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+--- Thread: Example of a symbolic equation (/thread-20331.html)
Example of a symbolic equation - komame - 08-17-2023 05:38 AM
I need an equation in symbolic mode (CAS) for testing purposes that will be relatively easy to input but will take a while to compute on the Prime G1. Ideally, the computation should last more than 10 seconds, but less than 30 seconds.
Can someone provide such an example?
It doesn't even have to be an equation, it can be any type of calculation, but it must be symbolic, not numeric.
RE: Example of a symbolic equation - Albert Chan - 08-17-2023 03:04 PM
There is a (undocumented?) @@ operator, (f @@ 3)(x) = f(f(f(x)))
You can generate huge mess easily
Cas> f(x) := (x-1)/(x+1)
Cas> normal(atanh(f(x)) → 1/2 * ln(x)
Cas> normal(f @@ 2) → (_x) -> -1 / _x
--> normal(f @@ 4n) will produce identity function.
Another example, to give a trig work-out
Cas> g(t) := 2t/(1-t*t)
Cas> simplify(g(tan(x/2))-tan(x)) → 0
--> simplify((g @@ n) (tan(x/2^n)) - tan(x)) = 0