Introduction

 
Constructions
      LocalField(L, f) : FldPad, RngUPolElt -> RngLocA
      Example RngLocA_construct (H50E1)
      sub< L | a₁, ..., a_n > : RngLocA, RngLocAElt, ..., RngLocAElt -> RngLocA
      Example RngLocA_sub (H50E2)

 
Operations with Fields
      BaseRing(L) : RngLocA -> Rng
      DefiningPolynomial(L) : RngLocA -> RngUPolElt
      Degree(L) : RngLocA -> RngIntElt
      Degree(L, R) : RngLocA, Rng -> RngIntElt
      InertiaDegree(L) : RngLocA -> RngIntElt
      Precision(L) : RngLocA -> RngIntElt
      Prime(L) : RngLocA -> RngElt
      Example RngLocA_ops (H50E3)
      QuotientRepresentation(L) : RngLocA -> RngUPolRes
      RamifiedRepresentation(L) : RngLocA -> FldPad, Map
      Example RngLocA_reps (H50E4)
      AssignNames(~L, S) : RngLocA, SeqEnum[MonStgElt] ->
      Name(L, i) : RngLocA, RngIntElt -> RngLocAElt
      Discriminant(L) : RngLocA -> RngElt
      ResidueClassField(L) : RngLocA -> Rng, Map
      RelativeField(L, m) : RngLocA, Map -> RngLocA, Map, Map

      Predicates on Fields
            IsRamified(L) : RngLocA -> BoolElt
            IsTamelyRamified(L) : RngLocA -> BoolElt
            IsTotallyRamified(L) : RngLocA -> BoolElt
            IsUnramified(L) : RngLocA -> BoolElt

 
Maximal Order
      IntegralBasis(L) : RngLocA -> SeqEnum
      IsIntegral(a) : RngLocAElt -> BoolElt, SeqEnum
      Example RngLocA_max-order (H50E5)

 
Homomorphisms
      hom< L -> R | a > : RngLocA, Rng, RngElt -> Map

 
Automorphisms and Galois Theory
      FrobeniusAutomorphism(L) : RngLocA -> Map
      AutomorphismGroup(L) : RngLocA -> Grp, Map
      DecompositionGroup(L) : RngLocA -> GrpPerm
      FixedField(L, G) : RngLocA, GrpPerm -> RngLocA
      Example RngLocA_auto-gal (H50E6)

 
Elements Operations
      L ! r : RngLocA, Any -> RngLocAElt
      L . i : RngLocA, RngIntElt -> RngLocAElt
      InertialElement(L) : RngLocA -> RngLocAElt
      UniformizingElement(L) : RngLocA -> RngLocAElt

      Arithmetic

      Predicates on Elements
            a eq b : RngLocAElt, RngLocAElt -> BoolElt
            IsOne(a) : RngLocAElt -> BoolElt
            IsWeaklyZero(a) : RngLocAElt -> BoolElt
            IsZero(a) : RngLocAElt -> BoolElt

      Other Operations on Elements
            Valuation(a) : RngLocAElt -> RngExtReElt
            RelativePrecision(a) : RngLocAElt -> RngExtReElt
            Eltseq(a) : RngLocAElt -> SeqEnum
            RepresentationMatrix(a) : RngLocAElt -> AlgMatElt
            Norm(a) : RngLocAElt -> RngElt
            Example RngLocA_elts (H50E7)

 
Polynomial Factorization
      Factorization(f) : RngUPolElt[RngLocA] -> SeqEnum, RngElt, Any
      SuggestedPrecision(f) : RngUPolElt[RngLocA] -> RngIntElt
      Roots(f) : RngUPolElt[RngLocA] -> SeqEnum
      Example RngLocA_poly-fact (H50E8)

[Next][Prev] [Right] [____] [Up] [Index] [Root]