Solution 1 to problem N1t2s14f1


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s14f1

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:
 q55, q54, q53, q52, q51, q50, q49, q48, q47, q46, q45, 
q44, q43, q42, q41, q40, 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.
 
{g0060*q55 + g0061*q54 + g0062*q53 + g0063*q52 + g0064*q51 + g0065*q50

  + g0066*q49 + g0067*q48 + g0068*q47 + g0069*q46 + g0070*q45 + g0071*q44

  + g0072*q43 + g0073*q42 + g0074*q41 + g0075*q40 + g0076*q39 + g0077*q38

  + g0078*q37 + g0079*q36 + g0080*q35 + g0081*q34 + g0082*q33 + g0083*q32

  + g0084*q31 + g0085*q30 + g0086*q29 + g0087*q28 + g0088*q27 + g0089*q26

  + g0090*q25 + g0091*q24 + g0092*q23 + g0093*q22 + g0094*q21 + g0095*q20

  + g0096*q19 + g0097*q18 + g0098*q17 + g0099*q16 + g0100*q15 + g0101*q14

  + g0102*q13 + g0103*q12 + g0104*q11 + g0105*q10 + g0106*q9 + g0107*q8

  + g0108*q7 + g0109*q6 + g0110*q5 + g0111*q4 + g0112*q3 + g0113*q2 + g0114*q1,

 g0005*q54 + g0006*q53 + g0007*q52 + g0008*q51 + g0009*q50 + g0010*q49

  + g0011*q48 + g0012*q47 + g0013*q46 + g0014*q45 + g0015*q44 + g0016*q43

  + g0017*q42 + g0018*q41 + g0019*q40 + g0020*q39 + g0021*q38 + g0022*q37

  + g0023*q36 + g0024*q35 + g0025*q34 + g0026*q33 + g0027*q32 + g0028*q31

  + g0029*q30 + g0030*q29 + g0031*q28 + g0032*q27 + g0033*q26 + g0034*q25

  + g0035*q24 + g0036*q23 + g0037*q22 + g0038*q21 + g0039*q20 + g0040*q19

  + g0041*q18 + g0042*q17 + g0043*q16 + g0044*q15 + g0045*q14 + g0046*q13

  + g0047*q12 + g0048*q11 + g0049*q10 + g0050*q9 + g0051*q8 + g0052*q7

  + g0053*q6 + g0054*q5 + g0055*q4 + g0056*q3 + g0057*q2 + g0058*q1,

 p2}


Relevance for the application:



The equation: 


f =f *p2
 t  x
The symmetry:
                                                                     2
f =Df  *f*q1 + Df  *Df*f*q2 + Df  *f *q26 + Df  *Df *f*q4 + Df  *(Df) *f*q3
 s   6x          5x             5x  x         4x   x          4x

 + Df  *Df*f *q25 + Df  *f  *q30 + Df  *Df  *f*q7 + Df  *Df *Df*f*q6
     4x     x         4x  2x         3x   2x          3x   x

                              3                 2
 + Df  *Df *f *q23 + Df  *(Df) *f*q5 + Df  *(Df) *f *q24 + Df  *Df*f  *q31
     3x   x  x         3x                3x        x         3x     2x

                        2                 2                    2
 + Df  *f  *q44 + (Df  ) *Df*f*q9 + (Df  ) *f *q22 + Df  *(Df ) *f*q11
     3x  3x          2x                2x    x         2x    x

                2
 + Df  *Df *(Df) *f*q10 + Df  *Df *Df*f *q20 + Df  *Df *f  *q33
     2x   x                 2x   x     x         2x   x  2x

            4                 3                   2
 + Df  *(Df) *f*q8 + Df  *(Df) *f *q21 + Df  *(Df) *f  *q32 + Df  *Df*f  *q43
     2x                2x        x         2x        2x         2x     3x

                                           3                 3
 + Df  *f  *q46 + Df  *f  *f *f*q27 + (Df ) *Df*f*q14 + (Df ) *f *q19
     2x  4x         2x  2x  x            x                 x    x

        2     3              2     2               2                   2
 + (Df ) *(Df) *f*q13 + (Df ) *(Df) *f *q17 + (Df ) *Df*f  *q35 + (Df ) *f  *q42
      x                    x          x          x       2x          x    3x

           5                 4                  3                   2
 + Df *(Df) *f*q12 + Df *(Df) *f *q18 + Df *(Df) *f  *q34 + Df *(Df) *f  *q41
     x                 x        x         x        2x         x        3x

 + Df *Df*f  *q47 + Df *Df*f  *f *f*q28 + Df *f  *q50 + Df *f  *f *f*q39
     x     4x         x     2x  x           x  5x         x  3x  x

       7             6              5               4               3
 + (Df) *f*q15 + (Df) *f *q16 + (Df) *f  *q36 + (Df) *f  *q40 + (Df) *f  *q48
                        x              2x              3x              4x

       3                    2               2
 + (Df) *f  *f *f*q29 + (Df) *f  *q49 + (Df) *f  *f *f*q38 + Df*f  *q51
          2x  x                5x              3x  x             6x

