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

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   Message 9,891 of 10,432   
   clicliclic@freenet.de to antispam@math.uni.wroc.pl   
   Re: elementarily integrable or not?   
   29 Apr 18 23:56:49   
   
   antispam@math.uni.wroc.pl schrieb:   
   >   
   > clicliclic@freenet.de wrote:   
   > >   
   > > However, the precision needed depends on the number of digits   
   > > contained in the integer coefficients, which is not known   
   > > beforehand. Can a bound be derived from the coefficients of the   
   > > polynomials defining the algebraics?   
   >   
   > AFAICS what you describe is equvalent to Lenstra factorization   
   > method (and yes, there is known bound on precision).   
      
   According to:   
      
   B. Just, Integer relations among algebraic numbers,   
   Math. Comp. 54 (1990) 467-477   
      
      
      
   no upper bound on the coefficient size of a possible integer relation   
   among given algebraic numbers was known in 1990.   
      
   Martin.   
      
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