Solution 1 to problem N1t2s7b1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s7b1

Expressions

The solution is given through the following expressions:


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:

 q8, q7, q6, q5, q4, q3, q2, q1, p2

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.

 
{g0005*q8 + g0006*q1,p2}

Relevance for the application:

The equation:


b =b *p2
 t  x

The symmetry:

    8                           2                      3
b =b *q7 + Db  *Db*q8 + Db *Db*b *q1 + b  *b*q2 + b  *b *q4 + b  *b *q3
 s           2x           x             3x         2x          2x  x

     2  2          5
 + b  *b *q5 + b *b *q6
    x           x

And now in machine readable form:

The system:

df(b(1),t)=df(b(1),x)*p2$

The symmetry:

df(b(1),s)=b(1)**8*q7 + d(1,df(b(1),x,2))*d(1,b(1))*q8 + d(1,df(b(1),x))*d(1,b(1
))*b(1)**2*q1 + df(b(1),x,3)*b(1)*q2 + df(b(1),x,2)*b(1)**3*q4 + df(b(1),x,2)*df
(b(1),x)*q3 + df(b(1),x)**2*b(1)**2*q5 + df(b(1),x)*b(1)**5*q6$