Solution 1 to problem N1t2s10b1


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s10b1

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:
 q19, q18, q17, q16, q15, q14, q13, q12, q11, q10, q9, 
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*q7 + g0006*q6 + g0007*q5 + g0008*q4 + g0009*q3 + g0010*q2 + g0011*q1,p2}


Relevance for the application:



The equation: 


b =b *p2
 t  x
The symmetry:
    11                               3
b =b  *q18 + Db  *Db*b*q7 + Db  *Db*b *q6 + Db  *Db*b *q5 + Db  *Db *b*q4
 s             3x             2x              2x     x        2x   x

           5                                 2                     2
 + Db *Db*b *q3 + Db *Db*b  *q1 + Db *Db*b *b *q2 + b  *q19 + b  *b *q8
     x              x     2x        x     x          5x        4x

        4                        2              6             2
 + b  *b *q10 + b  *b *b*q9 + b   *b*q13 + b  *b *q14 + b  *b  *q11
    3x           3x  x         2x           2x           2x  x

           3         3  2         2  5           8
 + b  *b *b *q12 + b  *b *q15 + b  *b *q16 + b *b *q17
    2x  x           x            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)**11*q18 + d(1,df(b(1),x,3))*d(1,b(1))*b(1)*q7 + d(1,df(b(1),x,2)
)*d(1,b(1))*b(1)**3*q6 + d(1,df(b(1),x,2))*d(1,b(1))*df(b(1),x)*q5 + d(1,df(b(1)
,x,2))*d(1,df(b(1),x))*b(1)*q4 + d(1,df(b(1),x))*d(1,b(1))*b(1)**5*q3 + d(1,df(b
(1),x))*d(1,b(1))*df(b(1),x,2)*q1 + d(1,df(b(1),x))*d(1,b(1))*df(b(1),x)*b(1)**2
*q2 + df(b(1),x,5)*q19 + df(b(1),x,4)*b(1)**2*q8 + df(b(1),x,3)*b(1)**4*q10 + df
(b(1),x,3)*df(b(1),x)*b(1)*q9 + df(b(1),x,2)**2*b(1)*q13 + df(b(1),x,2)*b(1)**6*
q14 + df(b(1),x,2)*df(b(1),x)**2*q11 + df(b(1),x,2)*df(b(1),x)*b(1)**3*q12 + df(
b(1),x)**3*b(1)**2*q15 + df(b(1),x)**2*b(1)**5*q16 + df(b(1),x)*b(1)**8*q17$