Solution 3 to problem N1t8s14f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s14f1

Expressions

The solution is given through the following expressions:


q55=0


q54=0


q53=0


q52=0


q51=0


q50=0


q49=0


q48=0


q47=0


q46=0


q45=0


q44=0


q43=0


q42=0


q41=0


     3
q40=----*q38
     20


q39=0


q37=0


q36=0


q35=0


     3
q34=----*q38
     20


q33=0


q32=0


q31=0


q30=0


q29=0


     5
q28=---*q38
     6


q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


        1
q21= - ---*q38
        4


q20=0


q19=0


q18=0


     1
q17=----*q38
     30


q16=0


q15=0


q13=0


q12=0


q11=0


     1
q10=----*q38
     10


q9=0


q8=0


q7=0


q6=0


       3
q5= - ----*q38
       20


q4=0


q3=0


q2=0


q1=0


p13=0


     7
p12=---*p3
     3


p11=0


p10=0


p9=0


p8=0


       4
p7= - ---*p3
       3


       4
p6= - ---*p4
       9


p5=0


p2=p3


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:

 q14, q38, p3, p4

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.

 
{q28,

 27*g0019*q38 + 180*g0021*q38 + 27*g0025*q38 + 150*g0031*q38 - 45*g0038*q38

  + 6*g0042*q38 - 6*g0045*q38 + 18*g0049*q38 - 27*g0054*q38 + 420*g0059*p3

  - 240*g0064*p3 - 80*g0065*p4 + 180*g0067*p4 + 180*g0068*p3 + 180*g0069*p3,

 q14,

 q5,

 q40,

 p7,

 p3,

 p2,

 q38,

 q10,

 21*g0127*p3 - 12*g0132*p3 - 4*g0133*p4 + 9*g0135*p4 + 9*g0136*p3 + 9*g0137*p3,

 p12}

Relevance for the application:

The equation:


                       2                2         4
f =Df  *Df*f*p3 + (Df ) *f*p3 + Df *(Df) *f*p4 - ---*Df *Df*f *p3
 t   2x              x            x               3    x     x

    4      3          7
 - ---*(Df) *f *p4 + ---*f  *f *f*p3
    9         x       3   2x  x

The symmetry:

       3            3          1                2          1           3
f = - ----*Df  *(Df) *f*q38 + ----*Df  *Df *(Df) *f*q38 - ---*Df  *(Df) *f *q38
 s     20    3x                10    2x   x                4    2x        x

        3             1        2     2           3           3
 + (Df ) *Df*f*q14 + ----*(Df ) *(Df) *f *q38 + ----*Df *(Df) *f  *q38
      x               30     x          x        20    x        2x

    5                         3       4               2
 + ---*Df *Df*f  *f *f*q38 + ----*(Df) *f  *q38 + (Df) *f  *f *f*q38
    6    x     2x  x          20         3x              3x  x

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*p3 + d(1,df(f(1),x))**2*f(1)*p3 + d(
1,df(f(1),x))*d(1,f(1))**2*f(1)*p4 - 4/3*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*p3
 - 4/9*d(1,f(1))**3*df(f(1),x)*p4 + 7/3*df(f(1),x,2)*df(f(1),x)*f(1)*p3$

The symmetry:

df(f(1),s)= - 3/20*d(1,df(f(1),x,3))*d(1,f(1))**3*f(1)*q38 + 1/10*d(1,df(f(1),x,
2))*d(1,df(f(1),x))*d(1,f(1))**2*f(1)*q38 - 1/4*d(1,df(f(1),x,2))*d(1,f(1))**3*
df(f(1),x)*q38 + d(1,df(f(1),x))**3*d(1,f(1))*f(1)*q14 + 1/30*d(1,df(f(1),x))**2
*d(1,f(1))**2*df(f(1),x)*q38 + 3/20*d(1,df(f(1),x))*d(1,f(1))**3*df(f(1),x,2)*
q38 + 5/6*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*df(f(1),x)*f(1)*q38 + 3/20*d(1,
f(1))**4*df(f(1),x,3)*q38 + d(1,f(1))**2*df(f(1),x,3)*df(f(1),x)*f(1)*q38$