oldk1331@gmail.com schrieb:   
   >   
   > > I am not so sure about counting purely algebraic Risch failures as   
   > > bugs. Even the purely algebraic case has never been implemented more   
   > > fully than in FriCAS - apparently because it proves too hard a task.   
   > > Considering that this situation has persisted for three decades, one   
   > > may suspect that the algorithm is not really practical.   
   >   
   > Something is not implemented for a long time is not necessarily   
   > because it is difficult.  Pure rational integration is very easy to   
   > implement, even SymPy implemented it in a GSOC, however Mathematica is   
   > still missing its implementation for 3 decades:   
   >   
   > INT( (72*x^7+256*x^6-192*x^5-1280*x^4-312*x^3+1440*x^2+576*x-96)   
   > /(9*x^8+36*x^7-32*x^6-252*x^5-78*x^4+468*x^3+288*x^2-108*x+9) ,x)   
   >   
   > INT( (2560*x^3-400*x^2-576*x-84)/(320*x^4+80*x^3-12*x^2+24*x+9) ,x)   
      
   Derive can do the second integral by explicitly factoring the   
   denominator, and it returns the first one unevaluated.   
      
   Mathematica's designers may have considered explicit results in terms of   
   the minimal algebraic extension of limited relevance, and thus prefer   
   antiderivatives in terms of symbolic denominator root objects instead.   
      
   All rational integrands can be handled in this way, whereas FriCAS will   
   never be able to handle arbitrary algebraic integrands by adding   
   specific rewrite rules.   
      
   Martin.   
      
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