N=1,   # of fermion fields: 0,   # of boson fields: 1
weight(t)=12,   weight(s)=13,   fermion weights={},   boson weights={3}


Problem | Unknowns | Inequalities | Equations | Computing time | Back to overview

Problem

Find equations

       5                                                  2
b  := b *p6 + Db  *Db*b*p2 + Db *Db*b *p1 + b  *p7 + b  *b *p3 + b  *b *b*p4
 t              2x             x     x       6x       3x          2x  x

           3
       + b  *p5
          x

with symmetries
                                         2
b  := Db  *Db*q7 + Db  *Db *q8 + Db *Db*b *q1 + b  *b*q2 + b  *b *q3
 s      4x           3x   x        x             5x         4x  x

                           3        2  2
       + b  *b  *q4 + b  *b *q5 + b  *b *q6
          3x  2x       2x          x

Unknowns

All solutions for the following 15 unknowns have to be determined:
p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7,q8

Inequalities

Each of the following lists represents one inequality which states that not all unknowns in this list may vanish. These inequalities filter out solutions which are trivial for the application.
{q8,q7,q1,p2,p1}
{q8,q7,q6,q5,q4,q3,q2,q1}
{p7,p6,p5,p4,p3,p2,p1}

Equations

All comma separated 72 expressions involving 421 terms have to vanish.
p6*q2,
p6*q7,
p7*q2,
p7*q7,
p6*q5,
p6*q1,
q8*(p1 - p2),
5*p7*(q2 + 2/5*q3),
15*p7*(q7 + 14/15*q8),
4*p7*(q7 + 3/4*q8),
5*p7*(q7 + 2/5*q8),
20*p6*(q5 + 7/20*q6),
7*(p3*q2 - 18/7*p7*q5),
6*p7*(q2 + 7/2*q3 + 35/6*q4),
15*p7*(q2 + 4/3*q3 + 7/5*q4),
20*p7*(q2 + 3/4*q3 + 3/10*q4),
5*(p2*q2 - 3/5*p3*q8 - p7*q1),
5*(p2*q2 - 3/5*p3*q7 - 6/5*p7*q1),
3*(p2*q2 + 8/3*p3*q7 - 4*p7*q1),
p3*q5 - 20*p6*q2 - p6*q3,
2*(p2*q5 - 3/2*p3*q1 + 5/2*p6*q8),
p4*q4 + 2*p5*q4 - 30*p7*q5 - 60*p7*q6,
10*(p2*q2 - 3/10*p3*q7 - 3/10*p3*q8 - 9/10*p7*q1),
p4*q6 + 2*p5*q6 - 60*p6*q2 - 60*p6*q3,
p2*q5 + p3*q1 - 20*p6*q7 - 5*p6*q8,
10*(p3*q2 - 3/10*p3*q4 + p4*q2 - 9/2*p7*q5 - 2*p7*q6),
6*(p3*q3 + 1/3*p4*q3 - 1/6*p5*q2 - 10*p7*q5 - 6*p7*q6),
