off rlabout;



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


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



P := {{111111111111111*x5-1111111111111000*x1, 138888889*x2-138888889*x1+20000000000, 1388888889*x3+138888889*x1-40000000000, 154320987666666512345679*x4+154320987777762345679000*x1-44444444444440000000000000, 15432098777777762345679*x6-154320987777762345679000*x1+22222222222220000000000000, 19290123473765432100000000*x1^2+36516918216796667837216506631*x1-11316872437447942387160000000000}};


p := {{ - 1111111111111000*x1 + 111111111111111*x5,

        - 138888889*x1 + 138888889*x2 + 20000000000,

       138888889*x1 + 1388888889*x3 - 40000000000,

       154320987777762345679000*x1 + 154320987666666512345679*x4

        - 44444444444440000000000000,

        - 154320987777762345679000*x1 + 15432098777777762345679*x6

        + 22222222222220000000000000,

                                    2
       19290123473765432100000000*x1  + 36516918216796667837216506631*x1

        - 11316872437447942387160000000000}}


classifyComponents P;


{{{x1,

   x2,

   x3,

   x4,

   x5,

   x6}},

 {{x1,

   x2,

   x3,

   x4,

   x5,

   x6}},

 {{x1 = ( - sqrt(2206700782673110631543878895056804174243876729415266970161)

          - 36516918216796667837216506631)/38580246947530864200000000,

   x2 = ( - sqrt(2206700782673110631543878895056804174243876729415266970161)

          - 42072473772796667837216506631)/38580246947530864200000000,

   x3 = (sqrt(2206700782673110631543878895056804174243876729415266970161)

          + 47628029328796667837216506631)/385802469197530864200000000,

   x4 = (1111111111111

         *sqrt(2206700782673110631543878895056804174243876729415266970161)

          + 52920032587546561149204029960240309277041)/42866941021947830933058\
   978052126200000,

   x5 = ( - 1111111111111

         *sqrt(2206700782673110631543878895056804174243876729415266970161)

          - 40574353574214462383772029960240309277041)/42866941052812028466392\
   28052126200000,

   x6 = ( - 1111111111111

         *sqrt(2206700782673110631543878895056804174243876729415266970161)

          - 46747193080880511766488029960240309277041)/42866941052812028466392\
   28052126200000}},

 {X},

 X}


end;

