Please help me to make sense of the ways to use the simplify function. In this particular case Maple does some computation and gives me some huge output which I paste below. When I try to simplify the huge output Maple just hangs. But if I use varied commands of simplify detailed below such as simplify(huge_output,symbolic) or simplify(huge_output,size) Maple gives me an output but none of the output are equal to each other and I also noticed that in one instance where I had an output for the command simplify(huge_output) on its own the value was different to when I used for example simplify(huge_output,symbolic).
So my request is would someone kindly say what the difference between these varied forms of the simplify command are
- Simplify(expression)
- Simplify(expression, symbolic)
- Simplify(expression, size)
- Simplify(expression, symbolic,size)
And which output should I ‘trust’. As I said I noticed in one instance (for a different output) that the value of simplify(expression) was different to simplify(expression,symbolic).
If I can’t get simplify(expression) to work on its own and I use simplify(expression,symbolic) for instance is it the case that I might get a wrong answer and if so how do I then get maple to stop hanging when using simplify (expression) on its own?
I paste what I tried below. This is my output that I want to simplify in the first place
huge_output := 1/4*2^(1/2)*exp(-1/2*x^2/sigma^2)*(1/4*Pi*(exp(-1\
/2*sigma^2*k^2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2\
+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+exp(-1/2*sigma^2*k^2)*beta*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)-2*I*Pi*exp(-1/2*sigma^2*k^2)*((-4*Pi^2-beta^2+4*beta^2*Q^2\
*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2*\
I*Pi*exp(-1/2*sigma^2*k^2)*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(\
4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*Q*Pi*exp(-1/2*sigma^2*k^\
2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*bet\
a^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*Q*Pi*exp(-1/2*sigma^2*k^2)*beta*((-4*Pi^2-b\
eta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q\
^2*Pi^2))^(1/2)+2*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi\
^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q*Pi+2*beta*((-4*Pi^2-beta^2+4\
*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2\
))^(1/2)*Q*Pi-beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+b\
eta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-beta*((-4*Pi^2-beta^2+4*beta^2*Q^2\
*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*\
I*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*\
Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi+2*I*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi)*(4*Pi^2+beta^\
2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2)^2*t*(1+2*Q*cos(k*psi)*Pi)*(-4*Pi^2*Q*beta*((-\
4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*\
beta^2*Q^2*Pi^2))^(1/2)+4*Pi^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*\
Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta*Q+4*I*Pi^2*((-4*P\
i^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*bet\
a^2*Q^2*Pi^2))^(1/2)+4*I*Pi^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q\
)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*I*Pi*((-4*Pi^2-beta^2\
+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi\
^2))^(1/2)*beta^2*Q-2*I*Pi*Q*beta^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+I*beta^2*((-4*Pi^\
2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^\
2*Q^2*Pi^2))^(1/2)+I*beta^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/\
(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2))/(beta^4*(-2*Q*beta*Pi+be\
ta+2*I*Pi)^2*(4*Pi^2+beta^2-4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)*(2*Q*beta*Pi-beta\
+2*I*Pi)^2*(-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q))+1/2*Q*cos(k*psi)*\
Pi^3*(-exp(-1/2*sigma^2*k^2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*be\
ta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-exp(-1/2*sigma^2*k^\
2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*bet\
a^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2*I*Pi*exp(-1/2*sigma^2*k^2)*((-4*Pi^2-beta^2\
+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi\
^2))^(1/2)-2*I*Pi*exp(-1/2*sigma^2*k^2)*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*P\
i^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2*Q*Pi*exp(-1\
/2*sigma^2*k^2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2\
+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2*Q*Pi*exp(-1/2*sigma^2*k^2)*bet\
a*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*\
Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q*Pi-2*beta*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)*Q*Pi+beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta\
*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+beta*((-4*Pi^2-beta^2\
+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi\
^2))^(1/2)+2*I*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^\
2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi-2*I*((-4*Pi^2-beta^2+4*beta^2*Q^2*P\
i^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi)*\
(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2)^2*t*(2*beta*((-4*Pi^2-beta^2+4*b\
eta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))\
^(1/2)*Q*Pi+2*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+b\
eta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q*Pi-beta*((-4*Pi^2-beta^2+4*beta^\
2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/\
2)-beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*bet\
a^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*I*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi\
