Dear All,   
      
   I am using a Gröbner Bases algorithm to compute the   
   GCD of two multi-variate polynomials.   
   For two polynomials p,q just apply the algorithm   
   to [p*t,q*(1-t)] where t is a fresh variable,(*)   
      
   you can then read of the LCM, and from this get   
   the GCD. I am currently experimenting with a randpoly   
   to generate test cases, and observed the Gröbner Bases    
   algorithm I am using has extremly varying runtime,   
      
   for polynomials of degree 3 it varies from a few millis   
   to a few secs. I read already about this horrible    
   complexity issue and in some cases heuristics might help.   
   For example this co-prime case runs through the roof:   
      
   ?- X is 5+(5+A^2)*B-A*B^2,   
   Y is 5*A^2*B-(A+4*A^2)*B^2,   
   time(Z is X/Y).   
      
   % Up 5,878 ms, GC 442 ms, Thread Cpu 5,438 ms (Current 06/08/17 01:07:39)    
      
   Z is (1+1/4+(1+1/4+1/4*A^2)*B-1/4*A*B^2)/((1+1/4)*A^2*B-(1/4*A+A^2)*B^2)   
      
   Any test cases around, that also show the corners of   
   the various heuristics that are around. Note: I am using    
   a very simple lexical ordering for the moment, different    
   orderings could of course also help.   
      
   Bye   
      
   (*)   
   "Moreover, Gröbner bases can be used to compute    
   greatest common divisors of multivariate    
   polynomials [Cox1997ideals] ..."    
   https://mattpap.github.io/masters-thesis/html/src/groebner.html   
      
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