 + Df*f  *f *f*q45 + Df*f  *f  *f*q37 + f  *q55 + f  *f *f*q52 + f  *f  *f*q53
       4x  x             3x  2x          7x        5x  x          4x  2x

 + f  *f  *f *q54
    3x  2x  x
And now in machine readable form:

The system:

df(f(1),t)=df(f(1),x)*p2$
The symmetry:
df(f(1),s)=d(1,df(f(1),x,6))*f(1)*q1 + d(1,df(f(1),x,5))*d(1,f(1))*f(1)*q2 + d(1
,df(f(1),x,5))*df(f(1),x)*q26 + d(1,df(f(1),x,4))*d(1,df(f(1),x))*f(1)*q4 + d(1,
df(f(1),x,4))*d(1,f(1))**2*f(1)*q3 + d(1,df(f(1),x,4))*d(1,f(1))*df(f(1),x)*q25 
+ d(1,df(f(1),x,4))*df(f(1),x,2)*q30 + d(1,df(f(1),x,3))*d(1,df(f(1),x,2))*f(1)*
q7 + d(1,df(f(1),x,3))*d(1,df(f(1),x))*d(1,f(1))*f(1)*q6 + d(1,df(f(1),x,3))*d(1
,df(f(1),x))*df(f(1),x)*q23 + d(1,df(f(1),x,3))*d(1,f(1))**3*f(1)*q5 + d(1,df(f(
1),x,3))*d(1,f(1))**2*df(f(1),x)*q24 + d(1,df(f(1),x,3))*d(1,f(1))*df(f(1),x,2)*
q31 + d(1,df(f(1),x,3))*df(f(1),x,3)*q44 + d(1,df(f(1),x,2))**2*d(1,f(1))*f(1)*
q9 + d(1,df(f(1),x,2))**2*df(f(1),x)*q22 + d(1,df(f(1),x,2))*d(1,df(f(1),x))**2*
f(1)*q11 + d(1,df(f(1),x,2))*d(1,df(f(1),x))*d(1,f(1))**2*f(1)*q10 + d(1,df(f(1)
,x,2))*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q20 + d(1,df(f(1),x,2))*d(1,df(f(1),
x))*df(f(1),x,2)*q33 + d(1,df(f(1),x,2))*d(1,f(1))**4*f(1)*q8 + d(1,df(f(1),x,2)
)*d(1,f(1))**3*df(f(1),x)*q21 + d(1,df(f(1),x,2))*d(1,f(1))**2*df(f(1),x,2)*q32 
+ d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x,3)*q43 + d(1,df(f(1),x,2))*df(f(1),x,4)*
q46 + d(1,df(f(1),x,2))*df(f(1),x,2)*df(f(1),x)*f(1)*q27 + d(1,df(f(1),x))**3*d(
1,f(1))*f(1)*q14 + d(1,df(f(1),x))**3*df(f(1),x)*q19 + d(1,df(f(1),x))**2*d(1,f(
1))**3*f(1)*q13 + d(1,df(f(1),x))**2*d(1,f(1))**2*df(f(1),x)*q17 + d(1,df(f(1),x
))**2*d(1,f(1))*df(f(1),x,2)*q35 + d(1,df(f(1),x))**2*df(f(1),x,3)*q42 + d(1,df(
f(1),x))*d(1,f(1))**5*f(1)*q12 + d(1,df(f(1),x))*d(1,f(1))**4*df(f(1),x)*q18 + d
(1,df(f(1),x))*d(1,f(1))**3*df(f(1),x,2)*q34 + d(1,df(f(1),x))*d(1,f(1))**2*df(f
(1),x,3)*q41 + d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,4)*q47 + d(1,df(f(1),x))*d(1,
f(1))*df(f(1),x,2)*df(f(1),x)*f(1)*q28 + d(1,df(f(1),x))*df(f(1),x,5)*q50 + d(1,
df(f(1),x))*df(f(1),x,3)*df(f(1),x)*f(1)*q39 + d(1,f(1))**7*f(1)*q15 + d(1,f(1))
**6*df(f(1),x)*q16 + d(1,f(1))**5*df(f(1),x,2)*q36 + d(1,f(1))**4*df(f(1),x,3)*
q40 + d(1,f(1))**3*df(f(1),x,4)*q48 + d(1,f(1))**3*df(f(1),x,2)*df(f(1),x)*f(1)*
q29 + d(1,f(1))**2*df(f(1),x,5)*q49 + d(1,f(1))**2*df(f(1),x,3)*df(f(1),x)*f(1)*
q38 + d(1,f(1))*df(f(1),x,6)*q51 + d(1,f(1))*df(f(1),x,4)*df(f(1),x)*f(1)*q45 + 
d(1,f(1))*df(f(1),x,3)*df(f(1),x,2)*f(1)*q37 + df(f(1),x,7)*q55 + df(f(1),x,5)*
df(f(1),x)*f(1)*q52 + df(f(1),x,4)*df(f(1),x,2)*f(1)*q53 + df(f(1),x,3)*df(f(1),
x,2)*df(f(1),x)*q54$