Testformeln für Mathematica auf den Raspberry Pi 3:

Test der Rechengeschwindigkeit und überprüfe ob die gleiche Komplexität wie auf Wolfram|Alpha: http://www.wolframalpha.com/ gegeben ist!

solve(a^((i pi(2n+1))/(log(b)-log(a)))+b^((i pi(2n+1))/(log(b)-log(a)))=(b^((2i pi n)/(log(b)-log(a))+(i pi)/(log(b)-log(a)))+a^((2i pi n)/(log(b)-log(a))+(i  pi)/(log(b)-log(a))))^(log(b)/(2i pi n+i pi)-log(a)/(2i pi n+i pi))^((i pi(2n+1))/(log(b)-log(a))),b);

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a^(W(n)e^(W(n)))+b^(W(n)e^(W(n)))

(a^(e^(W(0)) W(0))+b^(e^(W(0)) W(0)))+n e^(W(0)) (W(0)+1) W'(0) (a^(e^(W(0)) W(0)) log(a)+b^(e^(W(0)) W(0)) log(b))+n^2 (1/2 a^(e^(W(0)) W(0)) (e^(2 W(0)) (W(0)+1)^2
log^2(a) W'(0)^2+e^(W(0)) log(a) (W(0) W''(0)+W''(0)+W(0) W'(0)^2+2 W'(0)^2))+1/2 b^(e^(W(0)) W(0)) (e^(2 W(0)) (W(0)+1)^2 log^2(b) W'(0)^2+e^(W(0)) log(b) (W(0)
W''(0)+W''(0)+W(0) W'(0)^2+2 W'(0)^2)))+n^3 (1/3 a^(e^(W(0)) W(0)) (e^(2 W(0)) (W(0)+1) log^2(a) W'(0) (W(0) W''(0)+W''(0)+W(0) W'(0)^2+2 W'(0)^2)+1/2 e^(W(0)) (W
(0)+1) log(a) W'(0) (e^(2 W(0)) (W(0)+1)^2 log^2(a) W'(0)^2+e^(W(0)) log(a) (W(0) W''(0)+W''(0)+W(0) W'(0)^2+2 W'(0)^2))+1/2 e^(W(0)) log(a) (W(0) W^(3)(0)+W^(3)(0)+W
(0) W'(0)^3+3 W'(0)^3+3 W(0) W'(0) W''(0)+6 W'(0) W''(0)))+1/3 b^(e^(W(0)) W(0)) (e^(2 W(0)) (W(0)+1) log^2(b) W'(0) (W(0) W''(0)+W''(0)+W(0) W'(0)^2+2 W'(0)^2)+1/2
e^(W(0)) (W(0)+1) log(b) W'(0) (e^(2 W(0)) (W(0)+1)^2 log^2(b) W'(0)^2+e^(W(0)) log(b) (W(0) W''(0)+W''(0)+W(0) W'(0)^2+2 W'(0)^2))+1/2 e^(W(0)) log(b) (W(0) W^(3)
(0)+W^(3)(0)+W(0) W'(0)^3+3 W'(0)^3+3 W(0) W'(0) W''(0)+6 W'(0) W''(0))))+(1/4 (1/2 e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^3+3 W'(0)^3+3 W(0) W''(0) W'(0)+6 W''(0)
W'(0)+W(0) W^(3)(0)+W^(3)(0)) log^2(a)+1/2 e^(W(0)) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) (e^(2 W(0)) log^2(a) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(a) (W(0) W'(0)^2+2
W'(0)^2+W(0) W''(0)+W''(0))) log(a)+1/3 e^(W(0)) (W(0)+1) W'(0) (e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) log^2(a)+1/2 e^(W(0)) (W(0)+1)
W'(0) (e^(2 W(0)) log^2(a) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(a) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(a)+1/2 e^(W(0)) (W(0) W'(0)^3+3 W'(0)^3+3 W(0) W''(0)
W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log(a)) log(a)+1/6 e^(W(0)) (W(0) W'(0)^4+4 W'(0)^4+6 W(0) W''(0) W'(0)^2+18 W''(0) W'(0)^2+4 W(0) W^(3)(0) W'(0)+8 W^(3)
(0) W'(0)+3 W(0) W''(0)^2+6 W''(0)^2+W(0) W^(4)(0)+W^(4)(0)) log(a)) a^(e^(W(0)) W(0))+1/4 b^(e^(W(0)) W(0)) (1/2 e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^3+3 W'(0)^3+3
W(0) W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log^2(b)+1/2 e^(W(0)) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) (e^(2 W(0)) log^2(b) (W(0)+1)^2 W'(0)^2+e^
(W(0)) log(b) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(b)+1/3 e^(W(0)) (W(0)+1) W'(0) (e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))
log^2(b)+1/2 e^(W(0)) (W(0)+1) W'(0) (e^(2 W(0)) log^2(b) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(b) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(b)+1/2 e^(W(0)) (W(0)
W'(0)^3+3 W'(0)^3+3 W(0) W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log(b)) log(b)+1/6 e^(W(0)) (W(0) W'(0)^4+4 W'(0)^4+6 W(0) W''(0) W'(0)^2+18 W''(0)
W'(0)^2+4 W(0) W^(3)(0) W'(0)+8 W^(3)(0) W'(0)+3 W(0) W''(0)^2+6 W''(0)^2+W(0) W^(4)(0)+W^(4)(0)) log(b))) n^4+(1/5 (1/6 e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^4+4
W'(0)^4+6 W(0) W''(0) W'(0)^2+18 W''(0) W'(0)^2+4 W(0) W^(3)(0) W'(0)+8 W^(3)(0) W'(0)+3 W(0) W''(0)^2+6 W''(0)^2+W(0) W^(4)(0)+W^(4)(0)) log^2(a)+1/4 e^(W(0)) (e^(2
W(0)) log^2(a) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(a) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) (W(0) W'(0)^3+3 W'(0)^3+3 W(0) W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)
