off rlabout;



symbolic (infile "../../SUPPORT/real.red" where !*output=nil);


symbolic (infile "../../SUPPORT/strings.red" where !*output=nil);



basis := { - x1*x9 + 2*x2 + 5000, 200*x1*x9 + 20000*x12 - x13*x2 + 1000*x13*x7 - x14*x2 - x15*x2 - x16*x2 - x17*x2 - x18*x2 - x19*x2 - x2**2 - x2*x20 - x2*x37 - 1700*x2*x6 - 399*x2, 3*x13*x7 + 3*x14*x7 + 3*x15*x7 + 3*x16*x7 + 3*x17*x7 + 3*x18*x7 + 3*x19*x7 + 3*x20*x7 + 3*x21*x7 + 3*x22*x7 + 3*x23*x7 + 3*x24*x7 + 3*x25*x7 - 40*x3*x4, 15*x10*x5 - 2*x3*x4,  - x10*x5 + x11*x12 + 10*x11*x13 + 10*x11*x14 + 10*x11*x15 + 10*x11*x16 + 10*x11*x17 + 10*x11*x18 + 10*x11*x19, 1000*x11*x12 + 200*x12 - 17*x2*x6, 0,  - x16*x8 - x17*x8 - x18*x8 - x19*x8 - x20*x8 + x21*x7 - x37*x8, 0,  - 15*x10*x5 + 2*x3*x4, x10*x5 - x11*x12 - 10*x11*x13 - 10*x11*x14 - 10*x11*x15 - 10*x11*x16 - 10*x11*x17 - 10*x11*x18 - 10*x11*x19,  - 1000*x11*x12 - 200*x12 + 17*x2*x6, 100000*x11*x12 - 1000000*x11*x13 - x13**2 - x13*x14 - x13*x15 - x13*x16 - x13*x17 - x13*x18 - x13*x19 - x13*x2 - x13*x20 - x13*x37 - 1000*x13*x7 + x13 + 1000*x14*x7, 1000000*x11*x13 - 1000000*x11*x14 - x13*x14 - x14**2 - x14*x15 - x14*x16 - x14*x17 - x14*x18 - x14*x19 - x14*x2 - x14*x20 - x14*x37 - 1000*x14*x7 + x14 + 1000*x15*x7, 1000000*x11*x14 - 1000000*x11*x15 - x13*x15 - x14*x15 - x15**2 - x15*x16 - x15*x17 - x15*x18 - x15*x19 - x15*x2 - x15*x20 - x15*x37 - 1000*x15*x7 + x15 + 1000*x16*x7 + 1000*x21*x7, 1000000*x11*x15 - 1000000*x11*x16 - x13*x16 - x14*x16 - x15*x16 - x16**2 - x16*x17 - x16*x18 - x16*x19 - x16*x2 - x16*x20 - x16*x37 - 1000*x16*x7 - 1000*x16*x8 + x16 + 1000*x17*x7, 1000000*x11*x16 - 1000000*x11*x17 - x13*x17 - x14*x17 - x15*x17 - x16*x17 - x17**2 - x17*x18 - x17*x19 - x17*x2 - x17*x20 - x17*x37 - 1000*x17*x7 - 1000*x17*x8 + x17 + 1000*x18*x7, 1000000*x11*x17 - 1000000*x11*x18 - x13*x18 - x14*x18 - x15*x18 - x16*x18 - x17*x18 - x18**2 - x18*x19 - x18*x2 - x18*x20 - x18*x37 - 1000*x18*x7 - 1000*x18*x8 + x18 + 1000*x19*x7, 1000000*x11*x18 - 1000000*x11*x19 - x13*x19 - x14*x19 - x15*x19 - x16*x19 - x17*x19 - x18*x19 - x19**2 - x19*x2 - x19*x20 - x19*x37 - 1000*x19*x7 - 1000*x19*x8 + x19 + 1000*x20*x7, 1000000*x11*x19 - x13*x20 - x14*x20 - x15*x20 - x16*x20 - x17*x20 - x18*x20 - x19*x20 - x2*x20 - x20**2 - x20*x37 - 1000*x20*x7 - 1000*x20*x8 + x20, x16*x8 - x21*x7 + x22*x7, x17*x8 - x22*x7 + x23*x7, x18*x8 - x23*x7 + x24*x7, x19*x8 - x24*x7 + x25*x7, x20*x8 - x25*x7, 0, 0, 0, 0, 0, 0, 0, 0, 0, x1*x9, x2, x13**2 + 2*x13*x14 + 2*x13*x15 + 2*x13*x16 + 2*x13*x17 + 2*x13*x18 + 2*x13*x19 + 2*x13*x2 + 2*x13*x20 + 2*x13*x37 - x13 + x14**2 + 2*x14*x15 + 2*x14*x16 + 2*x14*x17 + 2*x14*x18 + 2*x14*x19 + 2*x14*x2 + 2*x14*x20 + 2*x14*x37 - x14 + x15**2 + 2*x15*x16 + 2*x15*x17 + 2*x15*x18 + 2*x15*x19 + 2*x15*x2 + 2*x15*x20 + 2*x15*x37 - x15 + x16**2 + 2*x16*x17 + 2*x16*x18 + 2*x16*x19 + 2*x16*x2 + 2*x16*x20 + 2*x16*x37 - x16 + x17**2 + 2*x17*x18 + 2*x17*x19 + 2*x17*x2 + 2*x17*x20 + 2*x17*x37 - x17 + x18**2 + 2*x18*x19 + 2*x18*x2 + 2*x18*x20 + 2*x18*x37 - x18 + x19**2 + 2*x19*x2 + 2*x19*x20 + 2*x19*x37 - x19 + x2**2 + 2*x2*x20 + 2*x2*x37 - x2 + x20**2 + 2*x20*x37 - x20 - 2000*x37*x8 - 200000*x37, x37, x37*x8};


