% Positive qe:
% Examples from
% Boulier et al. 2007
% http://dx.doi.org/10.1007/978-3-540-73433-8_6
% for n=9 they prove that a Hopf bifurcation exists

rlset r;


{}


ab2007_hopf_n_9 := ex(vv2,ex(vv1,ex(vv3,(( - vv1 < 0 and - vv3 < 0) and
- vv2 < 0) and (((((( gamma0*theta - theta*vv1*vv3**9 - theta*vv1 = 0
and gamma0*mu + lambda1*vv1 - vv2 = 0) and 9*alpha*gamma0 -
9*alpha*vv1*vv3**9 - 9*alpha*vv1 + delta*vv2 - delta*vv3 = 0) and -
9*delta*lambda1*theta*vv1*vv3**8 - delta*theta*vv3**9 - delta*theta < 0
and 6561*alpha**2*vv1**2*vv3**16 + 81*alpha*delta*theta*vv1*vv3 **17 +
81*alpha*delta*theta*vv1*vv3**8 + 162*alpha*delta*vv1*vv3**8 +
162*alpha* theta*vv1*vv3**17 + 162*alpha*theta*vv1*vv3**8 +
81*alpha*vv1*vv3**8 + delta**2* theta*vv3**9 + delta**2*theta + delta**2
- 9*delta*lambda1*theta*vv1*vv3**8 + delta*theta**2*vv3**18 +
2*delta*theta**2*vv3**9 + delta*theta**2 + 2*delta* theta*vv3**9 +
2*delta*theta + delta + theta**2*vv3**18 + 2*theta**2*vv3**9 + theta**2
+ theta*vv3**9 + theta = 0) and - theta < 0) and - gamma0 < 0) and - mu
< 0) and - delta < 0 and - alpha < 0)))$



rlposqea rlex ab2007_hopf_n_9;


{{true,

  {alpha = infinity1,

   delta = 1,

                        1/9          2
   gamma0 = (8*infinity2   *infinity2 *infinity3

                            1/9                                  1/9
              + 16*infinity2   *infinity2*infinity3 + 8*infinity2   *infinity3)/

                 2          3                 2          2
   (729*infinity1 *infinity2  + 1458*infinity1 *infinity2

                    2                                    2
     + 729*infinity1 *infinity2 - 486*infinity1*infinity2 *infinity3

                                                                2
     - 486*infinity1*infinity2*infinity3 + 9*infinity2*infinity3 ),

   lambda1 = infinity3,

                      2          3                 2          2
   mu = (729*infinity1 *infinity2  + 1458*infinity1 *infinity2

                         2                                    2
          + 729*infinity1 *infinity2 - 486*infinity1*infinity2 *infinity3

                                                                   2
          - 486*infinity1*infinity2*infinity3 + infinity2*infinity3

                       2              2
          - 8*infinity3 )/(8*infinity2 *infinity3 + 16*infinity2*infinity3

       + 8*infinity3),

                             4          4                  4          3
   theta = ( - 6561*infinity1 *infinity2  - 26244*infinity1 *infinity2

                              4          2                  4
             - 39366*infinity1 *infinity2  - 26244*infinity1 *infinity2

                             4                 3          3
             - 6561*infinity1  + 4374*infinity1 *infinity2 *infinity3

                              3          2
             + 13122*infinity1 *infinity2 *infinity3

                              3                                     3
             + 13122*infinity1 *infinity2*infinity3 + 4374*infinity1 *infinity3

                                               3                         3
             - 54*infinity1*infinity2*infinity3  - 54*infinity1*infinity3

                        4                 4          5
             + infinity3 )/(6561*infinity1 *infinity2

                        4          4                  4          3
       + 32805*infinity1 *infinity2  + 65610*infinity1 *infinity2

                        4          2                  4
       + 65610*infinity1 *infinity2  + 32805*infinity1 *infinity2

                       4                 3          4
       + 6561*infinity1  - 8748*infinity1 *infinity2 *infinity3

                        3          3
       - 34992*infinity1 *infinity2 *infinity3

                        3          2
       - 52488*infinity1 *infinity2 *infinity3

                        3                                     3
       - 34992*infinity1 *infinity2*infinity3 - 8748*infinity1 *infinity3

                       2          3          2
       + 3078*infinity1 *infinity2 *infinity3

                       2          2          2
       + 9234*infinity1 *infinity2 *infinity3

                       2                    2                 2          2
       + 9234*infinity1 *infinity2*infinity3  + 3078*infinity1 *infinity3

                                2          3
       - 108*infinity1*infinity2 *infinity3

                                          3                          3
       - 216*infinity1*infinity2*infinity3  - 108*infinity1*infinity3

                            4            4
       + infinity2*infinity3  + infinity3 ),

                     1/9                                  1/9
   vv1 = (8*infinity2   *infinity2*infinity3 + 8*infinity2   *infinity3)/(

                   2          3                 2          2
      729*infinity1 *infinity2  + 1458*infinity1 *infinity2

                      2                                    2
       + 729*infinity1 *infinity2 - 486*infinity1*infinity2 *infinity3

                                                                  2
       - 486*infinity1*infinity2*infinity3 + 9*infinity2*infinity3 ),

                  1/9
   vv2 = infinity2   ,

                  1/9
   vv3 = infinity2   }}}


end;

Tested on alfred running Linux 4.4.38.1.amd64-smp x86_64 CSL
Time (counter 1): 310 ms  plus GC time: 89 ms
1: real 0.72
user 0.58
sys 0.05