^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi+2*I*((-4*Pi\
^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta\
^2*Q^2*Pi^2))^(1/2)*Pi)/(beta^4*(2*Q*beta*Pi-beta-2*I*Pi)^2*(-4*Pi^2-beta^2+4*be\
ta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)*(2*Q*beta*Pi-beta+2*I*Pi)^2*(-4*Pi^2-beta^2+4*bet\
a^2*Q^2*Pi^2+8*I*Pi^2*beta*Q))+1/2*I*Pi*(-exp(-1/2*sigma^2*k^2)*beta*((-4*Pi^2-b\
eta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q\
^2*Pi^2))^(1/2)-exp(-1/2*sigma^2*k^2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*\
I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2*I*Pi*exp\
(-1/2*sigma^2*k^2)*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+b\
eta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*I*Pi*exp(-1/2*sigma^2*k^2)*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)+2*Q*Pi*exp(-1/2*sigma^2*k^2)*beta*((-4*Pi^2-beta^2+4*beta^\
2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/\
2)+2*Q*Pi*exp(-1/2*sigma^2*k^2)*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2\
*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2*beta*((-4*Pi^2\
-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2\
*Q^2*Pi^2))^(1/2)*Q*Pi-2*beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q\
)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q*Pi+beta*((-4*Pi^2-bet\
a^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2\
*Pi^2))^(1/2)+beta*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+b\
eta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2*I*((-4*Pi^2-beta^2+4*beta^2*Q^2*\
Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi-\
2*I*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*\
Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi)*t*(1+2*Q*cos(k*psi)*Pi)*(27648*Pi^10*((-4*Pi^\
2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^\
2*Q^2*Pi^2))^(1/2)*beta^4*Q^2-1280*beta^10*Q^6*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^\
2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+6\
144*beta^10*Q^8*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^\
2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+4480*I*Pi^7*((-4*Pi^2-beta^2+4*\
beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2)\
)^(1/2)*beta^11*Q^6-9216*I*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*bet\
a*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^3*Q^2+43008*Pi^\
10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q\
*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^8*Q^6-17408*I*Pi^11*((-4*Pi^2-beta^2+4*beta^2\
*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2\
)*beta^11*Q^10+6400*Pi^7*beta^6*Q*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*be\
ta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+12800*Pi^9*beta^4*Q\
*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*P\
i+4*beta^2*Q^2*Pi^2))^(1/2)+10*beta^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi\
^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi*Q+2048*beta\
^10*Pi^9*Q^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-\
4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+1280*beta^10*Pi^8*Q^6*((-4*Pi^2-beta^2+4\
*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2\
))^(1/2)+2560*beta^10*Pi^6*Q^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*\
Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+10240*Pi^11*beta^10*Q^\
9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*\
Pi+4*beta^2*Q^2*Pi^2))^(1/2)-49152*Pi^12*beta^4*Q^4*((-4*Pi^2-beta^2+4*beta^2*Q^\
2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-5\
3248*Pi^12*beta^6*Q^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^\
2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-896*beta^12*Q^6*Pi^6*((-4*Pi^2-\
beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*\
Q^2*Pi^2))^(1/2)+26624*Pi^9*beta^6*Q^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi\
^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+5120*beta^12*Q\
^10*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*b\
eta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-3584*beta^12*Q^9*Pi^9*((-4*Pi^2-beta^2+4*be\
ta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^\
(1/2)-1280*beta^12*Q^8*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/\
(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+53248*Pi^11*beta^8*Q^7*((\
-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4\
*beta^2*Q^2*Pi^2))^(1/2)-43008*Pi^10*beta^8*Q^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi\
^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-53248\
*Pi^10*beta^6*Q^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+be\
ta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-5632*Pi^8*beta^8*Q^4*((-4*Pi^2-beta\
^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*\
Pi^2))^(1/2)+77824*Pi^11*beta^6*Q^5*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+47104*Pi^11*beta^\
4*Q^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^\
2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-28672*Pi^12*beta^8*Q^8*((-4*Pi^2-beta^2+4*beta^\
2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/\
2)-6144*Pi^12*beta^10*Q^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(\
4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-448*beta^12*Q^5*Pi^5*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)-61440*I*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9*Q^8+3840*b\
eta^10*Q^5*Pi^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta\
^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+80*I*Pi^4*((-4*Pi^2-beta^2+4*beta^2*Q\
^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*\
beta^9*Q-4096*I*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2\
+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^8+640*I*Pi^6*((-4*Pi^2\
