Orders and Fractional Ideals

• Multiple relative extensions
• Maximal order, integral basis (Round 2 and Round 4 algorithms)
• Suborders, extension orders
• Construction of integral and fractional ideals
• Ideal arithmetic: product, quotient, gcd, lcm
• Determination of whether an ideal is: integral, prime, principal
• Decomposition of primes
• Valuations of order elements and ideals at prime ideals
• Ramification index
• Factorization of an ideal
• Residue field of an order modulo a prime ideal
• Reside class ring of an order modulo an arbitrary ideal
• Completion of absolute maximal orders at finite primes