Given an algebraic number field $F$ (I actually don't have an idea how to implement this data already, except for splitting fields of polynomials, but there is something in SAGE) is there free code available n the internet for the following operations:

- Compute the ring of integers $O$ and its units
- Factorize a given prime ideal of $\mathbb{Q}$ in $F$ with a choice for generators, ramification degree, etc.
- Compute the Galois groups over $\mathbb{Q}$
- Compute monic, irreducible, quadratic polynomials $X^2 + A X + D$ for $A, D \leq N$ (appropiately interpreted in terms of ideals) and give information at which places it factorizes.

What is the analogue for global function fields?