From: fateman@cs.berkeley.edu   
      
   Wow, 8 postings in a row.   
      
   On 7/8/2017 10:14 AM, bursejan@gmail.com wrote:   
    > I am accusing RJF of been dammned stupid. Everybody knows   
    > that polynomials are not an Euclidean Domain, so Algorithm E   
    > cannot work for polynomials.   
      
   Everybody apparently hasn't read the description of Algorithm E   
      
   Algorithm E (Generalized Euclidean algorithm). Given nonzero polynomials   
   U(Z) and W(Z) over a unique factorization domain S, this algorithm   
   calculates a   
   greatest common divisor of U(Z) and V(X).   
      
   from section 4.6.1 of Knuth..   
      
   And it works, if properly implemented.  The  answer of 2, or 3, or 9999   
   from pseudodivision  in  step E2, proceeds to E3,   
   which would be to "make remainder primitive"  Hence 2, 3, or 9999 would   
   become 1.   
      
      
      
   .........   
      
      
   Jan thinks that  "[Asksign nuttiness, noted by R. Dodier]   
     has probably elegant   
   solutions in logic programming and CLP(*) scheme, all   
   that is need is a marriage with CAS."   
      
   Jan is welcome to try. Maxima is open source.   
      
   Rewriting Maxima in prolog first is probably an   
   unnecessary diversion.   
      
   ...........   
   Division of one multivariate polynomial by another   
   does not use total degree, and so computing it   
   is irrelevant.  You seem to have GB on your mind.   
      
   The book/ by Takayuki Hibi points out as a historical matter,   
   the precedence of Macaulay, and then Hironaka   
   in defining what Buchberger later named Groebner...   
   It seems to be rather expensive.   
   And there are plenty of GB test cases, free.   
   yet another bunch of links are here   
   https://scicomp.stackexchange.com/questions/21699/benchmarks-for   
   gr%C3%B6bner-bases-and-polynomial-system-solution   
      
   .........   
   Enough, already.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)