N=1,   # of fermion fields: 0,   # of boson fields: 1
weight(t)=1,   weight(s)=11,   fermion weights={},   boson weights={1}


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

Problem

Find equations

       2
b  := b *p1
 t

with symmetries
       12                              2                              4
b  := b  *q23 + Db  *Db*q24 + Db  *Db*b *q8 + Db  *Db *q25 + Db  *Db*b *q6
 s                4x            3x              3x   x         2x

                                     2              6
       + Db  *Db*b *b*q7 + Db  *Db *b *q5 + Db *Db*b *q1 + Db *Db*b  *b*q4
           2x     x          2x   x           x              x     2x

                  2                 3                      3
       + Db *Db*b  *q3 + Db *Db*b *b *q2 + b  *b*q9 + b  *b *q11 + b  *b *q10
           x     x         x     x          5x         4x           4x  x

              5                             2          2  2            7
       + b  *b *q14 + b  *b  *q12 + b  *b *b *q13 + b   *b *q17 + b  *b *q18
          3x           3x  2x        3x  x           2x            2x

               2                 4         4         3  3         2  6
       + b  *b  *b*q16 + b  *b *b *q15 + b  *q22 + b  *b *q19 + b  *b *q20
          2x  x           2x  x           x         x            x

             9
       + b *b *q21
          x

Unknowns

All solutions for the following 26 unknowns have to be determined:
p1,q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13,q14,q15,q16,q17,q18,q19,q20,q21,
q22,q23,q24,q25

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.
{q25,q24,q8,q7,q6,q5,q4,q3,q2,q1}
{p1}

Equations

All comma separated 29 expressions involving 50 terms have to vanish.
q11,
q5,
q8,
q9,
q25,
q24,
q14,
q6,
q18,
q1,
q21,
q23,
q16 + 3*q22,
3*(q11 + 2/3*q17),
2*(q11 + 1/2*q13),
q10 + q12,
4*(q10 + 1/4*q12),
q12 + 10*q9,
q10 + 5*q9,
4*(q24 - 1/4*q25),
4*(q24 + 1/4*q25),
2*(q15 + 7/2*q19),
q14 + q15,
7*(q2 + 4/7*q6),
q18 + 4*q20,
6*(q13 + 5/6*q16 + 2/3*q17),
3*(q3 + 1/3*q4 + 2/3*q7),
5*(q4 - 2/5*q5 + 6/5*q8),
2*(q5 + 5/2*q7 + 3*q8)

Computing time

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