Solution 2 to problem N1f1b0o35w1

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

Expressions

The solution is given through the following expressions: 

      27    3
     ----*p7 *q3
      10
q21=-------------
           3
         p1


      3
     ---*p7*q3
      2
q20=-----------
        p1


q19=0


      9    2
     ---*p7 *q3
      2
q18=------------
          2
        p1


q17=0


q16=0


      3
     ---*p7*q3
      2
q15=-----------
        p1


         2
     9*p7 *q3
q14=----------
         2
       p1


     1
q13=---*q3
     2


         2
     9*p7 *q3
q12=----------
         2
       p1


     3*p7*q3
q11=---------
       p1


      9
     ---*p7*q3
      2
q10=-----------
        p1


    1
q9=---*q3
    2


q8=0


q7=0


    5
q6=---*q3
    2


     1
    ---*p1*q3
     6
q5=-----------
       p7


     21
    ----*p7*q3
     2
q4=------------
        p1


    3*p7*q3
q2=---------
      p1


     9    2
    ---*p7 *q3
     2
q1=------------
         2
       p1


p6=0


p5=p1


p4=0


p3=0


     1    2
    ---*p1
     3
p2=---------
      p7

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: 
 q3, p7, p1

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. 
 
{q6,

 p1,

 p7,

           2                           2
 3*g0050*p7  + 3*g0052*p1*p7 + g0055*p1  + 3*g0056*p1*p7,

 p2,

 q3,

 q1,

 q13,

              2                 3                   2                 3
 9*g0003*p1*p7 *q3 + 27*g0005*p7 *q3 + 9*g0008*p1*p7 *q3 + 54*g0009*p7 *q3

              2                    3                    2
  + 3*g0010*p1 *p7*q3 + 54*g0011*p7 *q3 + 18*g0012*p1*p7 *q3

                  2                2                    2                 3
  + 27*g0013*p1*p7 *q3 + 3*g0014*p1 *p7*q3 + 15*g0017*p1 *p7*q3 + g0018*p1 *q3

                  2                2                       2
  + 63*g0019*p1*p7 *q3 + 6*g0020*p1 *p7*q3 + 18*g0021*p1*p7 *q3

               3                3                4             3
  + 27*g0022*p7 *q3 + 6*g0024*p1 *p7 + 2*g0027*p1  + 6*g0028*p1 *p7,

 q4,

            4              2   2                  3              2   2
 81*g0029*p7  + 45*g0030*p1 *p7  + 135*g0032*p1*p7  + 45*g0035*p1 *p7

                   3              3                     3              2   2
  + 270*g0036*p1*p7  + 15*g0037*p1 *p7 + 270*g0038*p1*p7  + 90*g0039*p1 *p7

                2   2              3                 3                4
  + 135*g0040*p1 *p7  + 15*g0041*p1 *p7 + 75*g0044*p1 *p7 + 5*g0045*p1

                2   2              3                 2   2                  3
  + 315*g0046*p1 *p7  + 30*g0047*p1 *p7 + 90*g0048*p1 *p7  + 135*g0049*p1*p7 }

Relevance for the application:



The equation: 



                    1             2                        2
    Df  *f*p1*p7 + ---*Df *Df*f*p1  + Df *f *p1*p7 + f  *p7
      2x            3    x              x  x          3x
f =----------------------------------------------------------
 t                             p7


The symmetry: 

     9              3                    2   2                     3
f =(---*Df  *f*p1*p7 *q3 + 3*Df  *Df*f*p1 *p7 *q3 + 9*Df  *f *p1*p7 *q3
 s   2    4x                   3x                       3x  x

        21               2   2               2     3
     + ----*Df  *Df *f*p1 *p7 *q3 + Df  *(Df) *f*p1 *p7*q3
        2     2x   x                  2x

                      2   2                      3
     + 3*Df  *Df*f *p1 *p7 *q3 + 9*Df  *f  *p1*p7 *q3
           2x     x                  2x  2x

        5       2        3          9       2      2   2
     + ---*(Df ) *Df*f*p1 *p7*q3 + ---*(Df ) *f *p1 *p7 *q3
        2     x                     2     x    x

        1          3     4       1          2      3
     + ---*Df *(Df) *f*p1 *q3 + ---*Df *(Df) *f *p1 *p7*q3
        6    x                   2    x        x

        3               2   2       9               3
     + ---*Df *Df*f  *p1 *p7 *q3 + ---*Df *f  *p1*p7 *q3
        2    x     2x               2    x  3x

        1                3          27        4       3             2   2
     + ---*Df*f  *f *f*p1 *p7*q3 + ----*f  *p7 *q3 + ---*f  *f *f*p1 *p7 *q3)/(
        2      2x  x                10   5x           2   3x  x

     3
   p1 *p7)


And now in machine readable form: 

The system: 

df(f(1),t)=(d(1,df(f(1),x,2))*f(1)*p1*p7 + 1/3*d(1,df(f(1),x))*d(1,f(1))*f(1)*p1
**2 + d(1,df(f(1),x))*df(f(1),x)*p1*p7 + df(f(1),x,3)*p7**2)/p7$


The symmetry: 

df(f(1),s)=(9/2*d(1,df(f(1),x,4))*f(1)*p1*p7**3*q3 + 3*d(1,df(f(1),x,3))*d(1,f(1
))*f(1)*p1**2*p7**2*q3 + 9*d(1,df(f(1),x,3))*df(f(1),x)*p1*p7**3*q3 + 21/2*d(1,
df(f(1),x,2))*d(1,df(f(1),x))*f(1)*p1**2*p7**2*q3 + d(1,df(f(1),x,2))*d(1,f(1))
**2*f(1)*p1**3*p7*q3 + 3*d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*p1**2*p7**2*q3 +
 9*d(1,df(f(1),x,2))*df(f(1),x,2)*p1*p7**3*q3 + 5/2*d(1,df(f(1),x))**2*d(1,f(1))
*f(1)*p1**3*p7*q3 + 9/2*d(1,df(f(1),x))**2*df(f(1),x)*p1**2*p7**2*q3 + 1/6*d(1,
df(f(1),x))*d(1,f(1))**3*f(1)*p1**4*q3 + 1/2*d(1,df(f(1),x))*d(1,f(1))**2*df(f(1
),x)*p1**3*p7*q3 + 3/2*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p1**2*p7**2*q3 + 9
/2*d(1,df(f(1),x))*df(f(1),x,3)*p1*p7**3*q3 + 1/2*d(1,f(1))*df(f(1),x,2)*df(f(1)
,x)*f(1)*p1**3*p7*q3 + 27/10*df(f(1),x,5)*p7**4*q3 + 3/2*df(f(1),x,3)*df(f(1),x)
*f(1)*p1**2*p7**2*q3)/(p1**3*p7)$