Solution 1 to problem N1t2s14b2


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s14b2

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:
 q39, q38, q37, q36, q35, q34, q33, q32, q31, q30, q29, 
q28, q27, q26, q25, 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*q38 + g0006*q37 + g0007*q36 + g0008*q14 + g0009*q13 + g0010*q12

  + g0011*q11 + g0012*q10 + g0013*q9 + g0014*q8 + g0015*q7 + g0016*q6 + g0017*q5

  + g0018*q4 + g0019*q3 + g0020*q2 + g0021*q1,

 p2}


Relevance for the application:



The equation: 


b =b *p2
 t  x
The symmetry:
    8                                                             2
b =b *q35 + Db  *Db*q36 + Db  *Db*b*q14 + Db  *Db *q37 + Db  *Db*b *q12
 s            5x            4x              4x   x         3x

                                                              3
 + Db  *Db*b *q13 + Db  *Db  *q38 + Db  *Db *b*q11 + Db  *Db*b *q10
     3x     x         3x   2x         3x   x           2x

                                                2
 + Db  *Db*b  *q8 + Db  *Db*b *b*q9 + Db  *Db *b *q6 + Db  *Db *b *q7
     2x     2x        2x     x          2x   x           2x   x  x

           4                                                 2
 + Db *Db*b *q1 + Db *Db*b  *q5 + Db *Db*b  *b*q4 + Db *Db*b  *q3
     x              x     3x        x     2x          x     x

              2                                 2                         3
 + Db *Db*b *b *q2 + b  *q39 + b  *b*q15 + b  *b *q17 + b  *b *q16 + b  *b *q20
     x     x          7x        6x          5x           5x  x        4x

                                   2            4
 + b  *b  *q18 + b  *b *b*q19 + b   *q25 + b  *b *q24 + b  *b  *b*q21
    4x  2x        4x  x          3x         3x           3x  2x

         2               2          2  2          2               5
 + b  *b  *q22 + b  *b *b *q23 + b   *b *q29 + b   *b *q26 + b  *b *q30
    3x  x         3x  x           2x            2x   x        2x

         2                 3         4         3  2         2  4           6
 + b  *b  *b*q28 + b  *b *b *q27 + b  *q34 + b  *b *q31 + b  *b *q32 + b *b *q33
    2x  x           2x  x           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)**8*q35 + d(1,df(b(1),x,5))*d(1,b(1))*q36 + d(1,df(b(1),x,4))*d(1
,b(1))*b(1)*q14 + d(1,df(b(1),x,4))*d(1,df(b(1),x))*q37 + d(1,df(b(1),x,3))*d(1,
b(1))*b(1)**2*q12 + d(1,df(b(1),x,3))*d(1,b(1))*df(b(1),x)*q13 + d(1,df(b(1),x,3
))*d(1,df(b(1),x,2))*q38 + d(1,df(b(1),x,3))*d(1,df(b(1),x))*b(1)*q11 + d(1,df(b
(1),x,2))*d(1,b(1))*b(1)**3*q10 + d(1,df(b(1),x,2))*d(1,b(1))*df(b(1),x,2)*q8 + 
d(1,df(b(1),x,2))*d(1,b(1))*df(b(1),x)*b(1)*q9 + d(1,df(b(1),x,2))*d(1,df(b(1),x
))*b(1)**2*q6 + d(1,df(b(1),x,2))*d(1,df(b(1),x))*df(b(1),x)*q7 + d(1,df(b(1),x)
)*d(1,b(1))*b(1)**4*q1 + d(1,df(b(1),x))*d(1,b(1))*df(b(1),x,3)*q5 + d(1,df(b(1)
,x))*d(1,b(1))*df(b(1),x,2)*b(1)*q4 + 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)**2*q2 + df(b(1),x,7)*q39 + df(b(1),
x,6)*b(1)*q15 + df(b(1),x,5)*b(1)**2*q17 + df(b(1),x,5)*df(b(1),x)*q16 + df(b(1)
,x,4)*b(1)**3*q20 + df(b(1),x,4)*df(b(1),x,2)*q18 + df(b(1),x,4)*df(b(1),x)*b(1)
*q19 + df(b(1),x,3)**2*q25 + df(b(1),x,3)*b(1)**4*q24 + df(b(1),x,3)*df(b(1),x,2
)*b(1)*q21 + df(b(1),x,3)*df(b(1),x)**2*q22 + df(b(1),x,3)*df(b(1),x)*b(1)**2*
q23 + df(b(1),x,2)**2*b(1)**2*q29 + df(b(1),x,2)**2*df(b(1),x)*q26 + df(b(1),x,2
)*b(1)**5*q30 + df(b(1),x,2)*df(b(1),x)**2*b(1)*q28 + df(b(1),x,2)*df(b(1),x)*b(
1)**3*q27 + df(b(1),x)**4*q34 + df(b(1),x)**3*b(1)**2*q31 + df(b(1),x)**2*b(1)**
4*q32 + df(b(1),x)*b(1)**6*q33$