Solution 1 to problem N1f0b1o35w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f0b1o35w1

Expressions

The solution is given through the following expressions:


q19=0


q18=0


       2
     p4 *q15
q17=---------
         2
       p3


     2*p4*q15
q16=----------
        p3


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


    2*p4*q15
q3=----------
       p3


q2=2*q15


q1=0


p6=0


p5=0


p2=0


p1=p3

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:

 q15, p4, p3

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.

 
{q15,

 p3,

 p4,

 g0034*p4 + g0035*p3 + g0037*p3,

 p1,

                                           2
 2*g0009*p4*q15 + 2*g0010*p3*q15 + g0012*p3 ,

         2                           2                             2
 g0015*p4  + 2*g0016*p3*p4 + g0017*p3  + 2*g0029*p3*p4 + 2*g0030*p3 }

Relevance for the application:

The equation:


                   2            4
b =Db *Db*b*p3 + b  *b*p3 + b *b *p4
 t   x            x          x

The symmetry:

              5                          2   2         3  2   2
b =(2*Db *Db*b *p3*p4*q15 + 2*Db *Db*b *b *p3 *q15 + b  *b *p3 *q15
 s      x                       x     x               x

           2  5                 8   2        2
     + 2*b  *b *p3*p4*q15 + b *b *p4 *q15)/p3
          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)*p3 + df(b(1),x)**2*b(1)*p3 + df(b(1),x
)*b(1)**4*p4$

The symmetry:

df(b(1),s)=(2*d(1,df(b(1),x))*d(1,b(1))*b(1)**5*p3*p4*q15 + 2*d(1,df(b(1),x))*d(
1,b(1))*df(b(1),x)*b(1)**2*p3**2*q15 + df(b(1),x)**3*b(1)**2*p3**2*q15 + 2*df(b(
1),x)**2*b(1)**5*p3*p4*q15 + df(b(1),x)*b(1)**8*p4**2*q15)/p3**2$