What is the best way to approximate trigonometric functions in HC about homotopycontinuation.jl HOT 2 CLOSED

Hi,

unfortunately, there is no support for trigonometric functions. While in principle, it is possible to do homotopies for any analytic functions, our software only supports polynomial functions. The reason is that for polynomial systems there is a theory for start systems, so that the software can find all zeros of a given system. Such a theory does not exist for analytic functions, simply because there can be infinitely many roots (for instance, $\cos(x) = 0$).

In your example, the software correctly computes the 5 complex roots of f2. One of them is real. The Taylor approximation is only good locally around 0, that is why you will not find $\pi$.

from homotopycontinuation.jl.

Closed

from homotopycontinuation.jl.