Solution 2 to problem N2f1b0o35w7
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N2f1b0o35w7
Expressions
The solution is given through the following expressions:
q6= - i*q4
q5=q4
q3=i*q4
q2=0
q1=0
p2=i*p1
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
q8, q7, q4, p1
Inequalities
In the following not identically vanishing expressions are shown.
Any auxiliary variables g00?? are used to express that at least
one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3
means that either p4 or p3 or both are non-vanishing.
{q3,
q4,
p1,
g0011*q7 - g0012*i*q4 + g0013*q4 + g0014*i*q4 + g0016*p1,
p2,
g0005*q7 + g0006*q4 + g0007*q4 + g0008*i*q4 + g0010*p1}
Relevance for the application:
The equation:
f =D D f *p1 + f *i*p1
t 1 2 2x 3x
The symmetry:
f =D f*D D f*i*q4 + D f*f *q4 + D D f *q7 + D D f*D f*q4 - D f*f *i*q4 + f *q8
s 2 1 2 2 x 1 2 4x 1 2 1 1 x 5x
And now in machine readable form:
The system:
df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p1 + df(f(1),x,3)*i*p1$
The symmetry:
df(f(1),s)=d(2,f(1))*d(1,d(2,f(1)))*i*q4 + d(2,f(1))*df(f(1),x)*q4 + d(1,d(2,df(
f(1),x,4)))*q7 + d(1,d(2,f(1)))*d(1,f(1))*q4 - d(1,f(1))*df(f(1),x)*i*q4 + df(f(
1),x,5)*q8$