.org   
      
   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?   
   >>   
   >   
      
   > Derive 6.10 evaluates the integrals for n=1 through n=6 quickly. For   
   > the n=7 integrand, factors containing ATAN functions are produced,   
   > which bog the computation down. I have not tried to find out if Derive   
   > would eventually finish, churn on forever, or exhaust its memory in   
   > this case.   
   >   
   > Martin.   
   >   
      
   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.   
      
   --Nasser   
      
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