{VERSION 5 0 "IBM INTEL NT" "5.0" }
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6703 "s := array(1..7, [
]):  G := array(1..7, []):  L := array(1..7, []):\n\ns[1] := 1:       \+
s[2] := a:       s[3] := sqrt(a^2 - 2*a*c + 1):\ns[4] := 1:       s[5]
 := a:       s[6] := s[3]:           s[7] := 1:\nG[1] := 1:       G[2]
 := c:       G[3] := (a*c - 1)/s[3]:\nG[4] := -1:      G[5] := -c:    \+
  G[6] := - G[3]:         G[7] := 1:\nL[1] := 0:       L[2] := t:     \+
  L[3] := (a*t)/s[3]:\nL[4] := 0:       L[5] := -t:      L[6] := - L[3
]:         L[7] := 0:\n\nF1d1F1d1 := array(1..6, []):      F2d1F2d1 :=
 array(1..6, []):\nF1d1F2d1 := array(1..6, []):      F1d1F1d2 := array
(1..6, []):\nF1d1F2d2 := array(1..6, []):      F1d2F2d1 := array(1..6,
 []):\nF2d1F2d2 := array(1..6, []):      F1d1F3d1 := array(1..6, []):
\nF1d1F4d1 := array(1..6, []):      F2d1F3d1 := array(1..6, []):\nF1d1
F3d2 := array(1..6, []):      F1d2F3d1 := array(1..6, []):\nF1d1F4d2 :
= array(1..6, []):      F1d2F4d1 := array(1..6, []):\nF2d1F3d2 := arra
y(1..6, []):      F2d2F3d1 := array(1..6, []):\n\nfor i from 1 to 6 do
 \nF1d1F1d1[i] := G[i]*G[i]*g11 + 2*G[i]*L[i]*g12 + L[i]*L[i]*g22:\n\n
F2d1F2d1[i] := G[i]^4*g1111 + 4*G[i]^2*L[i]^2*g1212 + L[i]^4*g2222 + 4
*G[i]^3*L[i]*g1112 + 2*G[i]^2*L[i]^2*g1122 + 4*G[i]*L[i]^3*g1222:\n\nF
1d1F2d1[i] := G[i]^3*g111 + 2*G[i]^2*L[i]*g112 + G[i]*L[i]^2*g122 + G[
i]^2*L[i]*g211 + 2*G[i]*L[i]^2*g212 + L[i]^3*g222:\n\nF1d1F1d2[i] := G
[i]*G[i+1]*g11 +  G[i]*L[i+1]*g12 + G[i+1]*L[i]*g12+  L[i]*L[i+1]*g22:
\n\nF1d1F2d2[i] := G[i]*G[i+1]^2*g111 + 2*G[i]*G[i+1]*L[i+1]*g112 + G[
i]*L[i+1]^2*g122 + G[i+1]^2*L[i]*g211 + 2*G[i+1]*L[i]*L[i+1]*g212 + L[
i]*L[i+1]^2*g222:\n\nF1d2F2d1[i] := G[i+1]*G[i]^2*g111 + 2*G[i+1]*G[i]
*L[i]*g112 + G[i+1]*L[i]^2*g122 + G[i]^2*L[i+1]*g211 + 2*G[i]*L[i+1]*L
[i]*g212 + L[i+1]*L[i]^2*g222:\n\nF2d1F2d2[i] := G[i]^2*G[i+1]^2*g1111
 + 4*G[i]*G[i+1]*L[i]*L[i+1]*g1212 + L[i]^2*L[i+1]^2*g2222 + 2*G[i]^2*
G[i+1]*L[i+1]*g1112 + 2*G[i+1]^2*G[i]*L[i]*g1112+  G[i]^2*L[i+1]^2*g11
22 + G[i+1]^2*L[i]^2*g1122 + 2*G[i]*L[i]*L[i+1]^2*g1222 + 2*G[i+1]*L[i
+1]*L[i]^2*g1222:\n\nF1d1F3d1[i] := G[i]^4*e1111 + 3*G[i]^3*L[i]*e1112
 + 3*G[i]^2*L[i]^2*e1122 +  G[i]*L[i]^3*e1222 + G[i]^3*L[i]*e2111 + 3*
G[i]^2*L[i]^2*e2112 + 3*G[i]*L[i]^3*e2122 +  L[i]^4*e2222:\n\nF1d1F4d1
[i] := G[i]^5*e11111 + 4*G[i]^4*L[i]*e11112 + 6*G[i]^3*L[i]^2*e11122 +
 4*G[i]^2*L[i]^3*e11222 + G[i]*L[i]^4*e12222 + G[i]^4*L[i]*e21111 + 4*
G[i]^3*L[i]^2*e21112 + 6*G[i]^2*L[i]^3*e21122 + 4*G[i]*L[i]^4*e21222 +
