General Function Fields

Within Magma, general algebraic function fields can be created by adjoining a root of an irreducible, separable polynomial in k(x)[y] to the rational function field k(x). If k is a finite field, the function field is said to be global.

• Arithmetic
• Norm, trace of an element
• Minimal and characteristic polynomials of an element
• Representation matrices of algebraic functions with respect to the field extension F/k(x)
• Construction of (finite and infinite) equation orders
• Construction of (finite and infinite) maximal orders (Round 2 algorithm)