Solution 8 to problem N2t6s8f3

Remaining equations | Expressions | Parameters | Inequalities | Relevance | Back to problem N2t6s8f3

Equations

The following unsolved equations remain: 
    2     2
0=p7  + p8

Expressions

The solution is given through the following expressions: 

          2
      - p8 *q9
q13=-----------
          2
        p7


          3
      - p8 *q9
q12=-----------
          3
        p7


       3
     p8 *q9
q11=--------
        3
      p7


          2
      - p8 *q9
q10=-----------
          2
        p7


      3
    p8 *q9
q8=--------
       3
     p7


    p8*q9
q7=-------
     p7


         2
     - p8 *q9
q6=-----------
         2
       p7


q5=0


q4=0


q3=0


q2=0


q1=0


p6=0


p5=0


p4=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: 
 q15, q14, q9, p8, 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. 
 
         3                  2              3                 2              3
{g0003*p7 *q14 - g0004*p7*p8 *q9 - g0005*p8 *q9 - g0006*p7*p8 *q9 + g0007*p7 *q9

            2                    2              4
  + g0008*p7 *p8*q9 - g0009*p7*p8 *q9 + g0013*p7 ,

 g0067*p8 + g0068*p7,

 p7,

         3                  2              3              3              3
 g0018*p7 *q14 - g0019*p7*p8 *q9 - g0020*p8 *q9 + g0021*p8 *q9 + g0022*p8 *q9

            2                    2              4
  + g0023*p7 *p8*q9 - g0024*p7*p8 *q9 + g0028*p7 ,

         3               3                  2              3              3
 g0052*p7 *q15 + g0053*p7 *q14 - g0054*p7*p8 *q9 - g0055*p8 *q9 + g0056*p8 *q9

               2              3              3              2
  - g0057*p7*p8 *q9 + g0058*p7 *q9 + g0059*p8 *q9 + g0060*p7 *p8*q9

               2
  - g0061*p7*p8 *q9,

 q9,

            2           3           3              2           3           3
 g0033*p7*p8  + g0034*p8  - g0035*p8  + g0036*p7*p8  - g0037*p7  - g0038*p8

            2                 2
  - g0039*p7 *p8 + g0040*p7*p8 ,

 p8,

 q8}

Relevance for the application:



The equation: 



f =D D f  *p7 + f  *p8
 t  1 2 2x       3x


The symmetry: 

                 2                   3                   3
f =(D f *D D f*p7 *p8*q9 + D f *f *p7 *q9 - D f*D D f *p8 *q9
 s   2 x  1 2               2 x  x           2   1 2 x

                    2                3                       2
     - D f*f  *p7*p8 *q9 + D D f  *p7 *q14 - D D f *D f*p7*p8 *q9
        2   2x              1 2 3x            1 2 x  1

                       2                3                3            3        3
     - D D f*D f *p7*p8 *q9 + D f *f *p8 *q9 + D f*f  *p8 *q9 + f  *p7 *q15)/p7
        1 2   1 x              1 x  x           1   2x           4x


And now in machine readable form: 

The system: 

df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p7 + df(f(1),x,3)*p8$


The symmetry: 

df(f(1),s)=(d(2,df(f(1),x))*d(1,d(2,f(1)))*p7**2*p8*q9 + d(2,df(f(1),x))*df(f(1)
,x)*p7**3*q9 - d(2,f(1))*d(1,d(2,df(f(1),x)))*p8**3*q9 - d(2,f(1))*df(f(1),x,2)*
p7*p8**2*q9 + d(1,d(2,df(f(1),x,3)))*p7**3*q14 - d(1,d(2,df(f(1),x)))*d(1,f(1))*
p7*p8**2*q9 - d(1,d(2,f(1)))*d(1,df(f(1),x))*p7*p8**2*q9 + d(1,df(f(1),x))*df(f(
1),x)*p8**3*q9 + d(1,f(1))*df(f(1),x,2)*p8**3*q9 + df(f(1),x,4)*p7**3*q15)/p7**3
$