I read about arbitrary precision libraries. Its an interesting topic, but can you name me some examples in science where this is necessary and actualy? I know the reasons why and would like to see an example topic or a motivation, escpecially for enclosing zeros of nonlinear systems. Thank you.
How about this one?
Taken to arbitrary precision, the answer is exactly what Mathematica gives:
Isn't that more satisfying than a numerical answer like:
Why might this be useful? Consider an analytic function:
which simplifies very nicely to a polynomial, whereas the corresponding numerical version does not simplify: