Function Fields: Orders and Fractional Ideals

• Discriminant
• Integral closures resp. maximal orders
• Construction of integral and fractional ideals
• Ideal arithmetic: product, quotient, gcd, lcm
• Determination of whether an ideal is: integral, prime, principal (principal in the global case)
• Decomposition of primes
• Valuations of order elements and ideals at prime ideals
• Ideal factorization
• Basis reduction (in the global, tamely ramified case)
• Unit rank, independent, fundamental units, regulator (in the global case).