General \(p\)-Adic Extensions
- Introduction
- Constructions
LocalField(L, f): FldPad, RngUPolElt → RngLocALocalField(L, f): RngLocA, RngUPolElt → RngLocAExample: constructsub< L | a₁, ..., aₙ >: RngLocA, RngLocAElt, ..., RngLocAElt → RngLocAsub< L | S>: RngLocA, SeqEnum → RngLocAExample: sub
- Operations with Fields
BaseRing(L): RngLocA → RngCoefficientRing(L): RngLocA → RngDefiningPolynomial(L): RngLocA → RngUPolEltDegree(L): RngLocA → RngIntEltDegree(L, R): RngLocA, Rng → RngIntEltInertiaDegree(L): RngLocA → RngIntEltRamificationDegree(L): RngLocA → RngIntEltRamificationIndex(L): RngLocA → RngIntEltPrecision(L): RngLocA → RngIntEltPrime(L): RngLocA → RngEltExample: opsQuotientRepresentation(L): RngLocA → RngUPolResRamifiedRepresentation(L): RngLocA → FldPad, MapExample: repsAssignNames(~L, S): RngLocA, SeqEnum[MonStgElt]Name(L, i): RngLocA, RngIntElt → RngLocAEltDiscriminant(L): RngLocA → RngEltResidueClassField(L): RngLocA → Rng, MapRelativeField(L, m): RngLocA, Map → RngLocA, Map, Map- Predicates on Fields
- Maximal Order
- Homomorphisms
- Automorphisms and Galois Theory
- Elements Operations
- Polynomial Factorization