basis := { - x1*x9 + 2*x2 + 5000,

          200*x1*x9 + 20000*x12 - x13*x2 + 1000*x13*x7 - x14*x2 - x15*x2

                                                   2
           - x16*x2 - x17*x2 - x18*x2 - x19*x2 - x2  - x2*x20 - x2*x37

           - 1700*x2*x6 - 399*x2,

          3*x13*x7 + 3*x14*x7 + 3*x15*x7 + 3*x16*x7 + 3*x17*x7 + 3*x18*x7

           + 3*x19*x7 + 3*x20*x7 + 3*x21*x7 + 3*x22*x7 + 3*x23*x7 + 3*x24*x7

           + 3*x25*x7 - 40*x3*x4,

          15*x10*x5 - 2*x3*x4,

           - x10*x5 + x11*x12 + 10*x11*x13 + 10*x11*x14 + 10*x11*x15

           + 10*x11*x16 + 10*x11*x17 + 10*x11*x18 + 10*x11*x19,

          1000*x11*x12 + 200*x12 - 17*x2*x6,

          0,

           - x16*x8 - x17*x8 - x18*x8 - x19*x8 - x20*x8 + x21*x7 - x37*x8,

          0,

           - 15*x10*x5 + 2*x3*x4,

          x10*x5 - x11*x12 - 10*x11*x13 - 10*x11*x14 - 10*x11*x15 - 10*x11*x16

           - 10*x11*x17 - 10*x11*x18 - 10*x11*x19,

           - 1000*x11*x12 - 200*x12 + 17*x2*x6,

                                                2
          100000*x11*x12 - 1000000*x11*x13 - x13  - x13*x14 - x13*x15 - x13*x16

           - x13*x17 - x13*x18 - x13*x19 - x13*x2 - x13*x20 - x13*x37

           - 1000*x13*x7 + x13 + 1000*x14*x7,

                                                           2
          1000000*x11*x13 - 1000000*x11*x14 - x13*x14 - x14  - x14*x15 - x14*x16

           - x14*x17 - x14*x18 - x14*x19 - x14*x2 - x14*x20 - x14*x37

           - 1000*x14*x7 + x14 + 1000*x15*x7,

                                                                     2
          1000000*x11*x14 - 1000000*x11*x15 - x13*x15 - x14*x15 - x15  - x15*x16

