Creation of Structures
PowerSeriesRing(R) : Rng -> RngSerPow
LaurentSeriesRing(R) : Rng -> RngSerLaur
PuiseuxSeriesRing(R) : Rng -> RngSerPuis
Example RngSer_Creation (H49E1)
Special Options
AssertAttribute(S, "DefaultPrecision", n) : RngSer, MonStgElt, RngIntElt ->
HasAttribute(S, "DefaultPrecision") : RngSer, MonStgElt -> BoolElt, RngIntElt
AssignNames(~S, ["x"]) : RngSer, [ MonStgElt ] ->
Name(S, 1) : RngSer, RngIntElt -> RngSerElt
Creation of Elements
R . 1 : RngSer, RngInt -> RngSerElt
elt< R | v, [ a1, ..., ad], p > : RngIntElt, SeqEnum, RngIntElt -> RngSerElt
R ! s : RngSer, SeqEnum -> RngSerElt
BigO(f) : RngSerElt -> RngIntElt
Related Structures
BaseRing(R) : RngSer -> Rng
IntegerRing(R) : RngSer -> RngSerPow
FieldOfFractions(R) : RngSer -> RngSerLaur
ChangePrecision(R, r) : RngSer, Any -> RngSer
ChangeRing(R, C) : RngSer, Rng -> RngSer, Map
ResidueClassField(R) : RngSer -> Rng, Map
Invariants
Precision(R) : RngSer -> ExtReElt
Predicates on Ring Elements
IsWeaklyZero(f) : RngSerElt -> BoolElt
IsWeaklyEqual(f, g) : RngSerElt, RngSerElt -> BoolElt
IsIdentical(f, g) : RngSerElt, RngSerElt -> BoolElt
Precision
AbsolutePrecision(f) : RngSerElt -> RngIntElt
RelativePrecision(f) : RngSerElt -> RngIntElt
ChangePrecision(f, r) : RngSerElt, RngIntElt -> RngSerElt
Coefficients and Degree
Coefficients(f) : RngSerElt -> [ RngElt ], RngIntElt, RngIntElt
Coefficient(f, i) : RngSerElt, RngElt -> RngElt
LeadingCoefficient(f) : RngSerElt -> RngElt
LeadingTerm(f) : RngSerElt -> RngElt
Truncate(f) : RngSerElt -> RngSerElt
ExponentDenominator(f) : RngMSerElt -> RngElt
Degree(f) : RngSerElt -> RngIntElt
Valuation(f) : RngSerElt -> RngIntElt
ExponentDenominator(f) : RngSerElt -> RngIntElt
Evaluation and Derivative
Derivative(f) : RngSerElt -> RngSerElt
Derivative(f, n) : RngSerElt, RngIntElt -> RngSerElt
Integral(f) : RngSerElt -> RngSerElt
Evaluate(f, s) : RngSerElt, RngElt -> RngElt
Laplace(f) : RngSerElt -> RngSerElt
Square Root
SquareRoot(f) : RngSerElt -> RngSerElt
Composition and Reversion
Composition(f, g) : RngSerElt, RngSerElt -> RngSerElt
Reversion(f) : RngSerElt -> RngSerElt
Convolution(f, g) : RngSerElt, RngSerElt -> RngSerElt
Example RngSer_CompositionReversion (H49E2)
Exponential and Logarithmic Functions
Exp(f) : RngSerElt -> RngSerElt
Log(f) : RngSerElt -> RngSerElt
Example RngSer_Bernoulli (H49E3)
Trigonometric Functions and their Inverses
Sin(f) : RngSerElt -> RngSerElt
Cos(f) : RngSerElt -> RngSerElt
Sincos(f) : RngSerElt -> RngSerElt
Tan(f) : RngSerElt -> RngSerElt
Arcsin(f) : RngSerElt -> RngSerElt
Arccos(f) : RngSerElt -> RngSerElt
Arctan(f) : RngSerElt -> RngSerElt
Hyperbolic Functions and their Inverses
Sinh(f) : RngSerElt -> RngSerElt
Cosh(f) : RngSerElt -> RngSerElt
Tanh(f) : RngSerElt -> RngSerElt
Argsinh(f) : RngSerElt -> RngSerElt
Argcosh(f) : RngSerElt -> RngSerElt
Argtanh(f) : RngSerElt -> RngSerElt
The Hypergeometric Series
HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
Polynomials over Series Rings
HenselLift(f, L) : RngUPolElt[RngSer], SeqEnum[RngUPolElt] -> [RngUPolElt]
Factorization(f) : RngUPolElt[RngSerPow[FldFin]] -> [ < RngUPolElt[RngSerPow], RngIntElt > ], RngSerPowElt
Example RngSer_series_poly_fact (H49E4)
Constructions of Extensions
UnramifiedExtension(R, f) : RngSerPow[FldFin], RngUPolElt -> RngSerExt
TotallyRamifiedExtension(R, f) : RngSerPow[FldFin], RngUPolElt -> RngSerExt
ChangePrecision(E, r) : RngSerExt, RngIntElt -> RngSerExt
FieldOfFractions(E) : RngSerExt -> RngSerExt
Example RngSer_extensions_eg (H49E5)
Operations on Extensions
Precision(E) : RngSerExt -> RngIntElt
CoefficientRing(E) : RngSerExt -> Rng
DefiningPolynomial(E) : RngSerExt -> RngUPolElt
InertiaDegree(E) : RngSerExt -> RngIntElt
RamificationIndex(E) : RngSerExt -> RngIntElt
ResidueClassField(E) : RngSerExt -> FldFin
UniformizingElement(E) : RngSerExt -> RngSerExtElt
IntegerRing(E) : RngSerExt -> RngSerExt
E1 eq E2 : RngSerExt, RngSerExt -> BoolElt
E . i : RngSerExt, RngIntElt -> RngSerExtElt
AssignNames(~E, S) : RngSerExt, [ MonStgElt ] ->
Example RngSer_ext-ops (H49E6)
Elements of Extensions
Valuation(e) : RngSerExtElt -> RngIntElt
RelativePrecision(e) : RngSerExtElt -> RngIntElt
AbsolutePrecision(e) : RngSerExtElt -> RngIntElt
Coefficients(e) : RngSerExtElt -> [ RngElt ]
Example RngSer_serext-simple (H49E7)
Optimized Representation
OptimizedRepresentation(E) : RngSerExt -> RngSer, Map
Example RngSer_opt-rep (H49E8)
Bibliography
[Next][Prev] [Right] [____] [Up] [Index] [Root]
Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012