Bi-linear algebraic problem N1t7s10f6+7

N=1, # of fermion fields: 1, # of boson fields: 0
weight(t)=7, weight(s)=10, fermion weights={6+7}, boson weights={}

Problem

Find equations


f(1)  := Df(1)*f(1)*p4 + f(2)  *p5
    t                        3x

f(2)  := Df(2)*f(1)*p1 + Df(1)*f(2)*p2 + f(1)  *p3
    t                                        4x

with symmetries

f(1)  := Df(2) *f(1)*q7 + Df(1) *f(2)*q8 + Df(2)*f(1) *q9 + Df(1)*f(2) *q10
    s         x                x                     x                x

          + f(1)  *q11
                5x

f(2)  := Df(2) *f(2)*q2 + Df(1)  *f(1)*q1 + Df(1) *f(1) *q3 + Df(2)*f(2) *q4
    s         x                2x                x     x                x

          + Df(1)*f(1)  *q5 + f(2)  *q6
                      2x          5x

Unknowns

All solutions for the following 16 unknowns have to be determined:

p1,p2,p3,p4,p5,q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11

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.

{q10,q9,q8,q7,q5,q4,q3,q2,q1,p4,p2,p1}
{p5}
{q6,q5,q4,q3,q2,q1}
{q11,q10,q9,q8,q7}
{p3,p2,p1}

Equations

All comma separated 40 expressions involving 134 terms have to vanish.

p1*q7,
q4 - q9,
q2 + q4,
q2 - q8,
p2*q10,
q11 - q6,
q5*(p2 - 2*p4),
q2 + 3*q4 - q7,
q10 - 3*q2 - q4,
2*(p1*q2 - 1/2*p2*q7),
p3*q10 - p5*q5,
p3*q7 - p5*q1,
p2*q7 - 2*p4*q8,
5*(p2*q6 - 2/5*p3*q10 - 3/5*p3*q8),
5*(p1*q6 - 2/5*p3*q7 - 3/5*p3*q9),
p1*q10 - p1*q4 - p2*q4,
p2*q3 - 3*p4*q3 - 2*p4*q5,
p1*q3 - 2*p4*q1 - p4*q3,
p1*q10 + p1*q9 + p2*q9,
p2*q10 + p2*q8 + p4*q8,
p1*q11 - p1*q6 - p3*q4 + p3*q9,
5*(p2*q6 - 4/5*p3*q10 - 1/5*p3*q8 + 1/5*p5*q3),
10*(p2*q6 - 3/5*p3*q10 - 2/5*p3*q8 + 1/10*p5*q1),
5*(p2*q6 - 1/5*p3*q10 + 1/5*p3*q4 - 4/5*p3*q8),
p2*q11 - p2*q6 - p3*q2 + p3*q8,
5*(p1*q6 + 1/5*p3*q2 - 1/5*p3*q7 - 4/5*p3*q9),
10*(p1*q6 - 3/5*p3*q7 - 2/5*p3*q9 + 1/10*p5*q5),
5*(p1*q6 - 4/5*p3*q7 - 1/5*p3*q9 + 1/5*p5*q3),
p1*q2 - p2*q10 + p2*q2 - p2*q7,
p3*q8 + 5*p4*q11 - p5*q3 - 3*p5*q5,
10*(p4*q11 - 1/10*p5*q1 - 3/10*p5*q3 - 3/10*p5*q5),
10*(p4*q11 - 3/10*p5*q1 - 3/10*p5*q3 - 1/10*p5*q5),
p3*q9 + 5*p4*q11 - 3*p5*q1 - p5*q3,
p1*q7 + p1*q8 + p2*q7 - p4*q8,
p1*q3 - p1*q5 - p4*q1 + p4*q3 - p4*q5,
p1*q2 + p2*q10 - p2*q2 + p2*q4 - p2*q9,
p1*q1 + p1*q5 + p2*q1 - 3*p4*q1 - p4*q5,
p1*q7 - p1*q9 - p2*q7 + 2*p4*q10 - p4*q9,
p1*q10 + p1*q7 + p2*q7 - p4*q10 - p4*q7,
p1*q2 - p1*q8 + p2*q2 + p2*q4 - p2*q8 - p2*q9

Computing time