Dear Markus,
thank you very much for your reply. We apologize for our delay, but we have just started looking into the problem of complex interval arithmetic. Indeed, our main problem is to approximate as closely as possible to the (possibly complex) roots of polynomials. Our polynomials have usually integer coefficients, and we compute an exact formula for the roots whenever possible, but we do not insist on the fact that this is the best (more accurate, faster...) way of dealing with this kind of approximations.
More precisely, we always want to find exact formulas if it is at all possible, but we also want to compute approximations. It may be the case that, for our problem, it is better to approximate to the roots of the polynomial ignoring the exact (but sometimes cumbersome) formula given by our system. Indeed, some expressions that we obtain are several MB in size!
We probably have no problems with iterated logarithms, or with nested square roots (beside the ones arising from the solution of polynomial equations as explained above), since the majority of expressions that we want to approximate are (as of now; it may change in the future) of the general shape
a * x^n * n^k
where a is a numeric coefficient, x is a root of a polynomial equation, k is a positive integer and n is an integer variable. Of course, we also need to approximate sums of expressions like that. The reason why we mentioned sines and cosines is that we may use the trigonometric representation of complex numbers, if it happens to be useful.
There is at least one more thing that we would like to have: it would be more convenient for us if CoStLy answered with the whole complex plane instead of throwing exceptions (in the cases where the interval contains 0 or some real negative number, for instance). Would it be possible to have something like this (even as a temporary solution)?
Thank you very much again.
Tatiana Zolo & Alessandro Zaccagnini