N=1, # of fermion fields: 1, # of boson fields: 0
weight(t)=11, weight(s)=12, fermion weights={2}, boson weights={}
Problem | Unknowns |
Inequalities | Equations |
Solution 1 |
Computing time |
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Problem
Find equations
2
f := Df *f*p1 + Df *f *p4 + Df *f *p5 + Df *(Df) *f*p2 + Df *f *p6
t 4x 3x x 2x 2x x x 3x
3
+ (Df) *f *p3 + Df*f *p7
x 4x
with symmetries
2
f := Df *Df*f*q3 + Df *Df *f*q2 + Df *Df*f *q4 + (Df ) *f *q5
s 3x 2x x 2x x x x
4 2
+ Df *Df*f *q6 + (Df) *f*q1 + (Df) *f *q7 + f *q9 + f *f *f*q8
x 2x 3x 6x 3x x
Unknowns
All solutions for the following 16 unknowns have to be determined:
p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7,q8,q9
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.
{q9,q8,q7,q6,q5,q4,q3,q2,q1}
{p7,p6,p5,p4,p3,p2,p1}
Equations
All comma separated 73 expressions involving 627 terms have to vanish.
p7*q1,
p1*q1,
p7*q9,
p1*q9,
p3*q1,
p2*q1,
2*q9*(p6 + 5/2*p7),
5*q9*(p1 + 2/5*p4),
18*(p3*q9 - 5/18*p7*q7),
6*q9*(p5 + 5/2*p6 + 10/3*p7),
20*q9*(p1 + 3/4*p4 + 3/10*p5),
6*q9*(p4 + 5/2*p5 + 10/3*p6 + 5/2*p7),
15*q9*(p1 + 4/3*p4 + p5 + 2/5*p6),
6*q9*(p1 + 5/2*p4 + 10/3*p5 + 5/2*p6 + p7),
10*(p2*q9 + 4*p3*q9 - 1/10*p6*q6 - 1/5*p6*q7),
2*(p2*q7 + 9/2*p3*q7 - 5/2*p6*q1 - 8*p7*q1),
6*(p2*q9 + 15/2*p3*q9 - 1/2*p6*q7 - 1/6*p7*q6 - p7*q7),
6*(p2*q9 + 15/2*p3*q9 + 1/2*p6*q7 - 2/3*p7*q6 - 3/2*p7*q7),
p1*q4 + 3*p1*q7 + 6*p2*q9 - p4*q3 - 4*p7*q3,
p2*q6 + 3*p2*q7 + 9*p3*q7 - 5*p5*q1 - 24*p7*q1,
p2*q4 + 3*p2*q7 - 3*p3*q3 - 5*p4*q1 - 16*p7*q1,
p1*q3 + 2*p1*q4 - 2*p1*q7 + p1*q8 - 2*p4*q3 + p7*q3,
5*(p1*q3 + 1/5*p1*q4 + 8/5*p1*q7 - 12/5*p2*q9 - 1/5*p4*q3 + 1/5*p7*q3),
60*(p1*q1 - 3/20*p2*q3 + 1/60*p2*q6 - 1/10*p2*q7 - 3/20*p3*q3 + 3/5*p7*q1),
80*(p1*q1 - 9/80*p2*q3 + 1/80*p2*q4 - 1/20*p2*q7 - 3/20*p3*q3 + 3/5*p7*q1),
4*(p2*q6 + 3/2*p2*q7 + 9/4*p3*q6 + 9/2*p3*q7 - 5*p5*q1 - 3*p6*q1 - 18*p7*q1),
180*(p2*q9 + 1/2*p3*q9 - 1/60*p4*q2 - 1/60*p4*q4 - 1/30*p4*q5 - 1/60*p4*q6 - 1/
90*p5*q2 - 1/90*p5*q5),
15*(p2*q9 + 4*p3*q9 + 1/5*p5*q7 + 1/5*p6*q7 - 1/15*p7*q3 - 4/15*p7*q4 - 2/5*p7*