20*(p3*q2 + 2/5*p3*q3 + 3/20*p4*q2 - 9/2*p7*q5 - 6/5*p7*q6),
17*(p3*q2 - 3/17*p3*q3 + 5/17*p4*q2 - 45/17*p7*q5 - 12/17*p7*q6),
9*(p3*q5 + 2/3*p3*q6 - 2/9*p4*q5 - 200/9*p6*q2 - 5/9*p6*q4),
20*(p3*q2 - 3/20*p3*q3 - 3/20*p3*q4 + 3/4*p4*q2 - 39/10*p7*q5 - 3/2*p7*q6),
10*(p1*q2 + 1/2*p2*q2 + 1/10*p2*q8 + 3/5*p3*q8 + 2/5*p4*q8 - 3*p7*q1),
2*(p1*q3 - 1/2*p1*q8 + 4*p2*q3 - 1/2*p2*q8 + 1/2*p4*q8 - 30*p7*q1),
10*(p1*q2 + 2*p2*q2 + 3/10*p2*q4 - 1/5*p2*q8 + 1/10*p4*q8 - 6*p7*q1),
5*(p1*q2 + 5*p2*q2 + 6/5*p2*q3 - 2/5*p2*q7 - 2/5*p4*q8 - 12*p7*q1),
p1*q2 - 4*p2*q3 + 4*p2*q7 - 12*p3*q7 - 4*p4*q7 + 30*p7*q1,
8*(p3*q5 + 5/8*p3*q6 + 1/4*p4*q5 - 75/2*p6*q2 - 5*p6*q3 - 5/4*p6*q4),
p1*q5 + p2*q1 + p2*q5 - 3*p3*q1 - p4*q1 + 30*p6*q8,
4*(p3*q3 + 1/4*p3*q4 + 2*p4*q3 + 1/4*p4*q4 + 9/4*p5*q3 - 45*p7*q5 - 55*p7*q6),
20*(p3*q2 + 1/10*p3*q4 + 3*p4*q2 + 1/4*p4*q4 + 9/2*p5*q2 - 21*p7*q5 - 21*p7*q6),
24*(p3*q3 + 1/4*p3*q4 + 23/24*p4*q3 + 1/8*p4*q4 + p5*q3 - 105/4*p7*q5 - 105/4*p7
*q6),
10*(p3*q2 + 1/5*p3*q4 + 3/2*p4*q2 + 1/10*p4*q4 + 2*p5*q2 - 12*p7*q5 - 10*p7*q6),
2*(p2*q2 + 1/2*p2*q3 - p2*q7 + p2*q8 - 4*p3*q7 + p3*q8 - 1/2*p4*q7),
p1*q4 - p1*q8 + p2*q4 - p2*q8 + 3*p4*q8 + 6*p5*q8 - 30*p7*q1,
20*(p1*q2 + p2*q2 + 1/10*p2*q4 - 1/20*p2*q8 + 1/5*p3*q8 + 7/20*p4*q8 - 4*p7*q1),
5*(p1*q2 + 2*p2*q2 + 1/5*p2*q4 - 1/5*p2*q8 + 2/5*p3*q8 + 1/5*p4*q8 - 6*p7*q1),
5*(p1*q2 + 4*p2*q2 + 4/5*p2*q3 - 1/5*p2*q8 + 6/5*p3*q8 - 2/5*p4*q7 - 48/5*p7*q1)
,
p2*q1 - 6*p2*q5 - 2*p2*q6 + 2*p3*q1 + p4*q1 + 80*p6*q7 - 20*p6*q8,
p1*q5 - p2*q1 + 2*p2*q5 + 3*p2*q6 + 2*p3*q1 + p4*q1 - 120*p6*q7,
2*(p1*q5 - 1/2*p2*q1 - 3*p2*q5 - 2*p2*q6 - 3*p3*q1 + 1/2*p4*q1 + 60*p6*q7),
6*(p3*q3 + p3*q4 + 11/3*p4*q3 + 5/2*p4*q4 + 6*p5*q3 + 4*p5*q4 - 150*p7*q5 - 230*
p7*q6),
30*(p3*q2 + 1/5*p3*q3 + 1/10*p3*q4 + 17/30*p4*q2 + 1/30*p4*q3 + 1/2*p5*q2 - 33/5
*p7*q5 - 17/5*p7*q6),
5*(p1*q4 - 6/5*p1*q7 + 1/5*p2*q4 - 4/5*p2*q7 + 12/5*p3*q7 + 44/5*p4*q7 + 72/5*p5
*q7 - 24*p7*q1),
10*(p1*q2 + 1/2*p2*q2 - 3/10*p2*q4 + 1/10*p2*q8 + p3*q7 + 1/5*p3*q8 + p4*q7 - 3*
p7*q1),
