N=1,   # of fermion fields: 0,   # of boson fields: 1
weight(t)=2,   weight(s)=14,   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
       8                                                             2
b  := b *q35 + Db  *Db*q36 + Db  *Db*b*q14 + Db  *Db *q37 + Db  *Db*b *q12
 s               5x            4x              4x   x         3x

                                                                    3
       + Db  *Db*b *q13 + Db  *Db  *q38 + Db  *Db *b*q11 + Db  *Db*b *q10
           3x     x         3x   2x         3x   x           2x

                                                      2
       + Db  *Db*b  *q8 + Db  *Db*b *b*q9 + Db  *Db *b *q6 + Db  *Db *b *q7
           2x     2x        2x     x          2x   x           2x   x  x

                 4                                                 2
       + Db *Db*b *q1 + Db *Db*b  *q5 + Db *Db*b  *b*q4 + Db *Db*b  *q3
           x              x     3x        x     2x          x     x

                    2                                 2
       + Db *Db*b *b *q2 + b  *q39 + b  *b*q15 + b  *b *q17 + b  *b *q16
           x     x          7x        6x          5x           5x  x

              3                                       2            4
       + b  *b *q20 + b  *b  *q18 + b  *b *b*q19 + b   *q25 + b  *b *q24
          4x           4x  2x        4x  x          3x         3x

                               2               2          2  2          2
       + b  *b  *b*q21 + b  *b  *q22 + b  *b *b *q23 + b   *b *q29 + b   *b *q26
          3x  2x          3x  x         3x  x           2x            2x   x

              5             2                 3         4         3  2
       + b  *b *q30 + b  *b  *b*q28 + b  *b *b *q27 + b  *q34 + b  *b *q31
          2x           2x  x           2x  x           x         x

           2  4           6
       + b  *b *q32 + b *b *q33
          x            x

Unknowns

All solutions for the following 41 unknowns have to be determined:
p1,p2,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,q26,q27,q28,q29,q30,q31,q32,q33,q34,q35,q36,q37,q38,q39

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.
{q38,q37,q36,q14,q13,q12,q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1}
{p2,p1}

Equations

All comma separated 51 expressions involving 96 terms have to vanish.
p1*q17,
p1*q11,
p1*q14,
p1*q18,
p1*q15,
p1*q38,
p1*q37,
p1*q36,
p1*q20,
p1*q6,
p1*q12,
p1*q24,
p1*q10,
p1*q30,
p1*q1,
p1*q39,
p1*q33,
p1*q35,
3*p1*(q22 + 2/3*q26),
20*p1*(q17 + 3/20*q21),
10*p1*(q17 + 3/10*q19),
3*p1*(q11 + 2/3*q7),
3*p1*(q14 + 1/3*q8),
10*p1*(q15 + 1/10*q25),
5*p1*(q16 + 1/5*q18),
15*p1*(q15 + 1/15*q18),
6*p1*(q15 + 1/6*q16),
5*p1*(q36 - 1/5*q37),
2*p1*(q37 - 1/2*q38),
10*p1*(q36 - 1/10*q38),
2*p1*(q37 + 1/2*q38),
10*p1*(q36 + 1/10*q38),
5*p1*(q36 + 1/5*q37),
p1*(q28 + 3*q34),
3*p1*(q20 + 2/3*q29),
2*p1*(q20 + 1/2*q23),
p1*(q27 + 3*q31),
6*p1*(q24 + 5/6*q27),
2*p1*(q10 + 3/2*q2),
p1*(q30 + 3*q32),
3*p1*(q19 + q21 + 2/3*q26),
4*p1*(q19 + 1/4*q21 + 1/2*q22),
p1*(q11 - 4*q14 - 2*q5),
3*p1*(q13 + 1/3*q7 + 1/3*q8),
p1*(q11 + 2*q13 + 4*q14),
5*p1*(q16 + 2/5*q18 + 3/5*q25),
6*p1*(q23 + 5/6*q28 + 2/3*q29),
3*p1*(q3 + 1/3*q4 + 2/3*q9),
6*p1*(q12 + 5/6*q4 - 1/3*q6),
6*p1*(q12 + 1/3*q6 + 5/6*q9),
3*p1*(q13 + q5 - 1/3*q7 + 2/3*q8)

Computing time

On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM under Linux it took 15 sec.