q6 - 8/15*p7*q7),
p1*q6 + 3*p1*q7 + 15*p2*q9 + 18*p3*q9 + 3*p4*q7 - p5*q3 - 6*p7*q3 - 4*p7*q4,
8*(p1*q1 - 1/4*p2*q3 + 1/8*p2*q4 + 1/8*p2*q6 - 1/2*p2*q7 + 1/8*p2*q8 - p5*q1 +
p6*q1),
12*(p1*q1 - 1/6*p2*q3 + 1/6*p2*q4 - 1/6*p2*q7 + 1/12*p2*q8 - 1/4*p3*q3 - 2/3*p4*
q1 + 2/3*p7*q1),
60*(p1*q1 - 1/20*p2*q2 - 1/20*p2*q3 - 1/60*p2*q6 - 1/20*p3*q2 - 1/20*p3*q3 + 1/5
*p6*q1 + 1/5*p7*q1),
3*(p1*q3 + 5/3*p1*q4 - 8/3*p1*q7 + 5/3*p1*q8 - p4*q3 - 2/3*p5*q3 + 1/3*p6*q3 +
p7*q3 + 2*p7*q8),
240*(p2*q9 + 9/4*p3*q9 - 1/120*p5*q6 - 1/120*p5*q7 - 1/240*p6*q2 - 1/60*p6*q4 -
1/30*p6*q5 - 1/24*p6*q6 - 1/40*p6*q7),
22*(p1*q2 + 3/11*p1*q3 + p1*q4 + 18/11*p1*q5 + p1*q6 + 3/11*p1*q7 - 105/11*p2*q9
+ 1/22*p5*q2 - 1/22*p6*q2),
8*(p1*q2 + 1/2*p1*q3 + p1*q4 + 9/8*p1*q5 + p1*q6 + 1/2*p1*q7 - 35/4*p2*q9 - 1/8*
p5*q2 + 1/8*p6*q2),
2*(p1*q7 + 10*p2*q9 + 45/2*p3*q9 + 3/2*p4*q7 + 3/2*p5*q7 - 1/2*p6*q3 - 2*p7*q3 -
3*p7*q4 - 2*p7*q6),
4*(p1*q2 + 3/2*p1*q3 + 1/2*p1*q5 - 1/4*p1*q6 + 3/4*p1*q8 - 1/4*p4*q2 - 3/4*p4*q3
- 3/2*p4*q8 + 1/4*p5*q3),
3*(p1*q3 + 4/3*p1*q4 + 1/3*p1*q6 - 8/3*p1*q7 + 4/3*p1*q8 - p4*q3 - 2/3*p5*q3 + 1
/3*p6*q3 + p7*q3 + 4/3*p7*q8),
90*(p2*q9 + 4*p3*q9 - 2/45*p5*q7 - 1/90*p6*q6 - 1/15*p6*q7 - 1/90*p7*q2 - 2/45*
p7*q4 - 4/45*p7*q5 - 1/5*p7*q6 - 4/15*p7*q7),
120*(p2*q9 + 9/4*p3*q9 - 1/60*p5*q6 - 1/120*p6*q2 - 1/120*p6*q6 - 1/30*p7*q2 - 1
/20*p7*q4 - 1/10*p7*q5 - 1/10*p7*q6 - 1/20*p7*q7),
450*(p2*q9 + 6/5*p3*q9 - 1/150*p5*q2 - 1/90*p5*q4 - 1/45*p5*q5 - 1/90*p5*q6 - 1/
150*p6*q2 - 1/150*p6*q4 - 1/75*p6*q5 - 1/150*p6*q6),
2*(p1*q2 + 6*p1*q3 + 2*p1*q4 + p1*q5 + 2*p1*q6 + 6*p1*q7 - 21*p2*q9 - 1/2*p4*q2
+ 3/2*p6*q3 - p7*q2),
24*(p1*q1 - 1/24*p2*q2 - 1/12*p2*q3 + 1/24*p2*q4 + 1/12*p2*q5 - 1/24*p2*q6 - 1/
24*p2*q8 - 1/8*p3*q8 - 1/2*p4*q1 + 1/6*p5*q1),
72*(p1*q1 - 1/6*p2*q3 + 7/72*p2*q4 + 1/36*p2*q5 - 1/24*p2*q6 - 1/24*p2*q8 - 1/24
*p3*q2 - 1/8*p3*q8 - 1/2*p4*q1 + 1/6*p5*q1),
p4*q3 + p4*q4 - 2*p4*q7 + 2*p4*q8 - p5*q4 - p6*q3 + 2*p6*q7 - p6*q8 + 2*p7*q4 -
4*p7*q7 + 5*p7*q8,
2*(p1*q2 + 6*p1*q3 + 2*p1*q4 + 2*p1*q5 - 1/2*p1*q6 - 4*p1*q7 - p4*q2 - 3/2*p4*q3
+ 1/2*p4*q8 + 1/2*p7*q2 - 3/2*p7*q8),
