N=1, # of fermion fields: 1, # of boson fields: 0
weight(t)=2, weight(s)=14, fermion weights={1}, boson weights={}
Problem | Unknowns |
Inequalities | Equations |
Solution 1 |
Computing time |
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Problem
Find equations
f := Df*f*p1 + f *p2
t x
with symmetries
2
f := Df *f*q1 + Df *Df*f*q2 + Df *f *q26 + Df *Df *f*q4 + Df *(Df) *f*q3
s 6x 5x 5x x 4x x 4x
+ Df *Df*f *q25 + Df *f *q30 + Df *Df *f*q7 + Df *Df *Df*f*q6
4x x 4x 2x 3x 2x 3x x
3 2
+ Df *Df *f *q23 + Df *(Df) *f*q5 + Df *(Df) *f *q24 + Df *Df*f *q31
3x x x 3x 3x x 3x 2x
2 2 2
+ Df *f *q44 + (Df ) *Df*f*q9 + (Df ) *f *q22 + Df *(Df ) *f*q11
3x 3x 2x 2x x 2x x
2
+ Df *Df *(Df) *f*q10 + Df *Df *Df*f *q20 + Df *Df *f *q33
2x x 2x x x 2x x 2x
4 3 2
+ Df *(Df) *f*q8 + Df *(Df) *f *q21 + Df *(Df) *f *q32
2x 2x x 2x 2x
3
+ Df *Df*f *q43 + Df *f *q46 + Df *f *f *f*q27 + (Df ) *Df*f*q14
2x 3x 2x 4x 2x 2x x x
3 2 3 2 2
+ (Df ) *f *q19 + (Df ) *(Df) *f*q13 + (Df ) *(Df) *f *q17
x x x x x
2 2 5 4
+ (Df ) *Df*f *q35 + (Df ) *f *q42 + Df *(Df) *f*q12 + Df *(Df) *f *q18
x 2x x 3x x x x
3 2
+ Df *(Df) *f *q34 + Df *(Df) *f *q41 + Df *Df*f *q47
x 2x x 3x x 4x
7
+ Df *Df*f *f *f*q28 + Df *f *q50 + Df *f *f *f*q39 + (Df) *f*q15
x 2x x x 5x x 3x x
6 5 4 3
+ (Df) *f *q16 + (Df) *f *q36 + (Df) *f *q40 + (Df) *f *q48
x 2x 3x 4x
3 2 2
+ (Df) *f *f *f*q29 + (Df) *f *q49 + (Df) *f *f *f*q38 + Df*f *q51
2x x 5x 3x x 6x
+ Df*f *f *f*q45 + Df*f *f *f*q37 + f *q55 + f *f *f*q52
4x x 3x 2x 7x 5x x
+ f *f *f*q53 + f *f *f *q54
4x 2x 3x 2x x
Unknowns
All solutions for the following 57 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,q40,q41
,q42,q43,q44,q45,q46,q47,q48,q49,q50,q51,q52,q53,q54,q55
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.
{q54,q53,q52,q51,q50,q49,q48,q47,q46,q45,q44,q43,q42,q41,q40,q39,q38,q37,q36,q35
,q34,q33,q32,q31,q30,q29,q28,q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15
,q14,q13,q12,q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p1}
{q55,q54,q53,q52,q51,q50,q49,q48,q47,q46,q45,q44,q43,q42,q41,q40,q39,q38,q37,q36
,q35,q34,q33,q32,q31,q30,q29,q28,q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16
,q15,q14,q13,q12,q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1}
{p2,p1}
Equations
All comma separated 75 expressions involving 195 terms have to vanish.
p1*q49,
p1*q2,
p1*q48,
p1*q11,
p1*q3,
p1*q51,
p1*q1,
p1*q40,
p1*q5,
p1*q36,
p1*q8,
p1*q55,
p1*q16,
p1*q12,
p1*q15,
3*p1*(q47 + 5/3*q49),
2*p1*(q33 + 3/2*q42),
3*p1*(q43 + 10/3*q49),
p1*(q4 + q7),
3*p1*(q31 + 10/3*q49),
4*p1*(q4 + 1/4*q7),
20*p1*(q2 + 3/20*q7),
3*p1*(q25 + 5/3*q49),
10*p1*(q2 + 3/10*q4),
p1*(q41 + q48),
2*p1*(q32 + 3/2*q48),
3*p1*(q3 + 2/3*q9),
p1*(q24 + q48),
2*p1*(q3 + 1/2*q6),
p1*(q50 + 3*q51),
2*p1*(q46 + 5/2*q50),
2*p1*(q46 + 15/2*q51),
p1*(q30 + q46),
p1*(q44 + 10*q51),
2*p1*(q30 + 15/2*q51),
p1*(q26 + 3*q51),
5*p1*(q34 + 3/5*q40),
p1*(q10 + 3*q14),
5*p1*(q21 + 3/5*q40),
5*p1*(q10 + 6/5*q5),
3*p1*(q18 + 1/3*q36),
3*p1*(q13 + 1/3*q8),
2*p1*(q42 + 1/2*q43 + q47),
4*p1*(q22 + 3/2*q25 + 3/4*q43),
2*p1*(q32 + 5/2*q35 + 3/2*q41),
3*p1*(q19 + 1/3*q20 + 1/3*q35),
5*p1*(q11 + 6/5*q6 + 4/5*q9),
5*p1*(q26 - 3/5*q30 + 1/5*q46),
5*p1*(q1 - 2/5*q44 + 2/5*q46),
9*p1*(q1 - 2/9*q30 + 2/9*q50),
5*p1*(q1 - 2/5*q26 + 2/5*q51),
3*p1*(q44 + 2/3*q46 + 5/3*q50),
8*p1*(q30 + 3/8*q44 + 5/4*q50),
20*p1*(q26 + 3/20*q44 + 1/5*q46),
10*p1*(q26 + 1/5*q30 + 1/2*q50),
3*p1*(q17 + 1/3*q21 + 1/3*q34),
2*p1*(q25 - q31 + 1/2*q43 + q54),
5*p1*(q2 - 2/5*q31 + 2/5*q47 + 1/5*q53),
4*p1*(q2 - 1/2*q25 + q49 + 1/4*q52),
p1*(q33 - q4 - 2*q42 - 2*q53),
2*p1*(q22 - 1/2*q43 - 5/2*q52 - 1/2*q7),
6*p1*(q31 + 2/3*q33 + 1/2*q43 + q47),
4*p1*(q22 + 3/2*q23 + 1/2*q33 + 3/4*q42),
2*p1*(q23 + 2*q25 + 1/2*q31 + q47),
p1*(q3 - q32 + q37 + q41),
2*p1*(q24 - 3/2*q3 - q45 - 3*q48),
5*p1*(q20 + 6/5*q24 + 2/5*q32 + 3/5*q41),
2*p1*(q21 - 3/2*q38 - 4*q40 - q5),
2*p1*(q18 - 2*q29 - 5*q36 - 1/2*q8),
2*p1*(q23 - 3/2*q4 - q47 - 5/2*q52 - q53),
2*p1*(q23 - q31 - 5*q52 + 2*q53 - 1/2*q7),
p1*(q11 - 6*q19 + 2*q27 + 2*q35 + 3*q39),
p1*(q10 - 4*q17 + 4*q28 + 6*q34 + 3*q38),
2*p1*(q20 - q37 - 3/2*q39 - 2*q41 - 2*q45 - q6),
2*p1*(q20 - 3/2*q27 - 2*q32 + 3/2*q37 - 3*q45 - q9)
Computing time
On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120 MB RAM
under Linux it took 109 sec.