Solution 1 to problem N1t6s14b2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t6s14b2

Expressions

The solution is given through the following expressions: 

      7
     ---*p5*q39
      3
q38=------------
         p6


      7
     ---*p5*q39
      3
q37=------------
         p6


      7
     ---*p5*q39
      3
q36=------------
         p6


q35=0


      35    3
     ----*p5 *q39
      27
q34=--------------
           3
         p6


q33=0


q32=0


q31=0


q30=0


q29=0


q28=0


q27=0


      70    2
     ----*p5 *q39
      9
q26=--------------
           2
         p6


     7*p5*q39
q25=----------
        p6


q24=0


q23=0


      70    2
     ----*p5 *q39
      9
q22=--------------
           2
         p6


q21=0


q20=0


q19=0


      28
     ----*p5*q39
      3
q18=-------------
         p6


q17=0


      14
     ----*p5*q39
      3
q16=-------------
         p6


q15=0


q14=0


      49    2
     ----*p5 *q39
      9
q13=--------------
           2
         p6


q12=0


q11=0


q10=0


q9=0


     49    2
    ----*p5 *q39
     9
q8=--------------
          2
        p6


     7    2
    ---*p5 *q39
     9
q7=-------------
          2
        p6


q6=0


     56    2
    ----*p5 *q39
     9
q5=--------------
          2
        p6


q4=0


     35    3
    ----*p5 *q39
     9
q3=--------------
          3
        p6


q2=0


q1=0


p4=0


p3=p5


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: 
 q39, p5, p6

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. 
 
{p6,

 p5,

 q39,

 q3,

 p3,

 g0062*p6 + g0063*p5 + g0065*p5,

            2                  2                  2
 21*g0005*p6 *q39 + 21*g0006*p6 *q39 + 21*g0007*p6 *q39 + 49*g0009*p5*p6*q39

  + 49*g0014*p5*p6*q39 + 7*g0015*p5*p6*q39 + 56*g0017*p5*p6*q39

               2                 3
  + 35*g0019*p5 *q39 + 9*g0022*p6 ,

            3                 2                 2                 2
 27*g0023*p6  + 63*g0024*p5*p6  + 63*g0025*p5*p6  + 63*g0026*p5*p6

               3               2                     2               2
  + 35*g0028*p5  + 210*g0036*p5 *p6 + 189*g0037*p5*p6  + 210*g0040*p5 *p6

                   2                  2               2                  2
  + 252*g0044*p5*p6  + 126*g0046*p5*p6  + 147*g0049*p5 *p6 + 147*g0054*p5 *p6

               2                  2                  3
  + 21*g0055*p5 *p6 + 168*g0057*p5 *p6 + 105*g0059*p5 }

Relevance for the application:



The equation: 



                          2
b =Db *Db*p5 + b  *p6 + b  *p5
 t   x          3x       x


The symmetry: 

     7               2        7                2
b =(---*Db  *Db*p5*p6 *q39 + ---*Db  *Db *p5*p6 *q39
 s   3    5x                  3    4x   x

        49               2           7                 2
     + ----*Db  *Db*b *p5 *p6*q39 + ---*Db  *Db  *p5*p6 *q39
        9     3x     x               3    3x   2x

        49                2           7                2
     + ----*Db  *Db*b  *p5 *p6*q39 + ---*Db  *Db *b *p5 *p6*q39
        9     2x     2x               9    2x   x  x

        56               2           35           2   3             3
     + ----*Db *Db*b  *p5 *p6*q39 + ----*Db *Db*b  *p5 *q39 + b  *p6 *q39
        9     x     3x               9     x     x             7x

        14              2        28               2            2      2
     + ----*b  *b *p5*p6 *q39 + ----*b  *b  *p5*p6 *q39 + 7*b   *p5*p6 *q39
        3    5x  x               3    4x  2x                 3x

        70        2   2           70     2      2           35    4   3        3
     + ----*b  *b  *p5 *p6*q39 + ----*b   *b *p5 *p6*q39 + ----*b  *p5 *q39)/p6
        9    3x  x                9    2x   x               27   x


And now in machine readable form: 

The system: 

df(b(1),t)=d(1,df(b(1),x))*d(1,b(1))*p5 + df(b(1),x,3)*p6 + df(b(1),x)**2*p5$


The symmetry: 

df(b(1),s)=(7/3*d(1,df(b(1),x,5))*d(1,b(1))*p5*p6**2*q39 + 7/3*d(1,df(b(1),x,4))
*d(1,df(b(1),x))*p5*p6**2*q39 + 49/9*d(1,df(b(1),x,3))*d(1,b(1))*df(b(1),x)*p5**
2*p6*q39 + 7/3*d(1,df(b(1),x,3))*d(1,df(b(1),x,2))*p5*p6**2*q39 + 49/9*d(1,df(b(
1),x,2))*d(1,b(1))*df(b(1),x,2)*p5**2*p6*q39 + 7/9*d(1,df(b(1),x,2))*d(1,df(b(1)
,x))*df(b(1),x)*p5**2*p6*q39 + 56/9*d(1,df(b(1),x))*d(1,b(1))*df(b(1),x,3)*p5**2
*p6*q39 + 35/9*d(1,df(b(1),x))*d(1,b(1))*df(b(1),x)**2*p5**3*q39 + df(b(1),x,7)*
p6**3*q39 + 14/3*df(b(1),x,5)*df(b(1),x)*p5*p6**2*q39 + 28/3*df(b(1),x,4)*df(b(1
),x,2)*p5*p6**2*q39 + 7*df(b(1),x,3)**2*p5*p6**2*q39 + 70/9*df(b(1),x,3)*df(b(1)
,x)**2*p5**2*p6*q39 + 70/9*df(b(1),x,2)**2*df(b(1),x)*p5**2*p6*q39 + 35/27*df(b(
1),x)**4*p5**3*q39)/p6**3$