Overview of Real Numbers in Magma
Example FldRe_RealIntro (H25E1)
Homomorphisms
Example FldRe_Homomorphisms (H25E2)
Special Options
SetDefaultRealField(R) : FldRe ->
GetDefaultRealField() : -> FldRe
AssignNames(~C, [s]) : FldCom, [ MonStgElt ]) ->
Name(C, 1) : FldCom, RngIntElt -> FldComElt
Version Functions
GetGMPVersion() : ->
Creation of Structures
RealField(p) : RngIntElt -> FldRe
RealField() : -> FldRe
ComplexField(p) : RngIntElt -> FldCom
ComplexField() : -> FldCom
ComplexField(R) : FldRe -> FldCom
Example FldRe_CreateComplexField (H25E3)
Creation of Elements
d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
elt<R | m, n> : FldRe, FldReElt, RngIntElt -> FldReElt
elt<C | x, y> : FldCom, FldReElt, FldReElt -> FldComElt
R ! a : FldRe, RngElt -> FldReElt
C ! a : FldCom, RngElt -> FldComElt
Example FldRe_CreateElements (H25E4)
Other Structure Functions
Precision(R) : FldCom -> RngIntElt
BitPrecision(R) : FldCom -> RngIntElt
Generic Element Functions and Predicates
Other Predicates
IsIntegral(c) : FldReElt -> BoolElt
IsReal(c) : FldComElt -> BoolElt
Conversions
MantissaExponent(r) : FldReElt -> FldReElt, RngIntElt
ComplexToPolar(c) : FldComElt -> FldReElt, FldReElt
PolarToComplex(m, a) : FldReElt, FldReElt -> FldComElt
Argument(c) : FldComElt -> FldReElt
Modulus(c) : FldComElt -> FldReElt
Real(c) : FldComElt -> FldReElt
Imaginary(c) : FldComElt -> FldReElt
Rounding
Round(r) : FldReElt -> FldReElt
Truncate(r) : FldReElt -> RngIntElt
Ceiling(r) : Infty -> Infty
Floor(r) : Infty -> Infty
Precision
Precision(r) : FldReElt -> RngIntElt
BitPrecision(r) : FldReElt -> RngIntElt
Precision(L) : [FldReElt] -> RngIntElt
ChangePrecision(r, n) : FldReElt, RngIntElt -> FldReElt
Constants
Catalan(R) : FldRe -> FldReElt
EulerGamma(R) : FldRe -> FldReElt
Pi(R) : FldRe -> FldReElt
Simple Element Functions
AbsoluteValue(r) : FldReElt-> FldReElt
Sign(r) : FldReElt -> RngIntElt
ComplexConjugate(r) : FldReElt -> FldReElt
Norm(c) : FldComElt -> FldReElt
Root(r, n) : FldReElt, RngIntElt -> FldReElt
SquareRoot(c) : FldComElt -> FldComElt
Distance(x, L) : FldReElt, [FldReElt] -> FldReElt, RngIntElt
Diameter(L) : [FldReElt] -> FldReElt
Roots
Roots(p) : RngUPolElt -> [ <FldComElt, RngIntElt> ]
Example FldRe_Roots (H25E5)
RootsNonExact(p) : RngUPolElt[FldRe] -> [ FldComElt ], [ FldComElt ]
Example FldRe_RootsNonExact (H25E6)
HenselLift(f, R, k) : RngUPolElt, FldReElt, RngIntElt -> FldReElt
Continued Fractions
ContinuedFraction(r) : FldRatElt -> [ RngIntElt ]
BestApproximation(r, n) : FldReElt, RngIntElt -> FldReElt
Convergents(s) : [ RngIntElt ] -> ModMatRngElt
Algebraic Dependencies
LinearRelation(q: parameters) : [ FldComElt ] -> [ RngIntElt ]
AllLinearRelations(q,p): SeqEnum, RngIntElt -> Lat
