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Copy pathp=1 mod 12, n even, M not 1.txt
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p=1 mod 12, n even, M not 1.txt
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// p=1 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)*(t) + Sum[(d*p^(n-2*A)*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2*(1+d*p^(n-1)*(p+1)/12-2*e2/4-2*e3/3-einf*p^((n-2)/2)*(p+1)/2)-(-d*p^(n-1)*(p-1)/12)]
// row C_a, 0<a<n/2
Simplify[(d*p^(n-2*a)*(p-1)/12)*(t) + Sum[(d*p^(n-2*a)*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^(a-1)*(p-1)/2+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + e3*(t*p^(a-1)*(p-1)/3+1/3+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(3*p^(n-1)*(p+1)*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)*(t) + Sum[(d*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^(n/2-1)*(p-1)/2+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n/2-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + e3*(t*p^(n/2-1)*(p-1)/3+1/3+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n/2-1)*(p-1)/(3*p^(n-1)*(p+1)*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)*(t) + Sum[(d*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^(n-a-1)*(p-1)/2+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + e3*(t*p^(n-a-1)*(p-1)/3+1/3+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(3*p^(n-1)*(p+1)*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)*(t) + Sum[(d*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(6*n*(p-1)+12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(n-1)*(p-1)/12)]
// row E_a, 0<a<n/2+1
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-2)*(t*p^(a-1)*(p-1)/2+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-2))]
// row E_a, n/2<a<n
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-2)*(t*p^(n-a-1)*(p-1)/2+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-2))]
// row F_a, 0<a<n/2+1
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-3)*(t*p^(a-1)*(p-1)/3+1/3+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(3*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-3))]
// row F_a, n/2<a<n
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-3)*(t*p^(n-a-1)*(p-1)/3+1/3+(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(3*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-3))]
/////////////////////////////////////////////
// check V_\infty
// row C_0
Simplify[(-d*p^(n-1)*(p-1)/12)*(t) + Sum[(d*p^(n-2*A)*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2-(-d*p^(n-1)*(p-1)/12)]
// row C_a, 0<a<n/2
Simplify[(d*p^(n-2*a)*(p-1)/12)*(t) + Sum[(d*p^(n-2*a)*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^(a-1)*(p-1)/2+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + e3*(t*p^(a-1)*(p-1)/3+1/3+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(3*p^(n-1)*(p+1)*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)*(t) + Sum[(d*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^(n/2-1)*(p-1)/2+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n/2-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + e3*(t*p^(n/2-1)*(p-1)/3+1/3+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n/2-1)*(p-1)/(3*p^(n-1)*(p+1)*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)*(t) + Sum[(d*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + e2*(t*p^(n-a-1)*(p-1)/2+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + e3*(t*p^(n-a-1)*(p-1)/3+1/3+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(3*p^(n-1)*(p+1)*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)*(t) + Sum[(d*(p-1)/12)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-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)*(t+(-6*n*(p-1)-12)*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)/(p^(n-1)*(p+1)*d*(p-1))) + 2*(1+d/12-e2/4-e3/3-einf/2)-2*(1+d*p^(n-1)*(p+1)/12-2*e2/4-2*e3/3-einf*p^((n-2)/2)*(p+1)/2)-(-d*p^(n-1)*(p-1)/12)]
// row E_a, 0<a<n/2+1
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-2)*(t*p^(a-1)*(p-1)/2+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-2))]
// row E_a, n/2<a<n
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-2)*(t*p^(n-a-1)*(p-1)/2+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(2*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-2))]
// row F_a, 0<a<n/2+1
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-3)*(t*p^(a-1)*(p-1)/3+1/3+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(a-1)*(p-1)/(3*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-3))]
// row F_a, n/2<a<n
Simplify[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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(p^(n-1)*(p+1)*d*(p-1)) + (-3)*(t*p^(n-a-1)*(p-1)/3+1/3+(-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/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2))*2*(p^(n-1)*(p+1)*d/12-2*e2/4-2*e3/3-p^(n/2-1)*(p+1)*einf/2)*p^(n-a-1)*(p-1)/(3*p^(n-1)*(p+1)*d*(p-1))) + (-2-(-3))]