- Introduction
- Creation Functions
- Creation of Structures
- 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 (H26E4)
- Structure Operations
- Element Operations
- Generic Element Functions and Predicates
- Comparison of and Membership
- Other Predicates
- Arithmetic
- Conversions
- Rounding
- Precision
- Constants
- Simple Element Functions
- Roots
- Continued Fractions
- Linear and Algebraic Dependencies
- LinearRelation(q: parameters) : [ FldComElt ] -> [ RngIntElt ]
- AllLinearRelations(q,p): SeqEnum, RngIntElt -> Lat
- IntegerRelation(q): SeqEnum -> SeqEnum, FldReElt
- PowerRelation(r, k: parameters) : FldReElt, RngIntElt -> RngUPolElt
- MinimalPolynomial(r,d,N) : FldReElt, RngIntElt, RngIntElt -> RngUPolElt, FldReElt
- Example FldRe_LLLPolFact (H26E8)
- Transcendental Functions
- Elliptic and Modular Functions
- Theta Functions
- 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
- Summation of Infinite Series
- Numerical Integration
- Polynomial Interpolation
- Discrete Fourier Transform
- Integration of Complex Functions
- Gaussian Quadratures
- GaussLegendreIntegrationPoints(N,D) : RngIntElt, RngIntElt -> SeqEnum[FldReElt], SeqEnum[FldReElt]
- GaussJacobiIntegrationPoints(N,D,a,b) : RngIntElt, RngIntElt, RngReSubElt, RngReSubElt) -> SeqEnum, SeqEnum
- Clenshaw--Curtis Quadrature
- Tanh--Sinh Quadrature
- Romberg-Type Integration
- 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
- Bibliography
V2.28, 13 July 2023