Solution 6 to problem N1f1b0o37w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o37w1

Expressions

The solution is given through the following expressions:


q54=0


q53=0


q52=0


q51=0


q50=0


      7
     ---*p4*q55
      3
q49=------------
         p7


q48=0


      28
     ----*p4*q55
      3
q47=-------------
         p7


q46=0


q45=0


q44=0


     14*p4*q55
q43=-----------
        p7


      35
     ----*p4*q55
      3
q42=-------------
         p7


q41=0


      35    2
     ----*p4 *q55
      18
q40=--------------
           2
         p7


q39=0


q38=0


q37=0


q36=0


q35=0


      70    2
     ----*p4 *q55
      9
q34=--------------
           2
         p7


      70
     ----*p4*q55
      3
q33=-------------
         p7


q32=0


      28
     ----*p4*q55
      3
q31=-------------
         p7


q30=0


q29=0


q28=0


q27=0


q26=0


      14
     ----*p4*q55
      3
q25=-------------
         p7


q24=0


      28
     ----*p4*q55
      3
q23=-------------
         p7


     7*p4*q55
q22=----------
        p7


      70    2
     ----*p4 *q55
      9
q21=--------------
           2
         p7


q20=0


q19=0


q18=0


      35    2
     ----*p4 *q55
      3
q17=--------------
           2
         p7


      35    3
     ----*p4 *q55
      54
q16=--------------
           3
         p7


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p6=0


p5=0


p3=0


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:

 q55, p4, 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.

 
{g0118*p7 + g0121*p4,

 p7,

 q55,

            3                  2                  2                  2
 54*g0063*p7  + 126*g0069*p4*p7  + 504*g0071*p4*p7  + 756*g0075*p4*p7

                   2               2                  2                      2
  + 630*g0076*p4*p7  + 105*g0078*p4 *p7 + 420*g0084*p4 *p7 + 1260*g0085*p4*p7

                   2                  2                  2                  2
  + 504*g0087*p4*p7  + 252*g0093*p4*p7  + 504*g0095*p4*p7  + 378*g0096*p4*p7

                2                  2                 3
  + 420*g0097*p4 *p7 + 630*g0101*p4 *p7 + 35*g0102*p4 ,

 p4,

             2                   2                   2                   2
 126*g0008*p7 *q55 + 504*g0010*p7 *q55 + 756*g0014*p7 *q55 + 630*g0015*p7 *q55

                                                             2
  + 105*g0017*p4*p7*q55 + 420*g0023*p4*p7*q55 + 1260*g0024*p7 *q55

                2                   2                   2
  + 504*g0026*p7 *q55 + 252*g0032*p7 *q55 + 504*g0034*p7 *q55

                2
  + 378*g0035*p7 *q55 + 420*g0036*p4*p7*q55 + 630*g0040*p4*p7*q55

               2                  3
  + 35*g0041*p4 *q55 + 54*g0059*p7 ,

 q17}

Relevance for the application:

The equation:


       2
f =(Df) *f *p4 + f  *p7
 t        x       3x

The symmetry:

     14                  2        28                   2
f =(----*Df  *Df*f *p4*p7 *q55 + ----*Df  *Df *f *p4*p7 *q55
 s   3     4x     x               3     3x   x  x

        28                   2               2         2
     + ----*Df  *Df*f  *p4*p7 *q55 + 7*(Df  ) *f *p4*p7 *q55
        3     3x     2x                   2x    x

        70                    2        70           3      2
     + ----*Df  *Df *f  *p4*p7 *q55 + ----*Df  *(Df) *f *p4 *p7*q55
        3     2x   x  2x               9     2x        x

                           2        35       2     2      2
     + 14*Df  *Df*f  *p4*p7 *q55 + ----*(Df ) *(Df) *f *p4 *p7*q55
            2x     3x               3      x          x

        35       2          2        70          3       2
     + ----*(Df ) *f  *p4*p7 *q55 + ----*Df *(Df) *f  *p4 *p7*q55
        3      x    3x               9     x        2x

        28                  2        35      6      3
     + ----*Df *Df*f  *p4*p7 *q55 + ----*(Df) *f *p4 *q55
        3     x     4x               54         x

        35      4       2           7      2          2             3        3
     + ----*(Df) *f  *p4 *p7*q55 + ---*(Df) *f  *p4*p7 *q55 + f  *p7 *q55)/p7
        18         3x               3         5x               7x

And now in machine readable form:

The system:

df(f(1),t)=d(1,f(1))**2*df(f(1),x)*p4 + df(f(1),x,3)*p7$

The symmetry:

df(f(1),s)=(14/3*d(1,df(f(1),x,4))*d(1,f(1))*df(f(1),x)*p4*p7**2*q55 + 28/3*d(1,
df(f(1),x,3))*d(1,df(f(1),x))*df(f(1),x)*p4*p7**2*q55 + 28/3*d(1,df(f(1),x,3))*d
(1,f(1))*df(f(1),x,2)*p4*p7**2*q55 + 7*d(1,df(f(1),x,2))**2*df(f(1),x)*p4*p7**2*
q55 + 70/3*d(1,df(f(1),x,2))*d(1,df(f(1),x))*df(f(1),x,2)*p4*p7**2*q55 + 70/9*d(
1,df(f(1),x,2))*d(1,f(1))**3*df(f(1),x)*p4**2*p7*q55 + 14*d(1,df(f(1),x,2))*d(1,
f(1))*df(f(1),x,3)*p4*p7**2*q55 + 35/3*d(1,df(f(1),x))**2*d(1,f(1))**2*df(f(1),x
)*p4**2*p7*q55 + 35/3*d(1,df(f(1),x))**2*df(f(1),x,3)*p4*p7**2*q55 + 70/9*d(1,df
(f(1),x))*d(1,f(1))**3*df(f(1),x,2)*p4**2*p7*q55 + 28/3*d(1,df(f(1),x))*d(1,f(1)
)*df(f(1),x,4)*p4*p7**2*q55 + 35/54*d(1,f(1))**6*df(f(1),x)*p4**3*q55 + 35/18*d(
1,f(1))**4*df(f(1),x,3)*p4**2*p7*q55 + 7/3*d(1,f(1))**2*df(f(1),x,5)*p4*p7**2*
q55 + df(f(1),x,7)*p7**3*q55)/p7**3$