Calculate ring of integers for roots of cubic polynomials

Question

Consider the polynomials

$$f_ 1(X ): =X^ 3-X^2+1$$

and

$$f_2(X):=X^ 3+X+ 1$$

and their roots $c_1\in\mathbb{C}$ of $f_1$ and $c_2\in\mathbb{C}$ of $f_2$. Is there a concrete way to calculate the ring of integeres of $\mathbb{Q}(c_1)$ and $\mathbb{Q}(c_2)$? Can someone recommend a script for this problem?

Answer 1

There is a free script by J.S. Milne called Fields and Galois Theory, and one called Algebraic Number Theory