10*(p1*q2 + 4/5*p1*q3 + p1*q4 + p1*q6 + p1*q7 - 7*p2*q9 - 3/10*p4*q3 - 3/5*p5*q3
- 2/5*p6*q3 + p7*q2 + 3/10*p7*q3),
4*(p1*q2 + 9/4*p1*q3 + p1*q4 + 5/4*p1*q6 + 3*p1*q7 - 21/2*p2*q9 - 3/4*p4*q3 - 1/
4*p5*q3 - 3/4*p6*q3 + p7*q2 + 3/4*p7*q3),
96*(p1*q1 - 1/96*p2*q2 - 1/6*p2*q3 + 3/32*p2*q4 + 1/24*p2*q5 - 1/96*p2*q6 - 5/48
*p2*q7 - 1/32*p3*q2 - 3/32*p3*q8 - 3/8*p4*q1 + 1/8*p6*q1),
3*(p2*q4 + p2*q5 + 2/3*p2*q6 + p2*q7 + p3*q4 + p3*q5 + p3*q6 + p3*q7 - 10*p4*q1
- 6*p6*q1 - 16*p7*q1),
10*(p2*q4 + 1/5*p2*q5 + 1/5*p2*q6 + 9/5*p2*q7 - 3/10*p3*q2 + 9/10*p3*q4 + 9/5*p3
*q7 - 6*p4*q1 - 4/5*p5*q1 - 6/5*p6*q1 - 72/5*p7*q1),
3*(p1*q2 + 4/3*p1*q3 + 8/3*p1*q4 + 4/3*p1*q5 - 2/3*p1*q6 - 16/3*p1*q7 + 5/3*p1*
q8 - 1/3*p4*q2 - 1/3*p5*q2 - 1/3*p6*q3 + 4/3*p6*q8 + 2/3*p7*q2),
17*(p1*q2 + 6/17*p1*q3 + 12/17*p1*q4 + 16/17*p1*q5 - 8/17*p1*q6 - 24/17*p1*q7 -
1/17*p4*q2 - 4/17*p5*q2 - 1/17*p5*q3 + 4/17*p5*q8 + 1/17*p6*q2 + 2/17*p7*q2),
14*(p1*q2 + 1/7*p1*q3 + 2/7*p1*q4 + 6/7*p1*q5 - 3/7*p1*q6 - 4/7*p1*q7 - 3/14*p5*
q2 - 1/7*p5*q3 - 1/14*p5*q8 + 1/14*p6*q2 + 1/7*p6*q3 + 1/14*p6*q8),
16*(p1*q2 + 1/2*p1*q3 + 1/16*p1*q4 + 1/2*p1*q5 - 1/4*p1*q6 - 1/8*p1*q7 + 3/16*p1
*q8 - 1/4*p4*q2 - 3/16*p4*q3 - 3/8*p4*q8 - 3/16*p5*q8 + 1/16*p6*q3),
2*(p1*q5 + 90*p2*q9 + 45*p3*q9 - 3/2*p4*q2 - 3*p4*q3 - 3/2*p4*q4 - 3/2*p4*q6 - 3
*p4*q7 - 3/2*p6*q2 - 3*p6*q3 - 3/2*p6*q4 + p7*q5),
2*(p1*q4 + p1*q5 + p1*q6 + 36*p2*q9 + 18*p3*q9 - 1/2*p4*q2 - 3*p4*q3 - 3*p4*q7 -
3/2*p6*q3 - 2*p7*q2 - 6*p7*q3 - p7*q4),
360*(p1*q1 - 1/40*p2*q2 - 1/10*p2*q3 + 1/360*p2*q4 + 1/180*p2*q5 - 1/120*p2*q6 -
1/30*p2*q7 - 1/30*p3*q2 - 1/10*p3*q3 + 1/30*p5*q1 + 1/10*p6*q1 + 2/5*p7*q1),
15*(p1*q2 + 4/5*p1*q3 + 7/15*p1*q4 + 8/15*p1*q5 - 4/15*p1*q6 - 4/5*p1*q7 - 2/5*
p1*q8 - 1/3*p4*q2 - 1/5*p4*q3 + 1/5*p4*q8 - 1/5*p6*q8 + 1/15*p7*q2 - 1/5*p7*q8),
24*(p1*q2 + 7/24*p1*q3 + 1/6*p1*q4 + 1/2*p1*q5 - 1/4*p1*q6 - 1/3*p1*q7 - 5/24*p1
*q8 - 1/4*p4*q2 - 1/8*p4*q3 + 1/12*p4*q8 - 1/8*p5*q8 - 1/8*p6*q8 + 1/12*p7*q3),
300*(p2*q9 + 6/5*p3*q9 - 1/150*p5*q2 - 1/150*p5*q3 - 1/150*p5*q4 - 1/150*p5*q5 -