(0)+W^(3)(0)) log(a)+1/3 e^(W(0)) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) (e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) log^2(a)+1/2 e^(W
(0)) (W(0)+1) W'(0) (e^(2 W(0)) log^2(a) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(a) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(a)+1/2 e^(W(0)) (W(0) W'(0)^3+3 W'(0)^3+3
W(0) W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log(a)) log(a)+1/4 e^(W(0)) (W(0)+1) W'(0) (1/2 e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^3+3 W'(0)^3+3 W(0)
W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log^2(a)+1/2 e^(W(0)) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) (e^(2 W(0)) log^2(a) (W(0)+1)^2 W'(0)^2+e^(W(0))
log(a) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(a)+1/3 e^(W(0)) (W(0)+1) W'(0) (e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) log^2
(a)+1/2 e^(W(0)) (W(0)+1) W'(0) (e^(2 W(0)) log^2(a) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(a) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(a)+1/2 e^(W(0)) (W(0)
W'(0)^3+3 W'(0)^3+3 W(0) W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log(a)) log(a)+1/6 e^(W(0)) (W(0) W'(0)^4+4 W'(0)^4+6 W(0) W''(0) W'(0)^2+18 W''(0)
W'(0)^2+4 W(0) W^(3)(0) W'(0)+8 W^(3)(0) W'(0)+3 W(0) W''(0)^2+6 W''(0)^2+W(0) W^(4)(0)+W^(4)(0)) log(a)) log(a)+1/24 e^(W(0)) (W(0) W'(0)^5+5 W'(0)^5+10 W(0) W''(0)
W'(0)^3+40 W''(0) W'(0)^3+10 W(0) W^(3)(0) W'(0)^2+30 W^(3)(0) W'(0)^2+15 W(0) W''(0)^2 W'(0)+45 W''(0)^2 W'(0)+5 W(0) W^(4)(0) W'(0)+10 W^(4)(0) W'(0)+10 W(0) W''(0)
W^(3)(0)+20 W''(0) W^(3)(0)+W(0) W^(5)(0)+W^(5)(0)) log(a)) a^(e^(W(0)) W(0))+1/5 b^(e^(W(0)) W(0)) (1/6 e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^4+4 W'(0)^4+6 W(0)
W''(0) W'(0)^2+18 W''(0) W'(0)^2+4 W(0) W^(3)(0) W'(0)+8 W^(3)(0) W'(0)+3 W(0) W''(0)^2+6 W''(0)^2+W(0) W^(4)(0)+W^(4)(0)) log^2(b)+1/4 e^(W(0)) (e^(2 W(0)) log^2(b)
(W(0)+1)^2 W'(0)^2+e^(W(0)) log(b) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) (W(0) W'(0)^3+3 W'(0)^3+3 W(0) W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log
(b)+1/3 e^(W(0)) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) (e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) log^2(b)+1/2 e^(W(0)) (W(0)+1)
W'(0) (e^(2 W(0)) log^2(b) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(b) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(b)+1/2 e^(W(0)) (W(0) W'(0)^3+3 W'(0)^3+3 W(0) W''(0)
W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log(b)) log(b)+1/4 e^(W(0)) (W(0)+1) W'(0) (1/2 e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^3+3 W'(0)^3+3 W(0) W''(0) W'(0)+6
W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log^2(b)+1/2 e^(W(0)) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) (e^(2 W(0)) log^2(b) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(b) (W(0)
W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(b)+1/3 e^(W(0)) (W(0)+1) W'(0) (e^(2 W(0)) (W(0)+1) W'(0) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0)) log^2(b)+1/2 e^(W(0))
(W(0)+1) W'(0) (e^(2 W(0)) log^2(b) (W(0)+1)^2 W'(0)^2+e^(W(0)) log(b) (W(0) W'(0)^2+2 W'(0)^2+W(0) W''(0)+W''(0))) log(b)+1/2 e^(W(0)) (W(0) W'(0)^3+3 W'(0)^3+3 W(0)
W''(0) W'(0)+6 W''(0) W'(0)+W(0) W^(3)(0)+W^(3)(0)) log(b)) log(b)+1/6 e^(W(0)) (W(0) W'(0)^4+4 W'(0)^4+6 W(0) W''(0) W'(0)^2+18 W''(0) W'(0)^2+4 W(0) W^(3)(0) W'(0)+8
W^(3)(0) W'(0)+3 W(0) W''(0)^2+6 W''(0)^2+W(0) W^(4)(0)+W^(4)(0)) log(b)) log(b)+1/24 e^(W(0)) (W(0) W'(0)^5+5 W'(0)^5+10 W(0) W''(0) W'(0)^3+40 W''(0) W'(0)^3+10 W(0)
W^(3)(0) W'(0)^2+30 W^(3)(0) W'(0)^2+15 W(0) W''(0)^2 W'(0)+45 W''(0)^2 W'(0)+5 W(0) W^(4)(0) W'(0)+10 W^(4)(0) W'(0)+10 W(0) W''(0) W^(3)(0)+20 W''(0) W^(3)(0)+W(0)
W^(5)(0)+W^(5)(0)) log(b))) n^5+O(n^6) (Taylor series)

