off rlabout;



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


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



P := {{x10, x12, x2, x3, x4, x5, x6, x7, x8, -843000*x13+2629*x14, 2961*x15-2770*x13, x20-96, 3795454925*x21-5010000000*x17-20040000000*x19-15185456064, -x16*x19+x17*x18, 100*x13*x16-31*x16-2790*x17, 100*x13*x18-31*x18-2790*x19}, {x10, x12, x6, x9, -843000*x13+2629*x14, 2961*x15-2770*x13, x20-96, 46121*x7-210*x5, 46121*x8-210*x4, 768683348707*x2+4840500000000*x5+4840500000000*x4, 11530250000*x3-9681*x5-932101*x4, 3795454925*x21-5010000000*x17-20040000000*x19-15185456064, 138363*x1*x4-46125840500000*x5, -x16*x19+x17*x18, 5581217512500000*x1^2+1860632100413869634889989*x1+995309778500060246877301500000, 2985615988560768576969*x4^2+1860632100413869634889989*x4*x5+1860601091168750000000000*x5^2, 5581217512500000*x1*x5+2985615988560768576969*x4+1860632100413869634889989*x5, 100*x13*x16-31*x16-2790*x17, 100*x13*x18-31*x18-2790*x19}, {x11, x12, x6, -843000*x13+2629*x14, 2961*x15-2770*x13, x20-96, 46121*x7-210*x5, 46121*x8-210*x4, 768683348707*x2+4840500000000*x5+4840500000000*x4, 11530250000*x3-9681*x5-932101*x4, 3795454925*x21-5010000000*x17-20040000000*x19-15185456064, 138363*x1*x4-46125840500000*x5, -x16*x19+x17*x18, 5581217512500000*x1^2+1860632100413869634889989*x1+995309778500060246877301500000, 2985615988560768576969*x4^2+1860632100413869634889989*x4*x5+1860601091168750000000000*x5^2, 5581217512500000*x1*x5+2985615988560768576969*x4+1860632100413869634889989*x5, 100*x13*x16-31*x16-2790*x17, 100*x13*x18-31*x18-2790*x19, 323789112500000*x1*x10+569440624722145600*x4*x9+1798972345029446181*x10, 80*x4*x9+80*x5*x9-24081*x10, 78789513158430231652800*x4^2*x9+248911210575309261941703*x10*x4+14935044958811556250000000000*x10*x5}, {x13, x14, x15, x6, x16+90*x17, x18+90*x19, x20-96, 46121*x7-210*x5, 46121*x8-210*x4, 768683348707*x2+4840500000000*x5+4840500000000*x4, 11530250000*x3-9681*x5-932101*x4, 3795454925*x21-5010000000*x17-20040000000*x19-15185456064, 138363*x1*x4-46125840500000*x5, 353*x10*x11-5000000*x12, 5581217512500000*x1^2+1860632100413869634889989*x1+995309778500060246877301500000, 2985615988560768576969*x4^2+1860632100413869634889989*x4*x5+1860601091168750000000000*x5^2, 5581217512500000*x1*x5+2985615988560768576969*x4+1860632100413869634889989*x5, 323789112500000*x1*x10+569440624722145600*x4*x9+1798972345029446181*x10, 80*x4*x9+80*x5*x9-24081*x10, 78789513158430231652800*x4^2*x9+248911210575309261941703*x10*x4+14935044958811556250000000000*x10*x5, 125632837829323373*x11*x4*x9+1011840976562500000*x1*x12+5621788578217019315625*x12}, {x6, 2961*x15-2770*x13, x20-96, 46121*x7-210*x5, 46121*x8-210*x4, 768683348707*x2+4840500000000*x5+4840500000000*x4, 11530250000*x3-9681*x5-932101*x4, 3795454925*x21-5010000000*x17-20040000000*x19-15185456064, 138363*x1*x4-46125840500000*x5, 353*x10*x11-5000000*x12, -x16*x19+x17*x18, 5581217512500000*x1^2+1860632100413869634889989*x1+995309778500060246877301500000, 2985615988560768576969*x4^2+1860632100413869634889989*x4*x5+1860601091168750000000000*x5^2, 5581217512500000*x1*x5+2985615988560768576969*x4+1860632100413869634889989*x5, 30429*x12*x14-4215000*x13+13145*x14, 100*x13*x16-31*x16-2790*x17, 100*x13*x18-31*x18-2790*x19, 323789112500000*x1*x10+569440624722145600*x4*x9+1798972345029446181*x10, 80*x4*x9+80*x5*x9-24081*x10, 78789513158430231652800*x4^2*x9+248911210575309261941703*x10*x4+14935044958811556250000000000*x10*x5, 125632837829323373*x11*x4*x9+1011840976562500000*x1*x12+5621788578217019315625*x12}};


