reduce-historical/r37/packages/groebner/groebsor.red

module groebsor;
 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  maintenance of lists of critical pairs (sorting etc.)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

symbolic procedure groebcplistsortin (p,pl);
% Distributive polynomial critical pair list sort. pl is a
% special list for Groebner calculation, p is a pair.
% returns the updated list pl (p sorted into);
  if null pl then list p
    else
  <<groebcplistsortin1 (p,pl); pl>>;

symbolic procedure groebcplistsortin1(p,pl);
% destructive insert of p into nonnull pl
   if not groebcpcompless!?(car pl, p)
        then <<rplacd(pl,car pl . cdr pl); rplaca(pl,p)>>
      else
   if null cdr pl then rplacd(pl,list p)
      else
        groebcplistsortin1(p,cdr pl);


symbolic procedure groebcplistsort g;
  <<for each p in g do gg:=groebcplistsortin(p,gg); gg>>
      where gg=nil;

symbolic procedure groebcplistmerge(pl1,pl2);
% Distributive polynomial critical pair list merge. pl1 and pl2
% are critical pair lists used in the Groebner calculation.
% groebcplistmerge(pl1,pl2) returns the merged list.
begin scalar cpl1,cpl2,sl;
      if null pl1 then return pl2;
      if null pl2 then return pl1;
      cpl1 := car pl1; cpl2 := car pl2;
      sl := groebcpcompless!?(cpl1, cpl2);
      return
           (if sl then cpl1 . groebcplistmerge(cdr pl1,pl2)
                  else cpl2 . groebcplistmerge(pl1,cdr pl2) )
end;

symbolic procedure groebcpcompless!?(p1,p2);
% compare 2 pairs srt their sugar(=cadddr) or their lcm (=car).
    if !*gsugar then
         (if not(d=0) then d<0 else
          if not(q=0) then q<0 else
            vdpnumber(caddr p1)<vdpnumber(caddr p2)
         )  where d= cadddr p1 - cadddr p2, q=vevcomp(car p1,car p2)
       else vevcompless!?(car p1,car p2);

endmodule;

end;