-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathp=11 mod 12, n even, M not 1.txt
117 lines (41 loc) · 18.8 KB
/
p=11 mod 12, n even, M not 1.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
// p=11 mod 12
// n even
// Check on the software Mathematica
// "row C", for C a component of X_p, compute: \sum_{D component of X_p} (D.C)x_D - (constant term)
// The variables are the following:
// d:=d(M)
// einf:=\varepsilon_\infty(M)
// e2:=\varepsilon_2(M)
// e3:=\varepsilon_3(M)
/////////////////////////////////////////////
// check V_0
// row C_0
Simplify[(-d*p^(n-1)*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*p^(n-2*A)*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2-1}] + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2, n-1}] + (d*(p-1)/12-e3/3-e2/2)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(6*(n*(p-1)+6)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(2*(n*(p-1)+6)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2*(1+d*p^(n-1)*(p+1)/12-einf*p^((n-2)/2)*(p+1)/2)-(-d*p^(n-1)*(p-1)/12-e3/3-e2/2)]
// row C_a, 0<a<n/2
Simplify[(d*p^(n-2*a)*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*p^(n-2*a)*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, a-1}] + (-d*p^(n-2*a)/6-e2/2-e3/3)*(t*p^(a-1)*(p-1)+(6*(a*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(a*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))) + Sum[(d*p^(n-2*A)*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, a+1, n/2-1}] + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2, n-1}] + (d*(p-1)/12-e3/3-e2/2)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(6*(n*(p-1)+6)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(2*(n*(p-1)+6)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(n-2*a)/6-e2/2-e3/3)]
// row C_a, a=n/2
Simplify[(d*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2-1}] + (-d/6-e2/2-e3/3)*(t*p^(n/2-1)*(p-1)+(6*((n/2)*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n/2)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n/2-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2+1, n-1}] + (d*(p-1)/12-e3/3-e2/2)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(6*(n*(p-1)+6)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(2*(n*(p-1)+6)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d/6-e2/2-e3/3)]
// row C_a, n/2<a<n
Simplify[(d*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2}] + Sum[(d*p^(2*A-n)*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2+1, a-1}] + (-d*p^(2*a-n)/6-e2/2-e3/3)*(t*p^(n-a-1)*(p-1)+(6*(a*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-a)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))) + Sum[(d*p^(2*a-n)*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, a+1, n-1}] + (d*p^(2*a-n)*(p-1)/12-e3/3-e2/2)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(6*(n*(p-1)+6)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(2*(n*(p-1)+6)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(2*a-n)/6-e2/2-e3/3)]
// row C_n
Simplify[(d*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2}] + Sum[(d*p^(2*A-n)*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2+1, n-1}] + (-d*p^(n-1)*(p-1)/12-e3/3-e2/2)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(6*(n*(p-1)+6)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(2*(n*(p-1)+6)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(n-1)*(p-1)/12-e3/3-e2/2)]
// row E_\infty,
Simplify[t + Sum[t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, 1, n/2}] + Sum[t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, n/2+1, n-1}] + t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1)) + (-2)*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(6*(n*(p-1)+6)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + (-2-(-2))]
// row F_\infty
Simplify[t + Sum[t*p^(A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, 1, n/2}] + Sum[t*p^(n-A-1)*(p-1)+(6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, n/2+1, n-1}] + (t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + (-3)*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(2*(n*(p-1)+6)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + (-2-(-3))]
/////////////////////////////////////////////
// check V_\infty
// row C_0
Simplify[(-d*p^(n-1)*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*p^(n-2*A)*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2-1}] + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2, n-1}] + (d*(p-1)/12-e3/3-e2/2)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-6*(n*(p-1)-2)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-2*(n*(p-1)-2)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(n-1)*(p-1)/12-e3/3-e2/2)]
// row C_a, 0<a<n/2
Simplify[(d*p^(n-2*a)*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*p^(n-2*a)*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, a-1}] + (-d*p^(n-2*a)/6-e2/2-e3/3)*(t*p^(a-1)*(p-1)+(-6*(a*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(a*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))) + Sum[(d*p^(n-2*A)*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, a+1, n/2-1}] + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2, n-1}] + (d*(p-1)/12-e3/3-e2/2)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-6*(n*(p-1)-2)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-2*(n*(p-1)-2)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(n-2*a)/6-e2/2-e3/3)]
// row C_a, a=n/2
Simplify[(d*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2-1}] + (-d/6-e2/2-e3/3)*(t*p^(n/2-1)*(p-1)+(-6*((n/2)*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n/2)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n/2-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2+1, n-1}] + (d*(p-1)/12-e3/3-e2/2)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-6*(n*(p-1)-2)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-2*(n*(p-1)-2)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d/6-e2/2-e3/3)]
// row C_a, n/2<a<n
Simplify[(d*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2}] + Sum[(d*p^(2*A-n)*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2+1, a-1}] + (-d*p^(2*a-n)/6-e2/2-e3/3)*(t*p^(n-a-1)*(p-1)+(-6*(a*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-a)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))) + Sum[(d*p^(2*a-n)*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, a+1, n-1}] + (d*p^(2*a-n)*(p-1)/12-e3/3-e2/2)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-6*(n*(p-1)-2)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-2*(n*(p-1)-2)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(2*a-n)/6-e2/2-e3/3)]
// row C_n
Simplify[(d*(p-1)/12-e3/3-e2/2)*(t) + Sum[(d*(p-1)/12-e3/3-e2/2)*(t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, 1, n/2}] + Sum[(d*p^(2*A-n)*(p-1)/12-e3/3-e2/2)*(t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1))), {A, n/2+1, n-1}] + (-d*p^(n-1)*(p-1)/12-e3/3-e2/2)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-6*(n*(p-1)-2)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + e3*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-2*(n*(p-1)-2)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2*(1+d*p^(n-1)*(p+1)/12-einf*p^((n-2)/2)*(p+1)/2)-(-d*p^(n-1)*(p-1)/12-e3/3-e2/2)]
// row E_\infty,
Simplify[t + Sum[t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, 1, n/2}] + Sum[t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, n/2+1, n-1}] + t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1)) + (-2)*(t*p^((n-2)/2)*(p+1)/2+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-6*(n*(p-1)-2)+(-3*(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(2*p^(n-1)*(p+1)*d*(p-1))-2/(p-1)+6*einf/(d*(p-1))) + (-2-(-2))]
// row F_\infty,
Simplify[t + Sum[t*p^(A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*(A*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, 1, n/2}] + Sum[t*p^(n-A-1)*(p-1)+(-6*(A*(p-1)+1)+(p^(n-1)*(p+1)*d-3*((n-A)*(p-1)+1)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*p^(n-A-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)), {A, n/2+1, n-1}] + t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1)) + (-3)*(t*p^((n-2)/2)*(p+1)/3+1/3+p^(n/2-1)*(p+1)*(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2)*(-2*(n*(p-1)-2)+(-(n*(p-1)-2)*p^(n/2-1)*(p+1)*einf)/(p^(n-1)*(p+1)*d/12-p^(n/2-1)*(p+1)*einf/2))/(p^(n-1)*(p+1)*d*(p-1))-4/(3*(p-1))+4*einf/(d*(p-1))) + (-2-(-3))]