BTW, I expect there is a speed-up in all the   
   algorithm by using a method by Peter Henrici   
   originally deviced for rational numbers,   
      
   to keep the numbers small during basic   
   arithmetic. Possibly this can be also used   
   for multivariate polynomials here,   
      
   a cancellation of a fraction p/q would than   
   not anymore appear as a normalization operation   
   after the operation, but each operation would   
      
   proceed more cleverly. Anyway lets beat the   
   shit out of maxima in the future!   
      
   Am Dienstag, 11. Juli 2017 13:18:20 UTC+2 schrieb burs...@gmail.com:   
   > The small "bug" example pair I have is because   
   > the LCM gets too big, since I am not using the   
   > classical GB, a variant of it, which might still   
   >   
   > need some modding. But a bigger LCM, means also   
   > bigger p_new and q_new (look at the formulas), but   
   > we want the cancelled p,q as small as possible,   
   >   
   > so thats undesired.   
   >   
   > Am Dienstag, 11. Juli 2017 13:11:42 UTC+2 schrieb burs...@gmail.com:   
   > > The proof is very easy: Since p*q = GCD*LCM,   
   > > we have GCD = p*q/LCM, now check:   
   > >   
   > >   p_new = p/(p*q/LCM) = LCM*p/(p*q) = LCM/q   
   > >   
   > >   q_new = q/(p*q/LCM) = LCM*q/(p*q) = LCM/p   
   > >   
   > > See also here:   
   > > https://en.wikipedia.org/wiki/GCD_domain   
      
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