Local Fields

p-adic Rings and Their Extensions

p-adic ring background, creation and extensions.

p-Adic Rings and Their Extensions

General p-adic Extensions

General p-adic extension construction, operations and maximal orders.

General p-Adic Extensions

Power, Laurent and Puiseux Series

Power, Laurent and Puiseux series ring creation and operations.

Power, Laurent and Puiseux Series

Lazy Power Series Rings

Lazy power series ring creation, operations and elements.

Lazy Power Series Rings

Algebraic Power Series Rings

Algebraic power series ring construction and accessors.

Algebraic Power Series Rings

Valuation Rings

Valuation ring creation, structure and element operations.

Valuation Rings

Galois Rings

Galois ring creation, operations and elements.

Galois Rings

Newton Polygons

Newton polygon computation and applications to factorisation.

Newton Polygons

Series Rings over p-adic Rings

Series rings over p-adic rings, matrices and modules.

Series Rings over p-Adic Rings

Local Galois Representations

Local Galois representation functions, invariants and arithmetic.

Local Galois Representations