Constructions
LocalField(L, f) : FldPad, RngUPolElt -> RngLocA
Example RngLocA_construct (H51E1)
sub< L | a1, ..., an > : RngLocA, RngLocAElt, ..., RngLocAElt -> RngLocA
Example RngLocA_sub (H51E2)
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 (H51E3)
QuotientRepresentation(L) : RngLocA -> RngUPolRes
RamifiedRepresentation(L) : RngLocA -> FldPad, Map
Example RngLocA_reps (H51E4)
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 (H51E5)
Homomorphisms from Fields
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 (H51E6)
Local Field Elements
L ! r : RngLocA, Any -> RngLocAElt
L . i : RngLocA, RngIntElt -> RngLocAElt
InertialElement(L) : RngLocA -> RngLocAElt
UniformizingElement(L) : RngLocA -> RngLocAElt
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
Example RngLocA_elts (H51E7)
Polynomials over General Local Fields
Factorization(f) : RngUPolElt[RngLocA] -> SeqEnum, RngElt, Any
SuggestedPrecision(f) : RngUPolElt[RngLocA] -> RngIntElt
Roots(f) : RngUPolElt[RngLocA] -> SeqEnum
Example RngLocA_poly-fact (H51E8)
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012