Solution 1 to problem N1t8s14b2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s14b2

Expressions

The solution is given through the following expressions:


q39=0


q38=0


q37=0


q36=0


q35=0


q34=0


       2
     p6 *q31
q33=---------
         2
       p5


     2*p6*q31
q32=----------
        p5


q30=0


q29=0


q28=0


q27=0


q26=0


q25=0


q24=0


q23=0


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=0


q5=0


q4=0


q3=0


q2=2*q31


    2*p6*q31
q1=----------
       p5


p9=0


p8=0


p7=0


p4=0


p3=0


p2=0


p1=p5

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:

 q31, p6, p5

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.

 
{q31,

 p5,

 p6,

 g0066*p6 + g0067*p5 + g0071*p5,

 p1,

                                           2
 2*g0020*p5*q31 + 2*g0021*p6*q31 + g0023*p5 ,

         2                           2             2
 g0030*p6  + 2*g0031*p5*p6 + g0032*p5  + 2*g0061*p5  + 2*g0062*p5*p6}

Relevance for the application:

The equation:


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

The symmetry:

              4                          2   2         3  2   2
b =(2*Db *Db*b *p5*p6*q31 + 2*Db *Db*b *b *p5 *q31 + b  *b *p5 *q31
 s      x                       x     x               x

           2  4                 6   2        2
     + 2*b  *b *p5*p6*q31 + b *b *p6 *q31)/p5
          x                  x

And now in machine readable form:

The system:

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

The symmetry:

df(b(1),s)=(2*d(1,df(b(1),x))*d(1,b(1))*b(1)**4*p5*p6*q31 + 2*d(1,df(b(1),x))*d(
1,b(1))*df(b(1),x)*b(1)**2*p5**2*q31 + df(b(1),x)**3*b(1)**2*p5**2*q31 + 2*df(b(
1),x)**2*b(1)**4*p5*p6*q31 + df(b(1),x)*b(1)**6*p6**2*q31)/p5**2$