Solution 1 to problem N2t4s8f3

Remaining equations | Expressions | Parameters | Inequalities | Relevance | Back to problem N2t4s8f3

Equations

The following unsolved equations remain: 
    2     2
0=p3  + p4

Expressions

The solution is given through the following expressions: 

         2        2
     2*p3 *q6 + p4 *q6
q13=-------------------
              2
            p3


     p4*q6
q12=-------
      p3


      - p4*q6
q11=----------
        p3


          2
      - p4 *q6
q10=-----------
          2
        p3


q9=q6


     - p4*q6
q8=----------
       p3


    p4*q6
q7=-------
     p3


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: 
 q15, q14, q6, 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. 
 
{g0057*p4 + g0058*p3,

 p3,

         2                 2              2
 g0015*p3 *q14 + 2*g0016*p3 *q6 + g0016*p4 *q6 + g0017*p3*p4*q6 - g0018*p3*p4*q6

                                              2              3
  - g0019*p3*p4*q6 + g0020*p3*p4*q6 + g0021*p3 *q6 + g0025*p3 ,

         2                 2              2                               2
 g0003*p3 *q14 + 2*g0004*p3 *q6 + g0004*p4 *q6 + g0005*p3*p4*q6 - g0006*p4 *q6

            2                               2              3
  + g0007*p3 *q6 + g0008*p3*p4*q6 + g0009*p3 *q6 + g0013*p3 ,

         2               2                 2              2
 g0042*p3 *q15 + g0043*p3 *q14 + 2*g0044*p3 *q6 + g0044*p4 *q6 + g0045*p3*p4*q6

                             2              2
  - g0046*p3*p4*q6 - g0047*p4 *q6 + g0048*p3 *q6 - g0049*p3*p4*q6

                             2
  + g0050*p3*p4*q6 + g0051*p3 *q6,

 q6,

           2           2                                       2           2
 2*g0027*p3  + g0027*p4  + g0028*p3*p4 - g0029*p3*p4 - g0030*p4  + g0031*p3

                                        2
  - g0032*p3*p4 + g0033*p3*p4 + g0034*p3 ,

 q7,

 p4}

Relevance for the application:



The equation: 



f =D D f *p3 + f  *p4
 t  1 2 x       2x


The symmetry: 

                                    2                                      2
f =(D f *D D f*p3*p4*q6 + D f *f *p3 *q6 + D f*D D f *p3*p4*q6 - D f*f  *p4 *q6
 s   2 x  1 2              2 x  x           2   1 2 x             2   2x

                 2                      2                   2
     + D D f  *p3 *q14 + 2*D D f *D f*p3 *q6 + D D f *D f*p4 *q6
        1 2 3x              1 2 x  1            1 2 x  1

                    2                                                  2
     + D D f*D f *p3 *q6 - D f *f *p3*p4*q6 - D f*f  *p3*p4*q6 + f  *p3 *q15)/
        1 2   1 x           1 x  x             1   2x             4x

  2
p3


And now in machine readable form: 

The system: 

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


The symmetry: 

df(f(1),s)=(d(2,df(f(1),x))*d(1,d(2,f(1)))*p3*p4*q6 + d(2,df(f(1),x))*df(f(1),x)
*p3**2*q6 + d(2,f(1))*d(1,d(2,df(f(1),x)))*p3*p4*q6 - d(2,f(1))*df(f(1),x,2)*p4
**2*q6 + d(1,d(2,df(f(1),x,3)))*p3**2*q14 + 2*d(1,d(2,df(f(1),x)))*d(1,f(1))*p3
**2*q6 + d(1,d(2,df(f(1),x)))*d(1,f(1))*p4**2*q6 + d(1,d(2,f(1)))*d(1,df(f(1),x)
)*p3**2*q6 - d(1,df(f(1),x))*df(f(1),x)*p3*p4*q6 - d(1,f(1))*df(f(1),x,2)*p3*p4*
q6 + df(f(1),x,4)*p3**2*q15)/p3**2$