Solution 4 to problem N1t6s14f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t6s14f1

Expressions

The solution is given through the following expressions:


      9     2
     ----*p7 *q23
      49
q55=--------------
           2
         p5


     1
q54=---*q23
     7


q53=0


q52=0


q51=0


      3
     ---*p7*q23
      7
q50=------------
         p5


q49=0


q48=0


q47=0


      6
     ---*p7*q23
      7
q46=------------
         p5


q45=0


      9
     ---*p7*q23
      7
q44=------------
         p5


q43=0


     3
q42=---*q23
     7


q41=0


q40=0


q39=0


q38=0


q37=0


q36=0


q35=0


q34=0


     6
q33=---*q23
     7


q32=0


q31=0


      6
     ---*p7*q23
      7
q30=------------
         p5


q29=0


q28=0


q27=0


      3
     ---*p7*q23
      7
q26=------------
         p5


q25=0


q24=0


     4
q22=---*q23
     7


q21=0


q20=0


      5
     ----*p5*q23
      21
q19=-------------
         p7


q18=0


q17=0


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p6=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:

 q23, p5, 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.

 
{p7,

 p5,

 q23,

 g0120*p7 + g0122*p5,

            3              2                    2                  2
 27*g0065*p7  + 21*g0066*p5 *p7 + 63*g0070*p5*p7  + 126*g0074*p5*p7

                   2              2                  2                     2
  + 189*g0076*p5*p7  + 63*g0078*p5 *p7 + 126*g0087*p5 *p7 + 126*g0090*p5*p7

                  2               2                 2                 3
  + 63*g0094*p5*p7  + 147*g0097*p5 *p7 + 84*g0098*p5 *p7 + 35*g0101*p5 ,

                               2                  2                  2
 3*g0005*p5*p7*q23 + 9*g0009*p7 *q23 + 18*g0013*p7 *q23 + 27*g0015*p7 *q23

                                                        2                 2
  + 9*g0017*p5*p7*q23 + 18*g0026*p5*p7*q23 + 18*g0029*p7 *q23 + 9*g0033*p7 *q23

                                                        2                  2
  + 21*g0036*p5*p7*q23 + 12*g0037*p5*p7*q23 + 5*g0040*p5 *q23 + 21*g0060*p5 *p7}

Relevance for the application:

The equation:


f =Df *f *p5 + f  *p7
 t   x  x       3x

The symmetry:

     3               2        6                2                     2
f =(---*Df  *f *p5*p7 *q23 + ---*Df  *f  *p5*p7 *q23 + Df  *Df *f *p5 *p7*q23
 s   7    5x  x               7    4x  2x                3x   x  x

        9                2        4        2      2
     + ---*Df  *f  *p5*p7 *q23 + ---*(Df  ) *f *p5 *p7*q23
        7    3x  3x               7     2x    x

        6                 2           6                2
     + ---*Df  *Df *f  *p5 *p7*q23 + ---*Df  *f  *p5*p7 *q23
        7    2x   x  2x               7    2x  4x

        5        3      3        3       2       2
     + ----*(Df ) *f *p5 *q23 + ---*(Df ) *f  *p5 *p7*q23
        21     x    x            7     x    3x

        3               2        9         3        1               2
     + ---*Df *f  *p5*p7 *q23 + ----*f  *p7 *q23 + ---*f  *f  *f *p5 *p7*q23)/(
        7    x  5x               49   7x            7   3x  2x  x

     2
   p5 *p7)

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*df(f(1),x)*p5 + df(f(1),x,3)*p7$

The symmetry:

df(f(1),s)=(3/7*d(1,df(f(1),x,5))*df(f(1),x)*p5*p7**2*q23 + 6/7*d(1,df(f(1),x,4)
)*df(f(1),x,2)*p5*p7**2*q23 + d(1,df(f(1),x,3))*d(1,df(f(1),x))*df(f(1),x)*p5**2
*p7*q23 + 9/7*d(1,df(f(1),x,3))*df(f(1),x,3)*p5*p7**2*q23 + 4/7*d(1,df(f(1),x,2)
)**2*df(f(1),x)*p5**2*p7*q23 + 6/7*d(1,df(f(1),x,2))*d(1,df(f(1),x))*df(f(1),x,2
)*p5**2*p7*q23 + 6/7*d(1,df(f(1),x,2))*df(f(1),x,4)*p5*p7**2*q23 + 5/21*d(1,df(f
(1),x))**3*df(f(1),x)*p5**3*q23 + 3/7*d(1,df(f(1),x))**2*df(f(1),x,3)*p5**2*p7*
q23 + 3/7*d(1,df(f(1),x))*df(f(1),x,5)*p5*p7**2*q23 + 9/49*df(f(1),x,7)*p7**3*
q23 + 1/7*df(f(1),x,3)*df(f(1),x,2)*df(f(1),x)*p5**2*p7*q23)/(p5**2*p7)$