Solution 4 to problem N1f1b0o57w3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o57w3

Expressions

The solution is given through the following expressions: 

      225    2
     -----*p7 *q7
      112
q16=--------------
           2
         p5


q15=0


      15
     ----*p7*q7
      8
q14=------------
         p5


      75
     ----*p7*q7
      16
q13=------------
         p5


      105
     -----*p7*q7
      16
q12=-------------
         p5


     1
q11=---*q7
     2


     5
q10=---*q7
     4


     75
    ----*p7*q7
     16
q9=------------
        p5


     15
    ----*p7*q7
     8
q8=------------
        p5


    5
q6=---*q7
    8


     2
    ----*p5*q7
     45
q5=------------
        p7


q4=0


q3=0


q2=0


q1=0


    2
p6=---*p5
    3


    2
p4=---*p5
    3


     4     2
    ----*p5
     45
p3=----------
       p7


p2=0


p1=0

Parameters

Apart from the condition that they must not vanish to give a non-trivial solution and a non-singular solution with non-vanishing denominators, the following parameters are free: 
 q7, p5, p7

Inequalities

In the following not identically vanishing expressions are shown. Any auxiliary variables g00?? are used to express that at least one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3 means that either p4 or p3 or both are non-vanishing. 
 
{q12,

 p5,

 q7,

 p7,

 p6,

            2                                                                2
 45*g0040*p7  + 30*g0041*p5*p7 + 45*g0042*p5*p7 + 30*g0043*p5*p7 + 4*g0044*p5 ,

 p4,

              2                   2                   2
 1350*g0004*p7 *q7 + 3375*g0005*p7 *q7 + 4725*g0006*p7 *q7 + 360*g0007*p5*p7*q7

                                      2                   2
  + 900*g0008*p5*p7*q7 + 3375*g0009*p7 *q7 + 1350*g0010*p7 *q7

                                                         2                  2
  + 720*g0011*p5*p7*q7 + 450*g0012*p5*p7*q7 + 32*g0013*p5 *q7 + 480*g0018*p5 *p7

                2                  2                 3
  + 720*g0019*p5 *p7 + 480*g0020*p5 *p7 + 64*g0021*p5 ,

 q9,

               3                   2                    2                    2
 10125*g0024*p7  + 9450*g0026*p5*p7  + 23625*g0027*p5*p7  + 33075*g0028*p5*p7

                 2                   2                       2
  + 2520*g0029*p5 *p7 + 6300*g0030*p5 *p7 + 23625*g0031*p5*p7

                    2                2                   2                  3
  + 9450*g0032*p5*p7  + 5040*g0033*p5 *p7 + 3150*g0034*p5 *p7 + 224*g0035*p5 }

Relevance for the application:



The equation: 



     2                                   4       2      2    2
f =(---*Df  *f *p5*p7 + Df *f  *p5*p7 + ----*(Df) *f *p5  + ---*Df*f  *p5*p7
 t   3    2x  x           x  2x          45         x        3      3x

             2
     + f  *p7 )/p7
        5x


The symmetry: 

     15               2       75                2                   2
f =(----*Df  *f *p5*p7 *q7 + ----*Df  *f  *p5*p7 *q7 + Df  *Df*f *p5 *p7*q7
 s   8     4x  x              16    3x  2x               2x     x

        105                2       5       2      2
     + -----*Df  *f  *p5*p7 *q7 + ---*(Df ) *f *p5 *p7*q7
        16     2x  3x              8     x    x

        5               2          75               2       2       3      3
     + ---*Df *Df*f  *p5 *p7*q7 + ----*Df *f  *p5*p7 *q7 + ----*(Df) *f *p5 *q7
        4    x     2x              16    x  4x              45         x

        1      2       2          15              2       225        3        2
     + ---*(Df) *f  *p5 *p7*q7 + ----*Df*f  *p5*p7 *q7 + -----*f  *p7 *q7)/(p5
        2         3x              8       5x              112   7x

   *p7)


And now in machine readable form: 

The system: 

df(f(1),t)=(2/3*d(1,df(f(1),x,2))*df(f(1),x)*p5*p7 + d(1,df(f(1),x))*df(f(1),x,2
)*p5*p7 + 4/45*d(1,f(1))**2*df(f(1),x)*p5**2 + 2/3*d(1,f(1))*df(f(1),x,3)*p5*p7 
+ df(f(1),x,5)*p7**2)/p7$


The symmetry: 

df(f(1),s)=(15/8*d(1,df(f(1),x,4))*df(f(1),x)*p5*p7**2*q7 + 75/16*d(1,df(f(1),x,
3))*df(f(1),x,2)*p5*p7**2*q7 + d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*p5**2*p7*
q7 + 105/16*d(1,df(f(1),x,2))*df(f(1),x,3)*p5*p7**2*q7 + 5/8*d(1,df(f(1),x))**2*
df(f(1),x)*p5**2*p7*q7 + 5/4*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p5**2*p7*q7 
+ 75/16*d(1,df(f(1),x))*df(f(1),x,4)*p5*p7**2*q7 + 2/45*d(1,f(1))**3*df(f(1),x)*
p5**3*q7 + 1/2*d(1,f(1))**2*df(f(1),x,3)*p5**2*p7*q7 + 15/8*d(1,f(1))*df(f(1),x,
5)*p5*p7**2*q7 + 225/112*df(f(1),x,7)*p7**3*q7)/(p5**2*p7)$