(d)/(dn)(a^(e^(W(n)) W(n))+b^(e^(W(n)) W(n))) = e^(W(n)) (W(n)+1) W'(n) (log(a) a^(e^(W(n)) W(n))+log(b) b^(e^(W(n)) W(n)))

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a^x + b^x = c^x                       a^(-(i (π+2 n π))/(log(a)-log(b)))+b^(-(i (π+2 n π))/(log(a)-log(b)))=c^(-(i (π+2 n π))/(log(a)-log(b)))
                                              x = (-(i (π+2 n π))/(log(a)-log(b)))

Wolfram Language plaintext input:
a^(-(I (Pi + 2 n Pi))/(Log[a] - Log[b])) + b^(-(I (Pi + 2 n Pi))/(Log[a] - Log[b])) == c^(-(I (Pi + 2 n Pi))/(Log[a] - Log[b]))
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Alternate forms:

Wolfram Language plaintext input:
FullSimplify[a^(((-I) (Pi + 2 n Pi))/(Log[a] - Log[b])) + b^(((-I) (Pi + 2 n Pi))/(Log[a] - Log[b])) == c^(((-I) (Pi + 2 n Pi))/(Log[a] - Log[b]))

Wolfram Language plaintext output:
a^((I (1 + 2 n) Pi)/(-Log[a] + Log[b])) + b^((I (1 + 2 n) Pi)/(-Log[a] + Log[b])) == c^((I (1 + 2 n) Pi)/(-Log[a] + Log[b]))
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