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MathGroup Archive 2007

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Interpreting the solutions... better this time

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75225] Interpreting the solutions... better this time
  • From: "Apostolos E. A. S. Evangelopoulos" <a.e.a.evangelopoulos at sms.ed.ac.uk>
  • Date: Sat, 21 Apr 2007 23:06:39 -0400 (EDT)

Right, here goes the whole thing again, since I didn't present it well last time...

So, what I'm trying to solve is

(8*Pi*R^3*S)/(3*h^2) + (2*h*Pi*(S + 3*\[Gamma]))/3 + 
 ((R^2*(-h + 2*R)^2*(-h/(2*R^2) - (2*R)/h^2))/
    (Sqrt[3]*Sqrt[R^2*(-h^2/(4*R^2) + (2*R)/h)]) - 
   (4*(-h + 2*R)*Sqrt[R^2*(-h^2/(4*R^2) + (2*R)/h)])/
    Sqrt[3] - (8*R*(-h + 2*R)*(-h/(2*R^2) - (2*R)/h^2)*
     Sqrt[R^2*(-h^2/(4*R^2) + (2*R)/h)])/(3*Sqrt[3]) + 
   (16*(R^2*(-h^2/(4*R^2) + (2*R)/h))^(3/2))/
    (9*Sqrt[3]*R) + (16*(-h/(2*R^2) - (2*R)/h^2)*
     (R^2*(-h^2/(4*R^2) + (2*R)/h))^(3/2))/
    (9*Sqrt[3]))*\[CapitalKappa] == 0

with respect to h.

What Mathematica returns is

{{h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 1]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 2]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 3]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 4]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 5]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 6]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 7]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 8]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 9]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 10]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 11]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 12]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 13]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 14]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 15]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 16]}, 
 {h -> Root[-32768*R^17*\[CapitalKappa]^2 + 81920*R^16*\[CapitalKappa]^2*#1 - 86016*R^15*\[CapitalKappa]^2*#1^2 + 6912*Pi^2*R^12*S^2*#1^3 + (3456*Pi^2*R^11*S^2 + 73600*R^13*\[CapitalKappa]^2)*#1^4 + 
      (1728*Pi^2*R^10*S^2 - 76608*R^12*\[CapitalKappa]^2)*#1^5 + (3456*Pi^2*R^9*S^2 + 10368*Pi^2*R^9*S*\[Gamma] + 40608*R^11*\[CapitalKappa]^2)*#1^6 + 
      (1728*Pi^2*R^8*S^2 + 5184*Pi^2*R^8*S*\[Gamma] - 18608*R^10*\[CapitalKappa]^2)*#1^7 + (864*Pi^2*R^7*S^2 + 2592*Pi^2*R^7*S*\[Gamma] - 224*R^9*\[CapitalKappa]^2)*#1^8 + 
      (432*Pi^2*R^6*S^2 + 2592*Pi^2*R^6*S*\[Gamma] + 3888*Pi^2*R^6*\[Gamma]^2 + 14896*R^8*\[CapitalKappa]^2)*#1^9 + 
      (216*Pi^2*R^5*S^2 + 1296*Pi^2*R^5*S*\[Gamma] + 1944*Pi^2*R^5*\[Gamma]^2 - 13456*R^7*\[CapitalKappa]^2)*#1^10 + 
      (108*Pi^2*R^4*S^2 + 648*Pi^2*R^4*S*\[Gamma] + 972*Pi^2*R^4*\[Gamma]^2 + 8028*R^6*\[CapitalKappa]^2)*#1^11 - 4494*R^5*\[CapitalKappa]^2*#1^12 + 1921*R^4*\[CapitalKappa]^2*#1^13 - 564*R^3*\[CapitalKappa]^2*#1^14 + 
      114*R^2*\[CapitalKappa]^2*#1^15 - 14*R*\[CapitalKappa]^2*#1^16 + \[CapitalKappa]^2*#1^17 & , 17]}}

I hope this is more readable, now, in spite of its size, as I've converted it to InputForm and copied it in plain text format (as kindly advised).

I do not understand the # symbols and I do not know what I'm supposed to do with this, generally. How can I further evaluate these 'Root[blah]' forms?

Many thanks,
Apostolos


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