 L[i]^5*e22222:\n\nF2d1F3d1[i] := G[i]^5*f11111 + 3*G[i]^4*L[i]*f11112
 + 3*G[i]^3*L[i]^2*f11122 +  G[i]^2*L[i]^3*f11222 +2*G[i]^4*L[i]*f1211
1 + 6*G[i]^3*L[i]^2*f12112 + 6*G[i]^2*L[i]^3*f12122 +  2*G[i]*L[i]^4*f
12222 + G[i]^3*L[i]^2*f22111 + 3*G[i]^2*L[i]^3*f22112 + 3*G[i]*L[i]^4*
f22122 +  L[i]^5*f22222:\n\nF1d1F3d2[i] := G[i]*G[i+1]^3*e1111 + 3*G[i
]*G[i+1]^2*L[i+1]*e1112 + 3*G[i]*G[i+1]*L[i+1]^2*e1122 +  G[i]*L[i+1]^
3*e1222 +  G[i+1]^3*L[i]*e2111 + 3*G[i+1]^2*L[i]*L[i+1]*e2112 + 3*G[i+
1]*L[i]*L[i+1]^2*e2122 +  L[i+1]^3*L[i]*e2222:\n\nF1d2F3d1[i] := G[i+1
]*G[i]^3*e1111 + 3*G[i+1]*G[i]^2*L[i]*e1112 + 3*G[i+1]*G[i]*L[i]^2*e11
22 +  G[i+1]*L[i]^3*e1222 +  G[i]^3*L[i+1]*e2111 + 3*G[i]^2*L[i+1]*L[i
]*e2112 + 3*G[i]*L[i+1]*L[i]^2*e2122 +  L[i]^3*L[i+1]*e2222:\n\nF1d1F4
d2[i] := G[i]*G[i+1]^4*e11111 + 4*G[i]*G[i+1]^3*L[i+1]*e11112 + 6*G[i]
*G[i+1]^2*L[i+1]^2*e11122 + 4*G[i]*G[i+1]*L[i+1]^3*e11222 + G[i]*L[i+1
]^4*e12222 +  G[i+1]^4*L[i]*e21111 + 4*G[i+1]^3*L[i]*L[i+1]*e21112 + 6
*G[i+1]^2*L[i+1]^2*L[i]*e21122 + 4*G[i+1]*L[i+1]^3*L[i]*e21222 + L[i+1
]^4*L[i]*e22222:\n\nF1d2F4d1[i] := G[i+1]*G[i]^4*e11111 + 4*G[i+1]*G[i
]^3*L[i]*e11112 + 6*G[i+1]*G[i]^2*L[i]^2*e11122 + 4*G[i]*G[i+1]*L[i]^3
*e11222 + G[i+1]*L[i]^4*e12222 +  G[i]^4*L[i+1]*e21111 + 4*G[i]^3*L[i]
*L[i+1]*e21112 + 6*G[i]^2*L[i]^2*L[i+1]*e21122 + 4*G[i]*L[i]^3*L[i+1]*
e21222 + L[i]^4*L[i+1]*e22222:\n\nF2d1F3d2[i] := G[i]^2*G[i+1]^3*f1111
1 + 3*G[i]^2*G[i+1]^2*L[i+1]*f11112 + 3*G[i]^2*G[i+1]*L[i+1]^2*f11122 \+
+  G[i]^2*L[i+1]^3*f11222 +2*G[i]*G[i+1]^3*L[i]*f12111 + 6*G[i]*G[i+1]
^2*L[i]*L[i+1]*f12112 + 6*G[i]*G[i+1]*L[i]*L[i+1]^2*f12122 +  2*G[i]*L
[i]*L[i+1]^3*f12222 + G[i+1]^3*L[i]^2*f22111 + 3*G[i+1]^2*L[i]^2*L[i+1
]*f22112 + 3*G[i+1]*L[i]^2*L[i+1]^2*f22122 +  L[i]^2*L[i+1]^3*f22222:
\n\nF2d2F3d1[i] := G[i+1]^2*G[i]^3*f11111 + 3*G[i+1]^2*G[i]^2*L[i]*f11
112 + 3*G[i+1]^2*G[i]*L[i]^2*f11122 +  G[i+1]^2*L[i]^3*f11222 +2*G[i+1
]*G[i]^3*L[i+1]*f12111 + 6*G[i+1]*G[i]^2*L[i]*L[i+1]*f12112 + 6*G[i]*G
[i+1]*L[i+1]*L[i]^2*f12122 +  2*G[i+1]*L[i+1]*L[i]^3*f12222 + G[i]^3*L
[i+1]^2*f22111 + 3*G[i]^2*L[i+1]^2*L[i]*f22112 + 3*G[i]*L[i]^2*L[i+1]^
2*f22122 +  L[i+1]^2*L[i]^3*f22222:\nod:\n\nP1P1 := array(1..6, []):  \+
  P1P2 := array(1..6, []):\nfor i from 1 to 6 do \nP1P1[i] := s[i]^2*F
1d1F1d1[i] + s[i]^3*x*F1d1F2d1[i] + 1/4*s[i]^4*x^2*F2d1F2d1[i] + 1/3*s
[i]^4*x^2*F1d1F3d1[i] + 1/6*s[i]^5*x^3*F2d1F3d1[i] + 1/12*s[i]^5*x^3*F
1d1F4d1[i]:\n\nP1P2[i] := s[i]*s[i+1]*F1d1F1d2[i] + 1/2*s[i]*s[i+1]^2*
