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

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   Message 9,823 of 10,432   
   clicliclic@freenet.de to Nasser M. Abbasi   
   Re: what special about 18 in this integr   
   22 Feb 18 20:24:23   
   
   "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 ...   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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