PowerRelation(r, k: parameters) : FldReElt, RngIntElt -> RngUPolElt
Exponential, Logarithmic and Polylogarithmic Functions
Exp(f) : RngSerElt -> RngSerElt
Exp(c) : FldComElt -> FldComElt
Log(f) : RngSerElt -> RngSerElt
Log(r) : FldReElt -> FldReElt
Log(b, r) : FldReElt -> FldReElt
Dilog(s) : FldComElt -> FldComElt
Polylog(m, f) : RngIntElt, RngSerElt -> RngSerElt
Polylog(m, s) : RngIntElt, FldComElt -> FldComElt
PolylogD(m, s) : RngIntElt, FldComElt -> FldComElt
Trigonometric Functions
Sin(f) : RngSerElt -> RngSerElt
Sin(c) : FldComElt -> FldComElt
Cos(f) : RngSerElt -> RngSerElt
Cos(c) : FldComElt -> FldComElt
Sincos(f) : RngSerElt -> RngSerElt
Sincos(s) : FldReElt -> FldReElt, FldReElt
Tan(f) : RngSerElt -> RngSerElt
Tan(c) : FldComElt -> FldComElt
Cot(f) : RngSerElt -> RngSerElt
Cot(c) : FldComElt -> FldComElt
Sec(f) : RngSerElt -> RngSerElt
Sec(c) : FldComElt -> FldComElt
Cosec(f) : RngSerElt -> RngSerElt
Cosec(c) : FldComElt -> FldComElt
Inverse Trigonometric Functions
Arcsin(f) : RngSerElt -> RngSerElt
Arcsin(r) : FldReElt -> FldReElt
Arccos(f) : RngSerElt -> RngSerElt
Arccos(r) : FldReElt -> FldReElt
Arctan(f) : RngSerElt -> RngSerElt
Arctan(r) : FldReElt -> FldReElt
Arctan(x, y) : FldReElt, FldReElt -> FldReElt
Arccot(r) : FldReElt -> FldReElt
Arcsec(r) : FldReElt -> FldReElt
Arccosec(r) : FldReElt -> FldReElt
Hyperbolic Functions
Sinh(f) : RngSerElt -> RngSerElt
Sinh(s) : FldComElt -> FldComElt
Cosh(f) : RngSerElt -> RngSerElt
Cosh(r) : FldReElt -> FldReElt
Tanh(f) : RngSerElt -> RngSerElt
Tanh(r) : FldReElt -> FldReElt
Coth(r) : FldReElt -> FldReElt
Sech(r) : FldReElt -> FldReElt
Cosech(r) : FldReElt -> FldReElt
Inverse Hyperbolic Functions
Argsinh(f) : RngSerElt -> RngSerElt
Argsinh(r) : FldReElt -> FldReElt
Argcosh(f) : RngSerElt -> RngSerElt
Argcosh(r) : FldReElt -> FldReElt
Argtanh(f) : RngSerElt -> RngSerElt
Argtanh(s) : FldReElt -> FldReElt
Argsech(s) : FldReElt -> FldReElt
Argcosech(s) : FldReElt -> FldReElt
Argcoth(s) : FldReElt -> FldReElt
Elliptic and Modular Functions
Eisenstein Series
Eisenstein(k, z) : RngIntElt, RngSerElt -> RngSerElt
Eisenstein(k, t) : RngIntElt, FldComElt -> FldComElt
Eisenstein(k, L) : RngIntElt, SeqEnum -> FldComElt
Eisenstein(k, F) : RngIntElt, QuadBinElt -> RngSerElt
Example FldRe_Eisenstein (H25E7)
Weierstrass Series
WeierstrassSeries(z, q) : RngSerElt, RngSerElt -> RngSerElt
WeierstrassSeries(z, t) : RngSerElt, FldComElt -> RngSerElt
WeierstrassSeries(z, L) : RngSerElt, SeqEnum -> RngSerElt
WeierstrassSeries(z, F) : RngSerElt, QuadBinElt -> RngSerElt
The Jacobi θand Dedekind η- functions
JacobiTheta(q, z) : FldReElt, RngSerElt[FldRe] -> RngSerElt
JacobiTheta(q, z) : FldReElt, FldReElt -> FldReElt