-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2\
*Q^2*Pi^2))^(1/2)*beta^7*Q-384*I*Pi^5*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^\
2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^4-768\
*I*Pi^5*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*bet\
a^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9*Q^2-16384*I*Pi^9*((-4*Pi^2-beta^2+4*be\
ta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^\
(1/2)*beta^7*Q^4+49152*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*\
Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^5*Q^5-79872*I*Pi^\
11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q\
*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^7*Q^6+448*beta^12*((-4*Pi^2-beta^2+4*beta^2*Q\
^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*\
Q^5*Pi^5-4096*I*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2\
+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^8+22528*I*Pi^12*((-4*P\
i^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*bet\
a^2*Q^2*Pi^2))^(1/2)*beta^3*Q^3-896*I*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*\
I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^\
5+896*beta^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2\
-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^6*Pi^6+2560*I*Pi^6*((-4*Pi^2-beta^2+4\
*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2\
))^(1/2)*Q^3*beta^9+9984*I*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta\
*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^7*Q^3-10*beta^12\
*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*P\
i+4*beta^2*Q^2*Pi^2))^(1/2)*Q*Pi+45056*I*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^\
2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9\
*Q^7+20480*I*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+b\
eta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^5*Q^3+504*beta^10*((-4*Pi^2-b\
eta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q\
^2*Pi^2))^(1/2)*Pi^4*Q^2-2816*I*Pi^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2\
*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9*Q^4-((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)*beta^12+17408*I*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8\
*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q\
^9+beta^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*\
beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+248*I*Pi^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*P\
i^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta\
^11*Q^3-1280*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+be\
ta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^6-6144*Pi^10*((-4*Pi^2-beta^2+\
4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^\
2))^(1/2)*beta^2-24*Pi^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*\
Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^10-3840*Pi^8*((-4*Pi^2-\
beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*\
Q^2*Pi^2))^(1/2)*beta^4-240*Pi^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*bet\
a*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^8-4224*I*Pi^7*(\
(-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+\
4*beta^2*Q^2*Pi^2))^(1/2)*Q^2*beta^7-10240*I*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*\
Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*bet\
a^9*Q^6+6144*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2\
+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^11*beta^11+53248*I*Pi^12*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)*Q^7*beta^7+53248*Pi^12*beta^6*Q^6*((-4*Pi^2-beta^2+4*beta^\
2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/\
2)+40*beta^12*Q^3*Pi^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi\
^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+4*I*Pi^2*((-4*Pi^2-beta^2+4*be\
ta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^\
(1/2)*beta^11*Q-10240*I*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)\
/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^2*beta^5+22528*I*Pi^12\
*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*P\
i+4*beta^2*Q^2*Pi^2))^(1/2)*Q^3*beta^3+80*I*Pi^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*P\
i^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta\
^9*Q+4096*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta\
^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+28*beta^12*((-4*Pi^2-beta^2+4*beta^2*\
Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)\
*Q^2*Pi^2-352*beta^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^\
2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^4*Pi^4+5632*beta^8*Pi^8*Q^4*(\
(-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+\
4*beta^2*Q^2*Pi^2))^(1/2)-2560*beta^10*Pi^6*Q^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi\
^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-79872\
*I*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*be\
ta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^6*beta^7-61440*I*Pi^11*((-4*Pi^2-beta^2+4*\
beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2)\
)^(1/2)*Q^8*beta^9-9216*I*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta\
*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^2*beta^3-17408*I*Pi\
^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*\
Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^10*beta^11-45056*I*Pi^11*((-4*Pi^2-beta^2+4*bet\
a^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(\
1/2)*Q^4*beta^5-4096*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(\
4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+3712*Pi^6*((-4*Pi^2-beta^2\
+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi\
^2))^(1/2)*beta^8*Q^2-3840*Pi^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta\
