Solution 1 to problem N1t6s10b4+5

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t6s10b4+5

Expressions

The solution is given through the following expressions: 

q21=0


q20=0


q19=0


q18=2*q8


     p1*q8
q17=-------
      p6


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q7=0


    p1*q8
q6=-------
     p6


q5=0


q4=0


q3=0


q2=0


    2*p3*q8
q1=---------
      p6


p7=0


p5=p1


p4=0


p2=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: 
 q8, p1, p3, 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. 
 
{2*g0008*q8 + g0009*p6,

 p3,

 g0010*p3 + g0012*p1,

 p6,

 q8,

 2*g0028*p6 + g0029*p1,

 g0017*p6 + g0019*p1 + 2*g0024*p3}

Relevance for the application:



The system: 



          2
b(1) =b(2) *p6 + b(1) *b(1)*p1
    t                x

b(2) =Db(2)*Db(1)*p3 + b(2) *b(1)*p1
    t                      x


The symmetry: 

             2                        2
       2*b(2) *b(1)*p6*q8 + b(1) *b(1) *p1*q8
                                x
b(1) =----------------------------------------
    s                    p6

           3                                              2
       b(2) *p6*q8 + 2*Db(2)*Db(1)*b(1)*p3*q8 + b(2) *b(1) *p1*q8
                                                    x
b(2) =------------------------------------------------------------
    s                              p6


And now in machine readable form: 

The system: 

df(b(1),t)=b(2)**2*p6 + df(b(1),x)*b(1)*p1$

df(b(2),t)=d(1,b(2))*d(1,b(1))*p3 + df(b(2),x)*b(1)*p1$


The symmetry: 

df(b(1),s)=(2*b(2)**2*b(1)*p6*q8 + df(b(1),x)*b(1)**2*p1*q8)/p6$

df(b(2),s)=(b(2)**3*p6*q8 + 2*d(1,b(2))*d(1,b(1))*b(1)*p3*q8 + df(b(2),x)*b(1)**
2*p1*q8)/p6$