JacobiThetaNullK(q, k) : FldReElt, RngIntElt -> FldReElt
DedekindEta(z) : RngSerElt -> RngSerElt
DedekindEta(s) : FldComElt -> FldComElt
The j-invariant and the Discriminant
jInvariant(q) : RngSerElt -> RngSerElt
jInvariant(s) : FldComElt -> FldComElt
jInvariant(L) : SeqEnum -> FldComElt
jInvariant(F) : QuadBinElt -> FldComElt
Delta(z) : RngSerElt -> RngSerElt
Delta(t) : FldComElt -> FldComElt
Delta(L) : SeqEnum -> FldComElt
Weber's Functions
WeberF(s) : FldComElt -> FldComElt
WeberF2(g) : RngSerElt -> RngSerElt
WeberF1(s) : FldComElt -> FldComElt
Example FldRe_Eisenstein (H25E8)
Theta Functions
Theta(char, z, tau) : Mtrx, Mtrx, Mtrx -> FldComElt
Theta(char, z, A) : Mtrx, Mtrx, AnHcJac -> FldComElt
Gamma, Bessel and Associated Functions
Gamma(f) : RngSerElt -> RngSerElt
Gamma(r) : FldReElt -> FldReElt
Gamma(r, s) : FldReElt, FldReElt -> FldReElt
GammaD(s) : FldReElt -> FldReElt
LogGamma(f) : RngSerElt -> RngSerElt
LogGamma(r) : FldReElt -> FldReElt
LogDerivative(s) : FldReElt -> FldReElt
BesselFunction(n, r) : RngIntElt, FldReElt -> FldReElt
BesselFunctionSecondKind(n, r) : RngIntElt, FldReElt -> FldReElt
JBessel(n, s) : RngIntElt, FldReElt -> FldReElt
KBessel(n, s) : FldReElt, FldReElt -> FldReElt
The Hypergeometric Function
HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
HypergeometricU(a, b, s) : FldReElt, FldReElt, FldReElt -> FldReElt
Other Special Functions
ArithmeticGeometricMean(x, y) : RngSerElt, RngSerElt -> RngSerElt
ArithmeticGeometricMean(x, y) : FldReElt, FldReElt -> FldReElt
BernoulliNumber(n) : RngIntElt -> FldRatElt
BernoulliApproximation(n) : RngIntElt -> FldReElt
DawsonIntegral(r) : FldReElt -> FldReElt
ErrorFunction(r) : FldReElt -> FldReElt
ComplementaryErrorFunction(r) : FldReElt -> FldReElt
ExponentialIntegral(r) : FldReElt -> FldReElt
ExponentialIntegralE1(r) : FldReElt -> FldReElt
LogIntegral(r) : FldReElt -> FldReElt
ZetaFunction(s) : FldReElt -> FldReElt
Summation of Infinite Series
InfiniteSum(m, i) : Map, RngIntElt -> FldReElt
PositiveSum(m, i) : Map, RngIntElt -> FldReElt
AlternatingSum(m, i) : Map, RngIntElt -> FldReElt
Integration
Interpolation(P, V, x) : [FldReElt], [FldReElt], FldReElt -> FldReElt, FldReElt
RombergQuadrature(f, a, b: parameters) : Program, FldReElt, FldReElt -> FldReElt
SimpsonQuadrature(f, a, b, n) : Program, FldReElt, FldReElt, RngIntElt -> FldReElt
TrapezoidalQuadrature(f, a, b, n) : Program, FldReElt, FldReElt, RngIntElt -> FldReElt
Numerical Derivatives
NumericalDerivative(f, n, z) : UserProgram, RngIntElt, FldComElt -> FldComElt
Example FldRe_NumericalDerivative (H25E9)
Bibliography
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Mon Dec 17 14:40:36 EST 2012