p := {{x10,

       x12,

       x2,

       x3,

       x4,

       x5,

       x6,

       x7,

       x8,

        - 843000*x13 + 2629*x14,

        - 2770*x13 + 2961*x15,

       x20 - 96,

        - 5010000000*x17 - 20040000000*x19 + 3795454925*x21 - 15185456064,

        - x16*x19 + x17*x18,

       100*x13*x16 - 31*x16 - 2790*x17,

       100*x13*x18 - 31*x18 - 2790*x19},

      {x10,

       x12,

       x6,

       x9,

        - 843000*x13 + 2629*x14,

        - 2770*x13 + 2961*x15,

       x20 - 96,

        - 210*x5 + 46121*x7,

        - 210*x4 + 46121*x8,

       768683348707*x2 + 4840500000000*x4 + 4840500000000*x5,

       11530250000*x3 - 932101*x4 - 9681*x5,

        - 5010000000*x17 - 20040000000*x19 + 3795454925*x21 - 15185456064,

       138363*x1*x4 - 46125840500000*x5,

        - x16*x19 + x17*x18,

                          2
       5581217512500000*x1  + 1860632100413869634889989*x1

        + 995309778500060246877301500000,

                                2
       2985615988560768576969*x4  + 1860632100413869634889989*x4*x5

                                      2
        + 1860601091168750000000000*x5 ,

       5581217512500000*x1*x5 + 2985615988560768576969*x4

        + 1860632100413869634889989*x5,

       100*x13*x16 - 31*x16 - 2790*x17,

       100*x13*x18 - 31*x18 - 2790*x19},

      {x11,

       x12,

       x6,

        - 843000*x13 + 2629*x14,

        - 2770*x13 + 2961*x15,

       x20 - 96,

        - 210*x5 + 46121*x7,

        - 210*x4 + 46121*x8,

       768683348707*x2 + 4840500000000*x4 + 4840500000000*x5,

       11530250000*x3 - 932101*x4 - 9681*x5,

        - 5010000000*x17 - 20040000000*x19 + 3795454925*x21 - 15185456064,

       138363*x1*x4 - 46125840500000*x5,

        - x16*x19 + x17*x18,

                          2
       5581217512500000*x1  + 1860632100413869634889989*x1

        + 995309778500060246877301500000,

                                2
       2985615988560768576969*x4  + 1860632100413869634889989*x4*x5

                                      2
        + 1860601091168750000000000*x5 ,

       5581217512500000*x1*x5 + 2985615988560768576969*x4

        + 1860632100413869634889989*x5,

       100*x13*x16 - 31*x16 - 2790*x17,

       100*x13*x18 - 31*x18 - 2790*x19,

       323789112500000*x1*x10 + 1798972345029446181*x10

        + 569440624722145600*x4*x9,

        - 24081*x10 + 80*x4*x9 + 80*x5*x9,

       248911210575309261941703*x10*x4 + 14935044958811556250000000000*x10*x5

                                    2
        + 78789513158430231652800*x4 *x9},

      {x13,

       x14,

       x15,

       x6,

       x16 + 90*x17,

       x18 + 90*x19,

       x20 - 96,

        - 210*x5 + 46121*x7,

        - 210*x4 + 46121*x8,

       768683348707*x2 + 4840500000000*x4 + 4840500000000*x5,

       11530250000*x3 - 932101*x4 - 9681*x5,

        - 5010000000*x17 - 20040000000*x19 + 3795454925*x21 - 15185456064,

       138363*x1*x4 - 46125840500000*x5,

       353*x10*x11 - 5000000*x12,

                          2
       5581217512500000*x1  + 1860632100413869634889989*x1

        + 995309778500060246877301500000,

                                2
       2985615988560768576969*x4  + 1860632100413869634889989*x4*x5

                                      2
        + 1860601091168750000000000*x5 ,

