I have the following lines in Sage:
var('A, B, C, E, α, β, γ, d')
f = lambda n : (
(12*A + 6*B + 4*C + 2*E + 4*α + 2*β + γ)^n
- (11*A + 6*B + 4*C + 2*E + 4*α + 2*β + γ)^n
- (11*A + 5*B + 4*C + 2*E + 4*α + 2*β + γ)^n
+ (10*A + 5*B + 4*C + 2*E + 4*α + 2*β + γ)^n
- (10*A + 5*B + 3*C + 2*E + 4*α + 2*β + γ)^n
+ ( 9*A + 5*B + 3*C + 2*E + 4*α + 2*β + γ)^n
+ ( 9*A + 4*B + 3*C + 2*E + 4*α + 2*β + γ)^n
- ( 8*A + 4*B + 3*C + 2*E + 4*α + 2*β + γ)^n
- ( 8*A + 4*B + 3*C + E + 4*α + 2*β + γ)^n
+ ( 7*A + 4*B + 3*C + E + 4*α + 2*β + γ)^n
+ ( 7*A + 3*B + 3*C + E + 4*α + 2*β + γ)^n
- ( 6*A + 3*B + 3*C + E + 4*α + 2*β + γ)^n
+ ( 6*A + 3*B + 2*C + E + 4*α + 2*β + γ)^n
- ( 6*A + 3*B + 2*C + E + 3*α + 2*β + γ)^n
- ( 6*A + 3*B + 2*C + E + 3*α + β + γ)^n
+ ( 6*A + 3*B + 2*C + E + 2*α + β + γ)^n
- ( 6*A + 3*B + 2*C + E + 2*α + β)^n
+ ( 6*A + 3*B + 2*C + E + α + β)^n
+ ( 6*A + 3*B + 2*C + E + α)^n
- ( 6*A + 3*B + 2*C + E)^n
+ ( 6*A + 3*B + C + E)^n
- ( 5*A + 3*B + C + E)^n
- ( 5*A + 2*B + C + E)^n
+ ( 4*A + 2*B + C + E)^n
+ ( 4*A + 2*B + C)^n
- ( 3*A + 2*B + C)^n
- ( 3*A + B + C)^n
+ ( 2*A + B + C)^n
- ( 2*A + B)^n
+ ( A + B)^n
+ A^n
)/factorial(n)
solve([f(3) == 0, f(4) == 0, f(5) == d], α, β, γ)
I want Sage to solve this system of equations for the three Greek-letter variables in terms of the five English-letter variables. However, when I ask Sage to solve this, it just sits and spins at maximum CPU usage and steadily-increasing RAM usage until I kill the process. I've waited over fifteen minutes without it completing.
Are there any ways to make this more performant?
