N=1,   1 fermion field,   t-weights=3+5,   f-weight=1/2


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

Problem

Find systems
                                             3            2
f =Df  *f*p1 + Df *Df*f*p2 + Df *f *p5 + (Df) *f*p3 + (Df) *f *p4 + Df*f  *p6
 t   2x          x             x  x                          x          2x

 + f  *p7
    3x
with symmetries
                                                                     2
f =Df  *f*q1 + Df  *Df*f*q2 + Df  *f *q12 + Df  *Df *f*q4 + Df  *(Df) *f*q3
 s   4x          3x             3x  x         2x   x          2x

                                        2                2
 + Df  *Df*f *q11 + Df  *f  *q14 + (Df ) *Df*f*q6 + (Df ) *f *q10
     2x     x         2x  2x          x                x    x

           3                2                                            5
 + Df *(Df) *f*q5 + Df *(Df) *f *q9 + Df *Df*f  *q15 + Df *f  *q18 + (Df) *f*q7
     x                x        x        x     2x         x  3x

       4             3               2
 + (Df) *f *q8 + (Df) *f  *q16 + (Df) *f  *q17 + Df*f  *q19 + Df*f  *f *f*q13
          x             2x              3x           4x           2x  x

 + f  *q21 + f  *f *f*q20
    5x        3x  x

Unknowns

All solutions for the following 8 unknowns have to be determined:
p1,p2,q1,..,q6

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.
{q5,q4,q3,q2,q1,p1}
{q6,q5,q4,q3,q2,q1}
{p2,p1}

Equations

All comma separated 14 expressions involving 37 terms have to vanish.
p2*q5,
p1*q4,
p1*q1,
p1*(q3 + q4),
5*(p1*q6 - 3/5*p2*q4),
10*(p1*q6 - 3/10*p2*q1),
p1*(q1 - 2*q3 + 4*q4),
3*p1*(q1 + 2/3*q2 + 1/3*q4),
20*(p1*q6 - 3/20*p2*q3 - 3/10*p2*q4),
20*(p1*q6 - 3/20*p2*q1 - 3/20*p2*q3),
20*(p1*q6 - 3/20*p2*q1 - 3/10*p2*q2),
10*(p1*q6 - 1/10*p2*q1 - 1/5*p2*q2 - 1/10*p2*q3),
40*(p1*q6 - 3/20*p2*q1 - 3/20*p2*q2 - 3/40*p2*q3),
20*(p1*q6 - 1/20*p2*q1 - 1/10*p2*q2 - 3/20*p2*q3 - 1/10*p2*q4)

Computing time

On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM under Linux it took 1.8 sec.