x*F1d1F2d2[i] + 1/2*s[i+1]*s[i]^2*x*F1d2F2d1[i] + 1/6*s[i]*s[i+1]^3*x^
2*F1d1F3d2[i] + 1/6*s[i+1]*s[i]^3*x^2*F1d2F3d1[i] + 1/4*s[i]^2*s[i+1]^
2*x^2*F2d1F2d2[i] + 1/24*s[i]*s[i+1]^4*x^3*F1d1F4d2[i] + 1/24*s[i+1]*s
[i]^4*x^3*F1d2F4d1[i] + 1/12*s[i]^2*s[i+1]^3*x^3*F2d1F3d2 [i]+ 1/12*s[
i+1]^2*s[i]^3*x^3*F2d2F3d1[i]:\nod:\n\nCos1 := mtaylor(simplify(P1P2[1
]) , x=0, 4):   Cos2 := mtaylor(simplify(P1P2[2]) , x=0, 4):\nCos3 := \+
mtaylor(simplify(P1P2[3]) , x=0, 4):   Cos4 := mtaylor(simplify(P1P2[4
]) , x=0, 4):\nCos5 := mtaylor(simplify(P1P2[5]) , x=0, 4):   Cos6 := \+
mtaylor(simplify(P1P2[6]) , x=0, 4):\n\nSn1:= sqrt(normal(P1P1[1]*P1P1
[2] - P1P2[1]^2)):\nSn2:= sqrt(normal(P1P1[2]*P1P1[3] - P1P2[2]^2)):\n
Sn3:= sqrt(normal(P1P1[3]*P1P1[4] - P1P2[3]^2)):\nSn4:= sqrt(normal(P1
P1[4]*P1P1[5] - P1P2[4]^2)):\nSn5:= sqrt(normal(P1P1[5]*P1P1[6] - P1P2
[5]^2)):\nSn6:= sqrt(normal(P1P1[6]*P1P1[1] - P1P2[6]^2)):\n\nSin1:=mt
aylor(Sn1, x=0, 4):   Sin2:=mtaylor(Sn2, x=0, 4):\nSin3:=mtaylor(Sn3, \+
x=0, 4):   Sin4:=mtaylor(Sn4, x=0, 4):\nSin5:=mtaylor(Sn5, x=0, 4):   \+
Sin6:=mtaylor(Sn6, x=0, 4):\n\n\nCt1:=Cos1/Sin1:Ct2:=Cos2/Sin2:Ct3:=Co
s3/Sin3:Ct4:=Cos4/Sin4:Ct5:=Cos5/Sin5:Ct6:=Cos6/Sin6:\n\nCot1:=mtaylor
(Ct1, x=0, 4):   Cot2:=mtaylor(Ct2, x=0, 4):\nCot3:=mtaylor(Ct3, x=0, \+
4):   Cot4:=mtaylor(Ct4, x=0, 4):\nCot5:=mtaylor(Ct5, x=0, 4):   Cot6:
=mtaylor(Ct6, x=0, 4):\nL1:=mtaylor(P1P1[1]+P1P1[2]-2*P1P2[1],x=0,4); \+
L2:=mtaylor(P1P1[2]+P1P1[3]-2*P1P2[2],x=0,4);\nL3:=mtaylor(P1P1[3]+P1P
1[4]-2*P1P2[3],x=0,4); L4:=mtaylor(P1P1[4]+P1P1[5]-2*P1P2[4],x=0,4);\n
L5:=mtaylor(P1P1[5]+P1P1[6]-2*P1P2[5],x=0,4); L6:=mtaylor(P1P1[6]+P1P1
[1]-2*P1P2[6],x=0,4);\n\nArea2 :=1/2*(Sin1 + Sin2 + Sin3 + Sin4 + Sin5
 + Sin6):\n\na0 := simplify(tcoeff(Area2,x));           a1 := simplify
(coeff(Area2,x));\nSumCot:=Cot1*L1+Cot2*L2+Cot3*L3+Cot4*L4+Cot5*L5+Cot
6*L6:\nSumAreaCot:=1/2*Area2-1/8*SumCot:\nb0 := simplify(tcoeff(SumAre
aCot,x));           b1 := simplify(coeff(SumAreaCot,x));" }}{PARA 12 "
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{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a0G,$*$-%%sqrtG6#*(
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.\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a1G\"\"!" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#b0G**%\"tG\"\"#,&*$)%$g12GF'\"\"\"!\"\"*&%$g22G
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{XPPMATH 20 "6#>%#b1G\"\"!" }}}{PARA 12 "" 1 "" {TEXT -1 0 "" }}
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