From: fateman@cs.berkeley.edu   
      
   On 7/10/2017 1:46 PM, j4n bur53 wrote:   
   > Hi,   
   >   
   > See my other posts. There is a great misunderstanding what my   
   > requirements are, and what you think my requirements are.   
   >   
   > Type I: My requirements are: - Input f polynomial from Q[X,Y] - Input   
   > g polynomial from Q[X,Y] - Output GCD(f,g) polynomial from Q[X,Y]   
      
   That is what Algorithm E computes.   
   The coefficients are in Q[x][y]   which is algebraically   
   homomorphic to Q[x,y].   
      
      
   > I didn't use division in Q(X)[Y], I was using GB like reduction in   
   > Q[X,Y], so possibly the results are anyway not in a close   
   > relationship with Knuths   
      
   You are right,  the results are different, and your   
   "result"  -- that Algorithm E loops -- is wrong.   
      
   ...   
      
   > the Knuth algorithm E seems to do something else   
      
   yes.  It is correct. and you are incorrect.   
   >   
   > and would need a recursive implementation on my side. I would need to   
   > replace my GB based quotient field, by another quotient field.   
      
   As I've said before, I recommend that you spend time in   
   understanding the current state of the art with respect to   
   data representation (possibly recursive) or algorithms   
      before you program.   
      
   as far as your example for Maxima, if you compute   
   gcd(p,q)  you will get y+1.   
      
   If you wish to  compute , for p, q polynomials with   
   some common main variable the two   
   values  a,b  such that a*p+b*q= gcd(p,q)   
   then in general you need rational functions for a,b.   
   Also, the gcd may not be what you expect.   
      
   You will have to read and understand the DIFFERENT   
   domains used by gcdex.   I am not sure, but it looks   
   like in general the rhs of that equation may actually   
   be a multiple of the usual gcd, by an element of   
   the coefficient domain.   
      
   I am beginning to think that your problems stem from   
   careless reading of English.  I am confident that your   
   ability to read English is better than my ability to   
   read German.  But still, you seem to not quite get   
   the meaning of some statements, even those you quote.   
      
   Note that in a field, all elements except 0 divide any   
   other element.  The notion of a "greatest" divisor   
   degenerates to "1".   
      
   RJF   
      
   --- SoupGate-Win32 v1.05   
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