4*(p1*q3 - 1/2*p1*q7 - 1/4*p1*q8 + 3*p2*q3 - 3/4*p2*q8 + 3/2*p3*q8 + 3/4*p4*q8 -
 45/2*p7*q1),
5*(p1*q2 + 9/5*p2*q2 - 2/5*p2*q3 - 2/5*p2*q7 + 1/5*p2*q8 + 12/5*p3*q7 + 4/5*p4*
q7 - 6*p7*q1),
2*(p3*q5 + 3*p3*q6 + p4*q5 + 3/2*p4*q6 + p5*q5 - 200*p6*q2 - 60*p6*q3 - 10*p6*q4
),
18*(p3*q5 + 4/3*p3*q6 + 1/18*p4*q5 + 1/9*p4*q6 - 1/3*p5*q5 - 50*p6*q2 - 10/3*p6*
q3 - 10/3*p6*q4),
p1*q1 - 4*p1*q6 + p2*q1 - 4*p2*q6 - p4*q1 - 2*p5*q1 + 240*p6*q7 - 60*p6*q8,
50*(p3*q2 + 1/5*p3*q3 + 2/25*p3*q4 + 13/10*p4*q2 + 1/5*p4*q3 - 1/25*p4*q4 + 6/5*
p5*q2 - 54/5*p7*q5 - 38/5*p7*q6),
5*(p1*q2 - 1/5*p2*q2 - 2/5*p2*q3 - 1/5*p2*q4 + 3/5*p2*q7 - 2/5*p2*q8 + 12/5*p3*
q7 + p4*q7 - 12/5*p7*q1),
10*(p1*q2 + p2*q2 - 1/10*p2*q3 - 1/5*p2*q4 - 3/10*p2*q7 + 1/5*p2*q8 + p3*q7 + p4
*q7 - 4*p7*q1),
6*(p1*q7 - 1/2*p1*q8 + 2/3*p2*q7 - 1/6*p2*q8 + 4/3*p3*q7 - 1/3*p3*q8 + 8/3*p4*q7
 - 1/2*p4*q8 + 3*p5*q7 - 10/3*p7*q1),
8*(p1*q7 - 1/2*p1*q8 + 3/2*p2*q7 - 3/8*p2*q8 + 3*p3*q7 - 3/4*p3*q8 + 23/8*p4*q7 
- 1/2*p4*q8 + 3*p5*q7 - 15/4*p7*q1),
6*(p1*q3 + 1/3*p1*q4 - 1/2*p1*q8 + 2/3*p2*q3 + 1/3*p2*q4 - 1/6*p2*q8 + p3*q8 + 
13/6*p4*q8 + 3*p5*q8 - 20*p7*q1),
4*(p1*q3 - 1/4*p1*q4 - 1/2*p1*q7 - 1/4*p1*q8 + 1/4*p2*q3 + 7/4*p2*q7 + 6*p3*q7 +
 23/4*p4*q7 + 6*p5*q7 - 15*p7*q1),
8*(p1*q3 + 3/8*p1*q4 - 7/8*p1*q8 + 3/2*p2*q3 + 3/4*p2*q4 - 9/8*p2*q8 + 3/4*p3*q8
 + 7/4*p4*q8 + 3*p5*q8 - 30*p7*q1),
3*(p1*q4 - 8/3*p1*q7 + 1/3*p1*q8 + p2*q4 - 4*p2*q7 + 2*p3*q7 + 22/3*p4*q7 + 1/3*
p4*q8 + 12*p5*q7 - 30*p7*q1),
3*(p1*q3 - 5/3*p1*q7 + 1/3*p1*q8 + 2*p2*q3 + p2*q4 - 6*p2*q7 + 8*p3*q7 + 23/3*p4
*q7 + 8*p5*q7 - 40*p7*q1),
p1*q1 + 6*p1*q5 + 2*p1*q6 - 2*p2*q1 + 12*p2*q5 + 20*p2*q6 + 6*p3*q1 - 6*p5*q1 - 
720*p6*q7 + 180*p6*q8,
2*(p1*q2 + 1/2*p1*q3 + p1*q8 - 6*p2*q7 + 3/2*p2*q8 - 12*p3*q7 + 3*p3*q8 - 4*p4*
q7 + 1/2*p4*q8 - 3*p5*q7 + 6*p7*q1),
6*(p1*q3 - 1/6*p1*q4 - 4/3*p1*q7 + 1/3*p1*q8 + 2/3*p2*q3 + 1/3*p2*q4 - 2*p2*q7 +
 1/6*p2*q8 + 8/3*p3*q7 + 1/3*p3*q8 + 16/3*p4*q7 + 1/6*p4*q8 + 6*p5*q7 - 20*p7*q1
)

Computing time

On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM under Linux it took 1 sec.