//===========================================================================//
// LIBRARY:  lib2           procedures for elimination and saturation        //
//           type lib2();   to list the procedures                           //
//                          7/94 GMG+BM                                      //
// version for the regression test
//===========================================================================//
///////////////////////////////////////////////////////////////////////////////

proc sat (ideal i,ideal j)
USAGE:   sat(<i>,<j>);  i,j ideals
RETURNS: ideal, union_(k=1...) of i:j^k
{
  ideal @i;
  int @ii;
  while ( @ii<=size(@i))
  {
    @i=quotient(i,j);
    for ( @ii=1; @ii <= size(@i); @ii=@ii+1)
    {
      if (NF(@i[@ii],i)!=0)
        break;
    }
    i=@i;
  }
  return (@i);
}		
example
{  "EXAMPLE:";
   " ring r=2,(x,y,z),dp;";            ring @r=2,(x,y,z),dp;
   " poly F=x5+y5+(x-y)^2*xyz;";       poly @F=x5+y5+(x-y)^2*xyz;
   " ideal j=jacob(F);";               ideal @j= jacob(@F);
   " sat(j,maxideal(1));";             sat(@j,maxideal(1));
   kill @r;
}
///////////////////////////////////////////////////////////////////////////////