*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^8*Q^3+45056*I*Pi\
^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*\
Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9*Q^7+49152*I*Pi^12*((-4*Pi^2-beta^2+4*beta^\
2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/\
2)*Q^5*beta^5-19456*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*\
Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^8*Q^5+2560*I*Pi^8*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)*beta^5*Q-896*I*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I\
*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^5\
-200*beta^10*Pi^3*Q*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+\
beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-10240*I*Pi^9*((-4*Pi^2-beta^2+4*b\
eta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))\
^(1/2)*beta^9*Q^6+128*beta^10*Pi^5*Q^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi\
^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-16384*I*Pi^9*(\
(-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+\
4*beta^2*Q^2*Pi^2))^(1/2)*beta^7*Q^4-53248*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*P\
i^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta\
^8*Q^7-1600*beta^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+b\
eta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi^5*Q-4224*I*Pi^7*((-4*Pi^2-beta^\
2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*P\
i^2))^(1/2)*beta^7*Q^2+6144*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^11*beta^11+24*b\
eta^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta\
^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi^2-45056*I*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q\
^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*\
beta^5*Q^4+17408*I*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*\
Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^9*beta^11+20480*I*Pi^10*((\
-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4\
*beta^2*Q^2*Pi^2))^(1/2)*beta^5*Q^3+53248*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*\
Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^7\
*beta^7+28672*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^\
2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^9*beta^9+14080*beta^6*Pi^8*Q^\
2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*\
Pi+4*beta^2*Q^2*Pi^2))^(1/2)+1280*beta^12*Q^8*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^2\
*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+25\
60*I*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*b\
eta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9*Q^3+53248*Pi^10*beta^6*Q^4*((-4*Pi^2\
-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2\
*Q^2*Pi^2))^(1/2)+2048*beta^12*Q^11*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I\
*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-52*I*Pi^3*(\
(-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+\
4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^2-12800*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*P\
i^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta\
^4*Q-6400*Pi^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^\
2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^6*Q+6144*Pi^10*((-4*Pi^2-beta^2+4\
*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2\
))^(1/2)*beta^2-5120*beta^12*Q^10*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*P\
i^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+3840*Pi^8*((-\
4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*\
beta^2*Q^2*Pi^2))^(1/2)*beta^4+1280*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*\
Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^6-2816*\
beta^12*Q^7*Pi^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+bet\
a^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-2048*beta^10*Q^7*Pi^9*((-4*Pi^2-beta\
^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*\
Pi^2))^(1/2)+28672*beta^8*Q^8*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*\
beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+6144*beta^10*Q^10\
*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta\
^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-5376*I*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2\
+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11\
*Q^7+4*I*Pi^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2\
-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q+22528*Pi^12*beta^2*Q^2*((-4*P\
i^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*bet\
a^2*Q^2*Pi^2))^(1/2)+49152*Pi^12*beta^4*Q^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8\
*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+5120*I*Pi\
^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*\
Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^3*Q+43008*I*Pi^10*((-4*Pi^2-beta^2+4*beta^2*\
Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)\
*Q^5*beta^7+240*beta^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi\
^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi^4+4480*I*Pi^7*((-4*Pi^2-bet\
a^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2\
*Pi^2))^(1/2)*Q^6*beta^11-2816*I*Pi^7*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^\
2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^9*Q^4+4300\
8*I*Pi^10*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*b\
eta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^7*Q^5-768*I*Pi^5*((-4*Pi^2-beta^2+4*be\
ta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^\
(1/2)*beta^9*Q^2-26624*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/\
(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^6*Q^3+3584*beta^12*Q\
^9*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*bet\
