# Question:Understanding the simplify function - different options ?

## Question:Understanding the simplify function - different options ?

Maple

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 ?

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