       5581217512500000*x1*x5 + 2985615988560768576969*x4

        + 1860632100413869634889989*x5,

       323789112500000*x1*x10 + 1798972345029446181*x10

        + 569440624722145600*x4*x9,

        - 24081*x10 + 80*x4*x9 + 80*x5*x9,

       248911210575309261941703*x10*x4 + 14935044958811556250000000000*x10*x5

                                    2
        + 78789513158430231652800*x4 *x9,

       1011840976562500000*x1*x12 + 125632837829323373*x11*x4*x9

        + 5621788578217019315625*x12},

      {x6,

        - 2770*x13 + 2961*x15,

       x20 - 96,

        - 210*x5 + 46121*x7,

        - 210*x4 + 46121*x8,

       768683348707*x2 + 4840500000000*x4 + 4840500000000*x5,

       11530250000*x3 - 932101*x4 - 9681*x5,

        - 5010000000*x17 - 20040000000*x19 + 3795454925*x21 - 15185456064,

       138363*x1*x4 - 46125840500000*x5,

       353*x10*x11 - 5000000*x12,

        - x16*x19 + x17*x18,

                          2
       5581217512500000*x1  + 1860632100413869634889989*x1

        + 995309778500060246877301500000,

                                2
       2985615988560768576969*x4  + 1860632100413869634889989*x4*x5

                                      2
        + 1860601091168750000000000*x5 ,

       5581217512500000*x1*x5 + 2985615988560768576969*x4

        + 1860632100413869634889989*x5,

       30429*x12*x14 - 4215000*x13 + 13145*x14,

       100*x13*x16 - 31*x16 - 2790*x17,

       100*x13*x18 - 31*x18 - 2790*x19,

       323789112500000*x1*x10 + 1798972345029446181*x10

        + 569440624722145600*x4*x9,

        - 24081*x10 + 80*x4*x9 + 80*x5*x9,

       248911210575309261941703*x10*x4 + 14935044958811556250000000000*x10*x5

                                    2
        + 78789513158430231652800*x4 *x9,

       1011840976562500000*x1*x12 + 125632837829323373*x11*x4*x9

        + 5621788578217019315625*x12}}


classifyComponents P;


{{{x10,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x6,

   x7,

   x8},

  {x1,

   x10,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x6,

   x7,

   x8,

   x9},

  {x1,

   x10,

   x11,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x6,

   x7,

   x8,

   x9},

  {x1,

   x10,

   x11,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x6,

   x7,

   x8,

   x9},

  {x1,

   x10,

   x11,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x6,

   x7,

   x8,

   x9}},

 {{x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x20,

   x21},

  {x1,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x7,

   x8},

  {x1,

   x10,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x7,

   x8,

   x9},

  {x1,

   x10,

   x11,

   x12,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x7,

   x8,

   x9},

  {x1,

   x10,

   x11,

   x12,

   x13,

   x14,

   x15,

   x16,

   x17,

   x18,

   x19,

   x2,

   x20,

   x21,

   x3,

   x4,

   x5,

   x7,

   x8,

   x9}},

 {{x13 = -1,

           - 843000
   x14 = -----------,
            2629

           - 2770
   x15 = ---------,
           2961

   x16 = 1,

           - 131
   x17 = --------,
           2790

   x18 = 1,

           - 131
   x19 = --------,
           2790

   x20 = 96,

          1302862413952
   x21 = ---------------},
          352977308025

  {x1 = ( - 46125840500000

         *sqrt(3439731651626020127025768404495602725180132420121)

