N=1, 1 fermion field, t-weights=3+5, f-weight=1/2
Problem |Unknowns | Inequalities |
Equations |
Solution 1 |
Computing time |
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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.