Solution 1 to problem N1t4s10f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s10f1

Expressions

The solution is given through the following expressions: 

      16    4
     ----*p4 *q8
      5
q21=-------------
           4
         p3


q20=0


         3
     8*p4 *q8
q19=----------
         3
       p3


          3
     16*p4 *q8
q18=-----------
          3
        p3


         2
     8*p4 *q8
q17=----------
         2
       p3


     4*p4*q8
q16=---------
       p3


          2
     24*p4 *q8
q15=-----------
          2
        p3


          3
     16*p4 *q8
q14=-----------
          3
        p3


q13=0


         3
     8*p4 *q8
q12=----------
         3
       p3


          2
     16*p4 *q8
q11=-----------
          2
        p3


          2
     12*p4 *q8
q10=-----------
          2
        p3


    12*p4*q8
q9=----------
       p3


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=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: 
 q8, p4, p3

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
{16*g0028*p4  + 40*g0030*p3*p4  + 80*g0031*p3*p4  + 40*g0032*p3 *p4

               3                  2   2                 3                 3
  + 20*g0033*p3 *p4 + 120*g0034*p3 *p4  + 80*g0035*p3*p4  + 40*g0037*p3*p4

               2   2              2   2              3                4
  + 80*g0038*p3 *p4  + 60*g0039*p3 *p4  + 60*g0040*p3 *p4 + 5*g0041*p3 ,

 q8,

           3                 3                   2                2
 8*g0006*p4 *q8 + 16*g0007*p4 *q8 + 8*g0008*p3*p4 *q8 + 4*g0009*p3 *p4*q8

                  2                 3                3                    2
  + 24*g0010*p3*p4 *q8 + 16*g0011*p4 *q8 + 8*g0013*p4 *q8 + 16*g0014*p3*p4 *q8

                  2                 2                 3              4
  + 12*g0015*p3*p4 *q8 + 12*g0016*p3 *p4*q8 + g0017*p3 *q8 + g0025*p3 ,

 p3,

 g0049*p4 + g0050*p3}

Relevance for the application:



The equation: 



f =Df*f *p3 + f  *p4
 t     x       2x


The symmetry: 

                   3                      2   2                       3
f =(8*Df  *f *p3*p4 *q8 + 16*Df  *Df*f *p3 *p4 *q8 + 16*Df  *f  *p3*p4 *q8
 s      3x  x                  2x     x                   2x  2x

               2      2   2                 2      3
     + 12*(Df ) *f *p3 *p4 *q8 + 12*Df *(Df) *f *p3 *p4*q8
             x    x                   x        x

                       2   2                      3          4      4
     + 24*Df *Df*f  *p3 *p4 *q8 + 16*Df *f  *p3*p4 *q8 + (Df) *f *p3 *q8
            x     2x                   x  3x                    x

             3       3               2       2   2                    3
     + 4*(Df) *f  *p3 *p4*q8 + 8*(Df) *f  *p3 *p4 *q8 + 8*Df*f  *p3*p4 *q8
                2x                      3x                    4x

        16        4       4
     + ----*f  *p4 *q8)/p3
        5    5x


And now in machine readable form: 

The system: 

df(f(1),t)=d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,2)*p4$


The symmetry: 

df(f(1),s)=(8*d(1,df(f(1),x,3))*df(f(1),x)*p3*p4**3*q8 + 16*d(1,df(f(1),x,2))*d(
1,f(1))*df(f(1),x)*p3**2*p4**2*q8 + 16*d(1,df(f(1),x,2))*df(f(1),x,2)*p3*p4**3*
q8 + 12*d(1,df(f(1),x))**2*df(f(1),x)*p3**2*p4**2*q8 + 12*d(1,df(f(1),x))*d(1,f(
1))**2*df(f(1),x)*p3**3*p4*q8 + 24*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p3**2*
p4**2*q8 + 16*d(1,df(f(1),x))*df(f(1),x,3)*p3*p4**3*q8 + d(1,f(1))**4*df(f(1),x)
*p3**4*q8 + 4*d(1,f(1))**3*df(f(1),x,2)*p3**3*p4*q8 + 8*d(1,f(1))**2*df(f(1),x,3
)*p3**2*p4**2*q8 + 8*d(1,f(1))*df(f(1),x,4)*p3*p4**3*q8 + 16/5*df(f(1),x,5)*p4**
4*q8)/p3**4$