From: fateman@cs.berkeley.edu   
      
   On 8/5/2017 5:03 PM, bursejan@gmail.com wrote:   
      
   >> The measurment is document in the file   
   >> pac-1.3.0/prolog/pac/grobner/gb-top.pl, and it   
   >> is the measurement without vector(true). With vector(true)   
   >> the measurement is not that good:   
      
   thanks for the specific location.   
      
   In that same file, immediately after the timing data quoted previously   
   in this thread,   
     I see this:   
      
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
   %  Do not try the following two, which seem to take     %   
   %  unexpectedly long time. bug ?                        %   
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
      
   % ?- F1 = x^5+y^4+z^3-1, F2=x^3+y^3+z^2-1, gb:gb(F1;F2, X,   
   [order(total), vars([x,y, z]), vector(true)]).   
      
   ....................   
      
   I tried, in Maxima,   
      
   [F1 : x^5+y^4+z^3-1, F2: x^3+y^3+z^2-1]$   
      
   poly_grobner([F1,F2],[z,y,x])$   
   which took  0.031 seconds.   
   also   
   poly_grobner([F1,F2],[x,y,z])$   
   which took 0.5470 seconds.   
      
   so regardless of the ordering of the terms,( in default lex order)   
   it seems feasible. The answers are   
   large, though.  It may be that the prolog specification  order(total) makes   
   the computation different.  I tried two total orderings with ties broken   
   in lex and reverse lex order, without apparent difficulty.   
      
   As you see, Prof. Mukai admits that his system has some   
   problems, running too long, on problems that take a fraction of   
   a section in Maxima.  Perhaps a bug?   
      
   As for SWI-prolog using alien (to prolog) ideas such as   
   array references, see the file vector.pl  in that same directory, which has   
   conversions between lists and vectors.  Why do you suppose   
   that is in the grobner/  directory?   
      
   While it is certainly possible that Prof. Mukai's code is mathematically   
   more sophisticated than bursejan or Maxima code,   
   and running it in a non-SWI version of Prolog   
   will provide a big performance boost, I think there is more involved.   
      
   RJF   
      
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