a^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+248*I*Pi^4*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2\
-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11\
*Q^3-10240*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+bet\
a^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^2*Q-77824*Pi^11*((-4*Pi^2-beta^\
2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*P\
i^2))^(1/2)*beta^6*Q^5-47104*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*b\
eta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^4*Q^3-10240*I\
*Pi^9*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^\
2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^5*Q^2-10240*beta^10*Q^9*Pi^11*((-4*Pi^2-be\
ta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^\
2*Pi^2))^(1/2)-52*I*Pi^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*\
Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^2+5120*I*Pi^10*((-\
4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*\
beta^2*Q^2*Pi^2))^(1/2)*beta^3*Q+4096*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2\
-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta*Q+\
640*I*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*\
beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^7*Q+19456*Pi^9*beta^8*Q^5*((-4*Pi^2-b\
eta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q\
^2*Pi^2))^(1/2)-14080*Pi^8*beta^6*Q^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^\
2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-504*Pi^4*beta^1\
0*Q^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^\
2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-3840*Pi^7*beta^10*Q^5*((-4*Pi^2-beta^2+4*beta^2\
*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2\
)-2048*beta^12*Q^11*Pi^11*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4\
*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+2816*beta^12*Pi^7*Q^7*((-4*\
Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*be\
ta^2*Q^2*Pi^2))^(1/2)-28*beta^12*Pi^2*Q^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I\
*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-3712*beta^8\
*Q^2*Pi^6*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*b\
eta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-6144*Pi^10*beta^10*Q^8*((-4*Pi^2-beta^2+4*b\
eta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))\
^(1/2)+1600*Pi^5*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+bet\
a^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^8*Q+3840*Pi^7*beta^8*Q^3*((-4*P\
i^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*bet\
a^2*Q^2*Pi^2))^(1/2)+10240*Pi^11*beta^2*Q*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I\
*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-27648*Pi^10\
*beta^4*Q^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4\
*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+352*beta^12*((-4*Pi^2-beta^2+4*beta^2*Q^2\
*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Pi\
^4*Q^4+200*Pi^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta\
^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^10*Q-128*beta^10*Pi^5*Q^3*((-4*P\
i^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*bet\
a^2*Q^2*Pi^2))^(1/2)-22528*Pi^12*beta^2*Q^2*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8\
*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)-40*beta^1\
2*Pi^3*Q^3*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*\
beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)+4096*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2\
*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q*\
beta-5376*I*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+bet\
a^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^11*Q^7-384*I*Pi^5*((-4*Pi^2-bet\
a^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2\
*Pi^2))^(1/2)*beta^11*Q^4+28672*I*Pi^12*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*P\
i^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*Q^9*beta^9+99\
84*I*Pi^8*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*b\
eta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^7*Q^3+2560*I*Pi^8*((-4*Pi^2-beta^2+4*b\
eta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))\
^(1/2)*beta^5*Q)/((2*Q*beta*Pi-beta-2*I*Pi)*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8\
*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*(2*Q*beta\
*Pi-beta+2*I*Pi)*((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+bet\
a^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2)*beta^4*(8*Pi^3*Q^3*beta^3+24*I*Pi^3*\
Q^2*beta^2-24*Pi^3*beta*Q-8*I*Pi^3-4*Pi^2*beta^3*Q^2-8*I*Pi^2*Q*beta^2+4*Pi^2*be\
ta-2*Pi*beta^3*Q-2*I*Pi*beta^2+beta^3)^2*(8*Pi^3*Q^3*beta^3-24*I*Pi^3*beta^2*Q^2\
-24*Pi^3*beta*Q+8*I*Pi^3-4*Pi^2*beta^3*Q^2+8*I*Pi^2*beta^2*Q+4*Pi^2*beta-2*Pi*be\
ta^3*Q+2*I*Pi*beta^2+beta^3)^2))/(Pi^(3/2)*sigma);
but when I try
simplify(huge_output) assuming k::posint;
maple just hangs. For the following maple gives an output for each attempt
with_symbolic:=simplify(huge_output,symbolic) assuming k::posint;
with_size:= simplify(huge_output,size) assuming k::posint;
with_symbolic_size:= simplify(huge_output,symbolic,size) assuming k::posint;
simplify(huge_output,symbolic) assuming k::posint;with_symbolic_then_size:=simplify(%,size) assuming k::posint;
But none of these values are equal to each other – I test it using verify function.
verify(with_symbolic,with_size);verify(with_symbolic,with_symbolic_size);verify(with_symbolic,with_symbolic_then_size); verify(with_size,with_symbolic_size);verify(with_size,with_symbolic_size);
verify(with_size,with_symbolic_size);verify(with_size,with_symbolic_then_size);verify(with_symbolic_size,with_symbolic_then_size);
So what’s the best way forward ?
