Solution 1 to problem N1t2s12b2


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s12b2

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:
 q24, q23, q22, q21, q20, 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*q23 + g0006*q22 + g0007*q7 + g0008*q6 + g0009*q5 + g0010*q4 + g0011*q3

  + g0012*q2 + g0013*q1,

 p2}


Relevance for the application:



The equation: 


b =b *p2
 t  x
The symmetry:
    7                                                            2
b =b *q21 + Db  *Db*q22 + Db  *Db*b*q7 + Db  *Db *q23 + Db  *Db*b *q6
 s            4x            3x             3x   x         2x

                                           3
 + Db  *Db*b *q5 + Db  *Db *b*q4 + Db *Db*b *q1 + Db *Db*b  *q3 + Db *Db*b *b*q2
     2x     x        2x   x          x              x     2x        x     x

                             2                        3
 + b  *q24 + b  *b*q8 + b  *b *q10 + b  *b *q9 + b  *b *q13 + b  *b  *q11
    6x        5x         4x           4x  x       3x           3x  2x

                     2              4             2               2
 + b  *b *b*q12 + b   *b*q16 + b  *b *q17 + b  *b  *q14 + b  *b *b *q15
    3x  x          2x           2x           2x  x         2x  x

     3           2  3           5
 + b  *b*q18 + b  *b *q19 + b *b *q20
    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)**7*q21 + d(1,df(b(1),x,4))*d(1,b(1))*q22 + d(1,df(b(1),x,3))*d(1
,b(1))*b(1)*q7 + d(1,df(b(1),x,3))*d(1,df(b(1),x))*q23 + d(1,df(b(1),x,2))*d(1,b
(1))*b(1)**2*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)**3*q1 + d(1,df(b(1),x))
*d(1,b(1))*df(b(1),x,2)*q3 + d(1,df(b(1),x))*d(1,b(1))*df(b(1),x)*b(1)*q2 + df(b
(1),x,6)*q24 + df(b(1),x,5)*b(1)*q8 + df(b(1),x,4)*b(1)**2*q10 + df(b(1),x,4)*df
(b(1),x)*q9 + df(b(1),x,3)*b(1)**3*q13 + df(b(1),x,3)*df(b(1),x,2)*q11 + df(b(1)
,x,3)*df(b(1),x)*b(1)*q12 + df(b(1),x,2)**2*b(1)*q16 + df(b(1),x,2)*b(1)**4*q17 
+ df(b(1),x,2)*df(b(1),x)**2*q14 + df(b(1),x,2)*df(b(1),x)*b(1)**2*q15 + df(b(1)
,x)**3*b(1)*q18 + df(b(1),x)**2*b(1)**3*q19 + df(b(1),x)*b(1)**5*q20$