N=1,   # of fermion fields: 0,   # of boson fields: 1
weight(t)=2,   weight(s)=10,   fermion weights={},   boson weights={2}


Problem | Unknowns | Inequalities | Equations | Solution 1 | Computing time | Back to overview

Problem

Find equations

       2
b  := b *p1 + b *p2
 t             x

with symmetries
       6                                                           2
b  := b *q13 + Db  *Db*q14 + Db  *Db*b*q3 + Db  *Db *q15 + Db *Db*b *q1
 s               3x            2x             2x   x         x

                                                  2                     2
       + Db *Db*b *q2 + b  *q16 + b  *b*q4 + b  *b *q6 + b  *b *q5 + b   *q9
           x     x       5x        4x         3x          3x  x       2x

              3                      3         2  2           4
       + b  *b *q8 + b  *b *b*q7 + b  *q12 + b  *b *q10 + b *b *q11
          2x          2x  x         x         x            x

Unknowns

All solutions for the following 18 unknowns have to be determined:
p1,p2,q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13,q14,q15,q16

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.
{q15,q14,q3,q2,q1}
{p2,p1}

Equations

All comma separated 19 expressions involving 28 terms have to vanish.
p1*q4,
p1*q15,
p1*q14,
p1*q6,
p1*q3,
p1*q8,
p1*q1,
p1*q16,
p1*q11,
p1*q13,
3*p1*(q5 + 2/3*q9),
3*p1*(q4 + 1/3*q9),
4*p1*(q4 + 1/4*q5),
3*p1*(q14 - 1/3*q15),
3*p1*(q14 + 1/3*q15),
2*p1*(q12 + 1/2*q7),
2*p1*(q6 + 1/2*q7),
p1*(q2 + q3),
2*p1*(q10 + 1/2*q8)

Computing time

On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM under Linux it took 2 sec.