N=1, # of fermion fields: 0, # of boson fields: 1
weight(t)=2, weight(s)=11, fermion weights={}, boson weights={1}
Problem | Unknowns |
Inequalities | Equations |
Solution 1 |
Computing time |
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Problem
Find equations
3
b := b *p1 + b *p2
t x
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 27 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
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}
{p2,p1}
Equations
All comma separated 30 expressions involving 59 terms have to vanish.
p1*q11,
p1*q5,
p1*q8,
p1*q9,
p1*q25,
p1*q24,
p1*q14,
p1*q6,
p1*q18,
p1*q1,
p1*q21,
p1*q23,
18*p1*(q11 + 5/18*q17),
24*p1*(q11 + 5/24*q13),
6*p1*(q10 + 1/6*q12),
p1*(q12 + 20*q9),
p1*(q10 + 10*q9),
4*p1*(q24 - 1/4*q25),
4*p1*(q24 + 1/4*q25),
18*p1*(q14 + 7/18*q15),
3*p1*(q2 + 4/3*q6),
2*p1*(q18 + 3/2*q20),
2*p1*(q13 + q16 + 3/2*q22),
7*p1*(q4 - 6/7*q5 + 18/7*q8),
6*p1*(q5 + 7/6*q7 + 3*q8),
p1*(q10 + q12 + 5*q9),
4*p1*(q10 + 1/4*q12 + 5/2*q9),
2*p1*(q14 + q15 + 3/2*q19),
36*p1*(q11 + 1/2*q13 + 7/36*q16 + 1/3*q17),
3*p1*(q3 + 2/3*q4 - 2/3*q5 + 4/3*q7 + 2*q8)
Computing time
On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM
under Linux it took 5 sec.