Solution 2 to problem N1t8s14b4+5

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s14b4+5

Expressions

The solution is given through the following expressions:


q59=0


q58=0


q57=0


q56=0


q55=0


q54=0


      1
     ---*p3*q24
      3
q53=------------
         p9


q52=0


q51=0


q50=2*q24


q49=0


q48=0


q47=0


q46=0


q45=0


q44=0


q43=0


q42=0


q41=0


q40=0


q39=0


q38=0


q37=0


q36=0


q35=q24


q34=0


q33=0


q32=0


q31=0


q30=0


q29=0


q28=0


q27=0


q26=0


q25=0


     p3*q24
q23=--------
       p9


q22=0


q21=0


q20=0


q19=0


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=q24


q5=0


q4=0


    2*p3*q24
q3=----------
       p9


q2=0


q1=0


p13=0


p12=0


p11=0


     1
p10=---*p3
     2


p8=0


p7=0


p6=p3


p5=0


p4=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:

 q24, p3, p9

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,

 q24,

 p9,

 p3,

 p10,

 g0046*p9 + g0047*p3 + g0064*p9 + 2*g0067*p3,

 q6,

 g0011*p9*q24 + g0022*p9*q24 + 2*g0025*p3*q24 + g0029*p3*p9,

 g0076*p3 + 6*g0079*p9 + 3*g0094*p9}

Relevance for the application:

The system:


                       1       2
b(1) =b(2) *b(2)*p9 + ---*b(1)  *p3
    t     x            2      x

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

The symmetry:

                                                               1       3
       Db(1) *Db(2)*b(2)*p9*q24 + 2*b(2) *b(1) *b(2)*p9*q24 + ---*b(1)  *p3*q24
            x                           x     x                3      x
b(1) =--------------------------------------------------------------------------
    s                                     p9

b(2) =(Db(2) *Db(2)*b(2)*p9*q24 + 2*Db(1) *Db(2)*b(1) *p3*q24
    s       x                            x           x

               2                          2
        + b(2)  *b(2)*p9*q24 + b(2) *b(1)  *p3*q24)/p9
              x                    x     x

And now in machine readable form:

The system:

df(b(1),t)=df(b(2),x)*b(2)*p9 + 1/2*df(b(1),x)**2*p3$

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

The symmetry:

df(b(1),s)=(d(1,df(b(1),x))*d(1,b(2))*b(2)*p9*q24 + 2*df(b(2),x)*df(b(1),x)*b(2)
*p9*q24 + 1/3*df(b(1),x)**3*p3*q24)/p9$

df(b(2),s)=(d(1,df(b(2),x))*d(1,b(2))*b(2)*p9*q24 + 2*d(1,df(b(1),x))*d(1,b(2))*
df(b(1),x)*p3*q24 + df(b(2),x)**2*b(2)*p9*q24 + df(b(2),x)*df(b(1),x)**2*p3*q24)
/p9$