Solution 1 to problem N1t2s12f1


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s12f1

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:
 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.
 
{g0040*q35 + g0041*q34 + g0042*q33 + g0043*q32 + g0044*q31 + g0045*q30

  + g0046*q29 + g0047*q28 + g0048*q27 + g0049*q26 + g0050*q25 + g0051*q24

  + g0052*q23 + g0053*q22 + g0054*q21 + g0055*q20 + g0056*q19 + g0057*q18

  + g0058*q17 + g0059*q16 + g0060*q15 + g0061*q14 + g0062*q13 + g0063*q12

  + g0064*q11 + g0065*q10 + g0066*q9 + g0067*q8 + g0068*q7 + g0069*q6 + g0070*q5

  + g0071*q4 + g0072*q3 + g0073*q2 + g0074*q1,

 g0005*q34 + g0006*q33 + g0007*q32 + g0008*q31 + g0009*q30 + g0010*q29

  + g0011*q28 + g0012*q27 + g0013*q26 + g0014*q25 + g0015*q24 + g0016*q23

  + g0017*q22 + g0018*q21 + g0019*q20 + g0020*q19 + g0021*q18 + g0022*q17

  + g0023*q16 + g0024*q15 + g0025*q14 + g0026*q13 + g0027*q12 + g0028*q11

  + g0029*q10 + g0030*q9 + g0031*q8 + g0032*q7 + g0033*q6 + g0034*q5 + g0035*q4

  + g0036*q3 + g0037*q2 + g0038*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 *q18 + Df  *Df *f*q4 + Df  *(Df) *f*q3
 s   5x          4x             4x  x         3x   x          3x

                                         2
 + Df  *Df*f *q17 + Df  *f  *q21 + (Df  ) *f*q5 + Df  *Df *Df*f*q7
     3x     x         3x  2x          2x            2x   x

                              3                 2
 + Df  *Df *f *q15 + Df  *(Df) *f*q6 + Df  *(Df) *f *q16 + Df  *Df*f  *q22
     2x   x  x         2x                2x        x         2x     2x

                       3             2     2              2
 + Df  *f  *q29 + (Df ) *f*q8 + (Df ) *(Df) *f*q10 + (Df ) *Df*f *q13
     2x  3x          x             x                    x       x

        2                   4                3                  2
 + (Df ) *f  *q23 + Df *(Df) *f*q9 + Df *(Df) *f *q14 + Df *(Df) *f  *q24
      x    2x         x                x        x         x        2x

                                                         6             5
 + Df *Df*f  *q28 + Df *f  *q30 + Df *f  *f *f*q19 + (Df) *f*q11 + (Df) *f *q12
     x     3x         x  4x         x  2x  x                              x

       4               3               2               2
 + (Df) *f  *q25 + (Df) *f  *q27 + (Df) *f  *q31 + (Df) *f  *f *f*q20
          2x              3x              4x              2x  x

 + Df*f  *q32 + Df*f  *f *f*q26 + f  *q35 + f  *f *f*q33 + f  *f  *f*q34
       5x           3x  x          6x        4x  x          3x  2x
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,5))*f(1)*q1 + d(1,df(f(1),x,4))*d(1,f(1))*f(1)*q2 + d(1
,df(f(1),x,4))*df(f(1),x)*q18 + d(1,df(f(1),x,3))*d(1,df(f(1),x))*f(1)*q4 + d(1,
df(f(1),x,3))*d(1,f(1))**2*f(1)*q3 + d(1,df(f(1),x,3))*d(1,f(1))*df(f(1),x)*q17 
+ d(1,df(f(1),x,3))*df(f(1),x,2)*q21 + d(1,df(f(1),x,2))**2*f(1)*q5 + d(1,df(f(1
),x,2))*d(1,df(f(1),x))*d(1,f(1))*f(1)*q7 + d(1,df(f(1),x,2))*d(1,df(f(1),x))*df
(f(1),x)*q15 + d(1,df(f(1),x,2))*d(1,f(1))**3*f(1)*q6 + d(1,df(f(1),x,2))*d(1,f(
1))**2*df(f(1),x)*q16 + d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x,2)*q22 + d(1,df(f(
1),x,2))*df(f(1),x,3)*q29 + d(1,df(f(1),x))**3*f(1)*q8 + d(1,df(f(1),x))**2*d(1,
f(1))**2*f(1)*q10 + d(1,df(f(1),x))**2*d(1,f(1))*df(f(1),x)*q13 + d(1,df(f(1),x)
)**2*df(f(1),x,2)*q23 + d(1,df(f(1),x))*d(1,f(1))**4*f(1)*q9 + d(1,df(f(1),x))*d
(1,f(1))**3*df(f(1),x)*q14 + d(1,df(f(1),x))*d(1,f(1))**2*df(f(1),x,2)*q24 + d(1
,df(f(1),x))*d(1,f(1))*df(f(1),x,3)*q28 + d(1,df(f(1),x))*df(f(1),x,4)*q30 + d(1
,df(f(1),x))*df(f(1),x,2)*df(f(1),x)*f(1)*q19 + d(1,f(1))**6*f(1)*q11 + d(1,f(1)
)**5*df(f(1),x)*q12 + d(1,f(1))**4*df(f(1),x,2)*q25 + d(1,f(1))**3*df(f(1),x,3)*
q27 + d(1,f(1))**2*df(f(1),x,4)*q31 + d(1,f(1))**2*df(f(1),x,2)*df(f(1),x)*f(1)*
q20 + d(1,f(1))*df(f(1),x,5)*q32 + d(1,f(1))*df(f(1),x,3)*df(f(1),x)*f(1)*q26 + 
df(f(1),x,6)*q35 + df(f(1),x,4)*df(f(1),x)*f(1)*q33 + df(f(1),x,3)*df(f(1),x,2)*
f(1)*q34$