          + 85547791399104927094851499525865500000)/(

      138363*sqrt(3439731651626020127025768404495602725180132420121)

       - 257434058245199268207716451993),

   x13 = -1,

           - 843000
   x14 = -----------,
            2629

           - 2770
   x15 = ---------,
           2961

   x16 = 1,

           - 131
   x17 = --------,
           2790

   x18 = 1,

           - 131
   x19 = --------,
           2790

   x2 = 1,

   x20 = 96,

          1302862413952
   x21 = ---------------,
          352977308025

   x3 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860632100413869634889989)/465138667491750000000000000,

   x4 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860570081923630365110011)/37211093399340000000000,

   x5 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1854660868436748097736051)/37211093399340000000000,

   x7 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1854660868436748097736051)/8172442088909334000000000,

   x8 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860570081923630365110011)/8172442088909334000000000},

  {x1 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860632100413869634889989)/11162435025000000,

           - 768683348707
   x10 = ------------------,
          1457051006250000

   x13 = -1,

           - 843000
   x14 = -----------,
            2629

           - 2770
   x15 = ---------,
           2961

   x16 = 1,

           - 131
   x17 = --------,
           2790

   x18 = 1,

           - 131
   x19 = --------,
           2790

   x2 = 1,

   x20 = 96,

          1302862413952
   x21 = ---------------,
          352977308025

   x3 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860632100413869634889989)/465138667491750000000000000,

   x4 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860570081923630365110011)/37211093399340000000000,

   x5 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1854660868436748097736051)/37211093399340000000000,

   x7 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1854660868436748097736051)/8172442088909334000000000,

   x8 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860570081923630365110011)/8172442088909334000000000,

   x9 = 1},

  {x1 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860632100413869634889989)/11162435025000000,

           - 768683348707
   x10 = ------------------,
          1457051006250000

   x11 = -1,

             271345222093571
   x12 = ------------------------,
          7285255031250000000000

          703990128
   x16 = -----------,
           2609375

           - 117331688
   x17 = --------------,
            39140625

   x18 = 1,

           - 1
   x19 = ------,
           90

   x2 = 1,

   x20 = 96,

           - 40000
   x21 = ----------,
          2727273

   x3 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860632100413869634889989)/465138667491750000000000000,

   x4 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860570081923630365110011)/37211093399340000000000,

   x5 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1854660868436748097736051)/37211093399340000000000,

   x7 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1854660868436748097736051)/8172442088909334000000000,

   x8 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860570081923630365110011)/8172442088909334000000000,

   x9 = 1},

  {x1 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1860632100413869634889989)/11162435025000000,

           - 768683348707
   x10 = ------------------,
          1457051006250000

   x11 = -1,

             271345222093571
   x12 = ------------------------,
          7285255031250000000000

           - 66090190229499663964991
   x13 = ----------------------------,
          21192097968750000000000000

   x14 = -1,

           - 18306982693571406918302507
   x15 = -------------------------------,
          6274980208546875000000000000

   x16 = 1,

           - 6635640560541999663964991
   x17 = ------------------------------,
          591259533328125000000000000

   x18 = 1,

           - 6635640560541999663964991
   x19 = ------------------------------,
          591259533328125000000000000

   x2 = -1,

   x20 = 96,

          58748819131558725276117846503
   x21 = -------------------------------,
          14960659384822891148437500000

   x3 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1860632100413869634889989)/465138667491750000000000000,

   x4 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1860570081923630365110011)/37211093399340000000000,

   x5 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1854660868436748097736051)/37211093399340000000000,

   x7 = (sqrt(3439731651626020127025768404495602725180132420121)

          - 1854660868436748097736051)/8172442088909334000000000,

   x8 = ( - sqrt(3439731651626020127025768404495602725180132420121)

          + 1860570081923630365110011)/8172442088909334000000000,

   x9 = -1}},

 {x,x,x,x,x},

 5x}


end;