1/150*p5*q6 - 1/150*p5*q7 - 1/100*p6*q2 - 1/100*p6*q3 - 1/50*p6*q4 - 1/50*p6*q5
- 1/100*p6*q6),
300*(p2*q9 + 6/5*p3*q9 - 1/100*p5*q2 - 1/150*p5*q3 - 1/75*p5*q4 - 1/150*p5*q6 -
1/150*p5*q7 + 1/300*p6*q6 - 3/50*p7*q2 - 1/50*p7*q3 - 4/75*p7*q4 - 2/25*p7*q5 -
1/30*p7*q6),
120*(p2*q9 + 1/2*p3*q9 - 1/40*p4*q2 - 1/60*p4*q3 - 1/40*p4*q4 - 1/40*p4*q6 - 1/
60*p4*q7 + 1/60*p5*q4 + 1/120*p6*q4 - 1/10*p7*q2 - 1/30*p7*q3 - 1/30*p7*q4 - 1/
20*p7*q5),
21*(p1*q2 + 8/7*p1*q3 + 23/21*p1*q4 + 8/7*p1*q5 + 23/21*p1*q6 + 8/7*p1*q7 - 10*
p2*q9 - 1/7*p4*q2 - 1/21*p5*q2 + 2/21*p5*q3 + 1/21*p6*q2 + 1/7*p6*q3 - 2/21*p7*
q2),
5*(p1*q2 + 12/5*p1*q3 + 12/5*p1*q4 + 6/5*p1*q5 - 2/5*p1*q6 - 24/5*p1*q7 + 6/5*p1
*q8 - 2/5*p4*q2 - 2/5*p5*q2 - 2/5*p5*q3 + 1/5*p5*q8 + 1/5*p6*q2 + 3/5*p6*q8 + 2/
5*p7*q2),
160*(p2*q9 + 9/4*p3*q9 + 1/80*p5*q6 - 1/160*p6*q2 - 1/80*p6*q3 - 1/40*p6*q4 - 3/
160*p6*q6 - 1/80*p6*q7 - 1/40*p7*q2 - 1/40*p7*q3 - 3/40*p7*q4 - 3/40*p7*q5 - 1/
10*p7*q6 - 1/20*p7*q7),
p1*q4 - p1*q6 - 3*p4*q3 - p4*q4 - p4*q6 + 6*p4*q7 - 3*p4*q8 + 2*p5*q3 + 2*p5*q4
- 2*p5*q7 + p5*q8 - p6*q4 - 2*p7*q4 + p7*q6 - 6*p7*q8,
5*(p4*q2 + 3/5*p4*q4 + 6/5*p4*q5 - 3/5*p4*q6 - 6/5*p4*q7 - 4/5*p5*q2 - 2/5*p5*q4
- 4/5*p5*q5 + 2/5*p5*q6 + 2/5*p5*q7 + 3/5*p5*q8 + 1/5*p6*q2 + 1/5*p6*q4 + 2/5*
p6*q5 - 1/5*p6*q6),
2*(p1*q6 + 75*p2*q9 + 90*p3*q9 + 3/2*p4*q6 - 1/2*p5*q2 - 2*p5*q3 - 1/2*p5*q4 - 2
*p5*q7 - 3/2*p6*q3 - 3/2*p6*q4 - 3*p7*q2 - 6*p7*q3 - 6*p7*q4 - 4*p7*q5 - 3/2*p7*
q6),
2*(p1*q4 + 90*p2*q9 + 45*p3*q9 - 2*p4*q2 - 3*p4*q3 - 1/2*p4*q4 - 2*p4*q6 - 3*p4*
q7 - p5*q3 + 1/2*p5*q4 + p6*q4 - 8*p7*q2 - 6*p7*q3 - 5/2*p7*q4 - 4*p7*q5),
720*(p2*q9 + 1/2*p3*q9 - 13/720*p4*q2 - 1/120*p4*q3 - 13/720*p4*q4 - 1/40*p4*q5
- 13/720*p4*q6 - 1/120*p4*q7 - 1/360*p5*q2 - 1/360*p5*q3 - 1/360*p5*q4 + 1/360*
p5*q5 - 1/80*p6*q2 - 1/240*p6*q3 - 1/240*p6*q4 - 1/180*p6*q5),
3*(p4*q2 + p4*q3 + 2*p4*q4 + 2/3*p4*q5 - 1/3*p4*q6 - 4*p4*q7 + p4*q8 - 2/3*p5*q2
- 2/3*p5*q3 - 2/3*p5*q4 - 4/3*p5*q5 + 1/3*p5*q6 + 4/3*p5*q7 + 2/3*p6*q5 + p6*q8
+ 4/3*p7*q5 - 2/3*p7*q6)
Computing time
On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM
under Linux it took 272 sec.