Solution 1 to problem N1t8s14b4+5

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s14b4+5

Expressions

The solution is given through the following expressions:


q59=0


q58=0


q57=0


q56=0


q55=0


q54=0


      5
     ---*p6*q24
      3
q53=------------
         p9


q52=0


q51=0


q50=2*q24


q49=0


q48=0


q47=0


q46=0


q45=0


q44=0


q43=0


q42=0


q41=0


q40=0


q39=0


     1
q38=---*q24
     4


q37=0


      5
     ---*p6*q24
      4
q36=------------
         p9


     1
q35=---*q24
     2


     1
q34=---*q24
     4


q33=0


q32=0


q31=0


q30=0


q29=0


q28=0


q27=0


q26=0


q25=0


     2*p6*q24
q23=----------
        p9


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


    1
q6=---*q24
    2


q5=0


     1
    ---*p6*q24
     2
q4=------------
        p9


     7
    ---*p6*q24
     4
q3=------------
        p9


        1
     - ---*p6*q24
        4
q2=---------------
         p9


q1=0


p13=0


     1
p12=---*p6
     2


p11=0


     7
p10=---*p6
     4


p8=0


p7=0


p5=0


p4=0


p3=2*p6


p2=0


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, p6, p9

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.

 
{p10,

 p3,

 q24,

 p9,

 p6,

 p12,

 4*g0046*p9 + 8*g0047*p6 + 2*g0064*p9 + 2*g0066*p6 + 7*g0067*p6 - g0068*p6,

 q6,

 g0008*p9*q24 + 5*g0010*p6*q24 + 2*g0011*p9*q24 + g0012*p9*q24 + 2*g0022*p9*q24

  + 2*g0024*p6*q24 + 7*g0025*p6*q24 - g0026*p6*q24 + 2*g0028*p6*p9

  + 4*g0029*p6*p9,

 20*g0076*p6 + 24*g0079*p9 + 3*g0091*p9 + 15*g0093*p6 + 6*g0094*p9 + 3*g0095*p9}

Relevance for the application:

The system:


       1                                     7       2
b(1) =---*Db(1) *Db(1)*p6 + b(2) *b(2)*p9 + ---*b(1)  *p6
    t  2       x                x            4      x

b(2) =Db(1) *Db(2)*p6 + 2*b(2) *b(1) *p6
    t      x                  x     x

The symmetry:

        1                              1
b(1) =(---*Db(2)*Db(1)*b(2) *p9*q24 + ---*Db(2) *Db(1)*b(2)*p9*q24
    s   4                  x           4       x

           1                              5
        + ---*Db(1) *Db(2)*b(2)*p9*q24 + ---*Db(1) *Db(1)*b(1) *p6*q24
           2       x                      4       x           x

                                       5       3
        + 2*b(2) *b(1) *b(2)*p9*q24 + ---*b(1)  *p6*q24)/p9
                x     x                3      x

           1                               1
b(2) =( - ---*Db(2)*Db(1)*b(1)  *p6*q24 + ---*Db(2) *Db(2)*b(2)*p9*q24
    s      4                  2x           2       x

           7                               1
        + ---*Db(1) *Db(2)*b(1) *p6*q24 + ---*Db(1) *Db(1)*b(2) *p6*q24
           4       x           x           2       x           x

               2                            2
        + b(2)  *b(2)*p9*q24 + 2*b(2) *b(1)  *p6*q24)/p9
              x                      x     x

And now in machine readable form:

The system:

df(b(1),t)=1/2*d(1,df(b(1),x))*d(1,b(1))*p6 + df(b(2),x)*b(2)*p9 + 7/4*df(b(1),x
)**2*p6$

df(b(2),t)=d(1,df(b(1),x))*d(1,b(2))*p6 + 2*df(b(2),x)*df(b(1),x)*p6$

The symmetry:

df(b(1),s)=(1/4*d(1,b(2))*d(1,b(1))*df(b(2),x)*p9*q24 + 1/4*d(1,df(b(2),x))*d(1,
b(1))*b(2)*p9*q24 + 1/2*d(1,df(b(1),x))*d(1,b(2))*b(2)*p9*q24 + 5/4*d(1,df(b(1),
x))*d(1,b(1))*df(b(1),x)*p6*q24 + 2*df(b(2),x)*df(b(1),x)*b(2)*p9*q24 + 5/3*df(b
(1),x)**3*p6*q24)/p9$

df(b(2),s)=( - 1/4*d(1,b(2))*d(1,b(1))*df(b(1),x,2)*p6*q24 + 1/2*d(1,df(b(2),x))
*d(1,b(2))*b(2)*p9*q24 + 7/4*d(1,df(b(1),x))*d(1,b(2))*df(b(1),x)*p6*q24 + 1/2*d
(1,df(b(1),x))*d(1,b(1))*df(b(2),x)*p6*q24 + df(b(2),x)**2*b(2)*p9*q24 + 2*df(b(
2),x)*df(b(1),x)**2*p6*q24)/p9$