Number Fields

• Arithmetic
• Construction of equation orders, maximal orders, arbitrary orders
• Simple and relative extensions, extension defined by several polynomials
• Subfields
• transfer between relative and absolute representations
• Discriminant, reduced discriminant, signature
• Factorization of polynomials over number fields
• Completion of absolute fields at finite primes
• Number fields with arbitray bases
• Computation of Hilbert class fields