Solution 3 to problem N1f1b0o35w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o35w1

Expressions

The solution is given through the following expressions: 

       4
     p5 *q8
q21=--------
         4
     5*p4


q20=0


         3
     2*p5 *q8
q18=----------
         3
       p4


         2
     2*p5 *q8
q17=----------
         2
       p4


     2*p5*q8
q16=---------
       p4


         2
     6*p5 *q8
q15=----------
         2
       p4


         3
     2*p5 *q8
q14=----------
         3
       p4


q13=0


       3
     p5 *q8
q12=--------
        3
      p4


         2
     4*p5 *q8
q11=----------
         2
       p4


         2
     3*p5 *q8
q10=----------
         2
       p4


    6*p5*q8
q9=---------
      p4


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


      2
    p5
p7=------
    3*p4


p6=p5


p3=0


p2=0


p1=0


       3
     p5 *q8
q19=--------
        3
      p4

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: 
 q8, p4, p5

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. 
 
         4                3                 3              2   2
{g0029*p5  + 5*g0031*p4*p5  + 10*g0032*p4*p5  + 10*g0033*p4 *p5

               3                 2   2                 3                3
  + 10*g0034*p4 *p5 + 30*g0035*p4 *p5  + 10*g0036*p4*p5  + 5*g0038*p4*p5

               2   2              2   2              3                4
  + 20*g0039*p4 *p5  + 15*g0040*p4 *p5  + 30*g0041*p4 *p5 + 5*g0042*p4 ,

         2                                             2
 g0050*p5  + 3*g0051*p4*p5 + 3*g0052*p4*p5 + 3*g0053*p4 ,

 p4,

 q8}

Relevance for the application:



The equation: 



                       2      2                   1        2
    Df *f *p4*p5 + (Df) *f *p4  + Df*f  *p4*p5 + ---*f  *p5
      x  x                x           2x          3   3x
f =----------------------------------------------------------
 t                             p4


The symmetry: 

                 3                     2   2                      3
f =(Df  *f *p4*p5 *q8 + 4*Df  *Df*f *p4 *p5 *q8 + 2*Df  *f  *p4*p5 *q8
 s    3x  x                 2x     x                  2x  2x

              2      2   2                2      3
     + 3*(Df ) *f *p4 *p5 *q8 + 6*Df *(Df) *f *p4 *p5*q8
            x    x                  x        x

                      2   2                     3          4      4
     + 6*Df *Df*f  *p4 *p5 *q8 + 2*Df *f  *p4*p5 *q8 + (Df) *f *p4 *q8
           x     2x                  x  3x                    x

             3       3               2       2   2                  3
     + 2*(Df) *f  *p4 *p5*q8 + 2*(Df) *f  *p4 *p5 *q8 + Df*f  *p4*p5 *q8
                2x                      3x                  4x

        1        4       4
     + ---*f  *p5 *q8)/p4
        5   5x


And now in machine readable form: 

The system: 

df(f(1),t)=(d(1,df(f(1),x))*df(f(1),x)*p4*p5 + d(1,f(1))**2*df(f(1),x)*p4**2 + d
(1,f(1))*df(f(1),x,2)*p4*p5 + 1/3*df(f(1),x,3)*p5**2)/p4$


The symmetry: 

df(f(1),s)=(d(1,df(f(1),x,3))*df(f(1),x)*p4*p5**3*q8 + 4*d(1,df(f(1),x,2))*d(1,f
(1))*df(f(1),x)*p4**2*p5**2*q8 + 2*d(1,df(f(1),x,2))*df(f(1),x,2)*p4*p5**3*q8 + 
3*d(1,df(f(1),x))**2*df(f(1),x)*p4**2*p5**2*q8 + 6*d(1,df(f(1),x))*d(1,f(1))**2*
df(f(1),x)*p4**3*p5*q8 + 6*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p4**2*p5**2*q8
 + 2*d(1,df(f(1),x))*df(f(1),x,3)*p4*p5**3*q8 + d(1,f(1))**4*df(f(1),x)*p4**4*q8
 + 2*d(1,f(1))**3*df(f(1),x,2)*p4**3*p5*q8 + 2*d(1,f(1))**2*df(f(1),x,3)*p4**2*
p5**2*q8 + d(1,f(1))*df(f(1),x,4)*p4*p5**3*q8 + 1/5*df(f(1),x,5)*p5**4*q8)/p4**4
$