           - x15*x17 - x15*x18 - x15*x19 - x15*x2 - x15*x20 - x15*x37

           - 1000*x15*x7 + x15 + 1000*x16*x7 + 1000*x21*x7,

                                                                               2
          1000000*x11*x15 - 1000000*x11*x16 - x13*x16 - x14*x16 - x15*x16 - x16

           - x16*x17 - x16*x18 - x16*x19 - x16*x2 - x16*x20 - x16*x37

           - 1000*x16*x7 - 1000*x16*x8 + x16 + 1000*x17*x7,

          1000000*x11*x16 - 1000000*x11*x17 - x13*x17 - x14*x17 - x15*x17

                          2
           - x16*x17 - x17  - x17*x18 - x17*x19 - x17*x2 - x17*x20 - x17*x37

           - 1000*x17*x7 - 1000*x17*x8 + x17 + 1000*x18*x7,

          1000000*x11*x17 - 1000000*x11*x18 - x13*x18 - x14*x18 - x15*x18

                                    2
           - x16*x18 - x17*x18 - x18  - x18*x19 - x18*x2 - x18*x20 - x18*x37

           - 1000*x18*x7 - 1000*x18*x8 + x18 + 1000*x19*x7,

          1000000*x11*x18 - 1000000*x11*x19 - x13*x19 - x14*x19 - x15*x19

                                              2
           - x16*x19 - x17*x19 - x18*x19 - x19  - x19*x2 - x19*x20 - x19*x37

           - 1000*x19*x7 - 1000*x19*x8 + x19 + 1000*x20*x7,

          1000000*x11*x19 - x13*x20 - x14*x20 - x15*x20 - x16*x20 - x17*x20

                                             2
           - x18*x20 - x19*x20 - x2*x20 - x20  - x20*x37 - 1000*x20*x7

           - 1000*x20*x8 + x20,

          x16*x8 - x21*x7 + x22*x7,

          x17*x8 - x22*x7 + x23*x7,

          x18*x8 - x23*x7 + x24*x7,

          x19*x8 - x24*x7 + x25*x7,

          x20*x8 - x25*x7,

          0,

          0,

          0,

          0,

          0,

          0,

          0,

          0,

          0,

          x1*x9,

          x2,

             2
          x13  + 2*x13*x14 + 2*x13*x15 + 2*x13*x16 + 2*x13*x17 + 2*x13*x18

                                                                     2
           + 2*x13*x19 + 2*x13*x2 + 2*x13*x20 + 2*x13*x37 - x13 + x14

           + 2*x14*x15 + 2*x14*x16 + 2*x14*x17 + 2*x14*x18 + 2*x14*x19

                                                         2
           + 2*x14*x2 + 2*x14*x20 + 2*x14*x37 - x14 + x15  + 2*x15*x16

           + 2*x15*x17 + 2*x15*x18 + 2*x15*x19 + 2*x15*x2 + 2*x15*x20

                                  2
           + 2*x15*x37 - x15 + x16  + 2*x16*x17 + 2*x16*x18 + 2*x16*x19

                                                         2
           + 2*x16*x2 + 2*x16*x20 + 2*x16*x37 - x16 + x17  + 2*x17*x18

                                                                     2
           + 2*x17*x19 + 2*x17*x2 + 2*x17*x20 + 2*x17*x37 - x17 + x18

                                                                     2
           + 2*x18*x19 + 2*x18*x2 + 2*x18*x20 + 2*x18*x37 - x18 + x19

                                                        2
           + 2*x19*x2 + 2*x19*x20 + 2*x19*x37 - x19 + x2  + 2*x2*x20 + 2*x2*x37

                     2
           - x2 + x20  + 2*x20*x37 - x20 - 2000*x37*x8 - 200000*x37,

          x37,

          x37*x8}


classifyComponents {basis};


{{{x1,

   x10,

   x11,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x22,

   x23,

   x24,

   x25,

   x3,

   x37,

   x4,

   x5,

   x6,

   x7,

   x8,

   x9}},

 {{}},

 {{1 = 0}},

 {o},

 o}


end;

