Data.Number.Flint.Calcium.Fexpr.Builtin

This module defines symbol names with a predefined meaning for use in symbolic expressions. These symbols will eventually all support LaTeX rendering as well as symbolic and numerical evaluation (where applicable).

By convention, all builtin symbol names are at least two characters long and start with an uppercase letter. Single-letter symbol names and symbol names beginning with a lowercase letter are reserved for variables.

Here we define a data type FEXR_Builtin where all the C macros are map to constructors. See the instances of Fexpr on how to use the maps.

Documentation

fexpr_builtin_name :: CLong -> IO CString

fexpr_builtin_name n

Returns a pointer for a string giving the name of the builtin symbol with index n

fexpr_builtin_lookup :: CString -> IO CLong

fexpr_builtin_lookup s

Returns the internal index used to encode the builtin symbol with name s in expressions. If s is not the name of a builtin symbol, returns -1

fexpr_builtin_length :: Integer

fexpr_builtin_length

Returns the number of builtin symbols.

Hash maps

fexpr_builtin_hash :: Map FEXR_Builtin CLong

fexpr_builtin_hash_name :: Map String CLong

Built in tags

data FEXR_Builtin

Constructors

FEXPR_AGM

FEXPR_AGMSequence

FEXPR_Abs

FEXPR_Acos

FEXPR_Acosh

FEXPR_Acot

FEXPR_Acoth

FEXPR_Acsc

FEXPR_Acsch

FEXPR_Add

FEXPR_AiryAi

FEXPR_AiryAiZero

FEXPR_AiryBi

FEXPR_AiryBiZero

FEXPR_AlgebraicNumberSerialized

FEXPR_AlgebraicNumbers

FEXPR_All

FEXPR_AnalyticContinuation

FEXPR_And

FEXPR_AngleBrackets

FEXPR_Approximation

FEXPR_Arg

FEXPR_ArgMax

FEXPR_ArgMaxUnique

FEXPR_ArgMin

FEXPR_ArgMinUnique

FEXPR_Asec

FEXPR_Asech

FEXPR_Asin

FEXPR_Asinh

FEXPR_AsymptoticTo

FEXPR_Atan

FEXPR_Atan2

FEXPR_Atanh

FEXPR_BarnesG

FEXPR_BellNumber

FEXPR_BernoulliB

FEXPR_BernoulliPolynomial

FEXPR_BernsteinEllipse

FEXPR_BesselI

FEXPR_BesselJ

FEXPR_BesselJZero

FEXPR_BesselK

FEXPR_BesselY

FEXPR_BesselYZero

FEXPR_BetaFunction

FEXPR_Binomial

FEXPR_Braces

FEXPR_Brackets

FEXPR_CC

FEXPR_Call

FEXPR_CallIndeterminate

FEXPR_Cardinality

FEXPR_CarlsonHypergeometricR

FEXPR_CarlsonHypergeometricT

FEXPR_CarlsonRC

FEXPR_CarlsonRD

FEXPR_CarlsonRF

FEXPR_CarlsonRG

FEXPR_CarlsonRJ

FEXPR_CartesianPower

FEXPR_CartesianProduct

FEXPR_Case

FEXPR_Cases

FEXPR_CatalanConstant

FEXPR_Ceil

FEXPR_Characteristic

FEXPR_ChebyshevT

FEXPR_ChebyshevU

FEXPR_ClosedComplexDisk

FEXPR_ClosedOpenInterval

FEXPR_Coefficient

FEXPR_Column

FEXPR_ColumnMatrix

FEXPR_CommutativeRings

FEXPR_ComplexBranchDerivative

FEXPR_ComplexDerivative

FEXPR_ComplexInfinities

FEXPR_ComplexLimit

FEXPR_ComplexSignedInfinities

FEXPR_ComplexSingularityClosure

FEXPR_ComplexZeroMultiplicity

FEXPR_Concatenation

FEXPR_CongruentMod

FEXPR_Conjugate

FEXPR_ConreyGenerator

FEXPR_Cos

FEXPR_CosIntegral

FEXPR_Cosh

FEXPR_CoshIntegral

FEXPR_Cot

FEXPR_Coth

FEXPR_CoulombC

FEXPR_CoulombF

FEXPR_CoulombG

FEXPR_CoulombH

FEXPR_CoulombSigma

FEXPR_Csc

FEXPR_Csch

FEXPR_Csgn

FEXPR_CurvePath

FEXPR_Cyclotomic

FEXPR_Decimal

FEXPR_DedekindEta

FEXPR_DedekindEtaEpsilon

FEXPR_DedekindSum

FEXPR_Def

FEXPR_Delta

FEXPR_Delta_

FEXPR_Derivative

FEXPR_Det

FEXPR_DiagonalMatrix

FEXPR_DigammaFunction

FEXPR_DigammaFunctionZero

FEXPR_DirichletCharacter

FEXPR_DirichletGroup

FEXPR_DirichletL

FEXPR_DirichletLZero

FEXPR_DirichletLambda

FEXPR_DiscreteLog

FEXPR_Div

FEXPR_Divides

FEXPR_DivisorProduct

FEXPR_DivisorSigma

FEXPR_DivisorSum

FEXPR_DoubleFactorial

FEXPR_EisensteinE

FEXPR_EisensteinG

FEXPR_Element

FEXPR_Ellipsis

FEXPR_EllipticE

FEXPR_EllipticK

FEXPR_EllipticPi

FEXPR_EllipticRootE

FEXPR_Enclosure

FEXPR_Equal

FEXPR_EqualAndElement

FEXPR_EqualNearestDecimal

FEXPR_EqualQSeriesEllipsis

FEXPR_Equivalent

FEXPR_Erf

FEXPR_Erfc

FEXPR_Erfi

FEXPR_Euler

FEXPR_EulerE

FEXPR_EulerPhi

FEXPR_EulerPolynomial

FEXPR_EulerQSeries

FEXPR_Exists

FEXPR_Exp

FEXPR_ExpIntegralE

FEXPR_ExpIntegralEi

FEXPR_ExtendedRealNumbers

FEXPR_Factorial

FEXPR_FallingFactorial

FEXPR_False

FEXPR_Fibonacci

FEXPR_Fields

FEXPR_FiniteField

FEXPR_Floor

FEXPR_For

FEXPR_FormalLaurentSeries

FEXPR_FormalPowerSeries

FEXPR_FormalPuiseuxSeries

FEXPR_FresnelC

FEXPR_FresnelS

FEXPR_Fun

FEXPR_GCD

FEXPR_Gamma

FEXPR_GaussLegendreWeight

FEXPR_GaussSum

FEXPR_GegenbauerC

FEXPR_GeneralLinearGroup

FEXPR_GeneralizedBernoulliB

FEXPR_GeneralizedRiemannHypothesis

FEXPR_GlaisherConstant

FEXPR_GoldenRatio

FEXPR_Greater

FEXPR_GreaterEqual

FEXPR_GreekGamma

FEXPR_GreekGamma_

FEXPR_GreekPi

FEXPR_GreekPi_

FEXPR_Guess

FEXPR_HankelH1

FEXPR_HankelH2

FEXPR_HarmonicNumber

FEXPR_HermiteH

FEXPR_HilbertClassPolynomial

FEXPR_HilbertMatrix

FEXPR_HurwitzZeta

FEXPR_Hypergeometric0F1

FEXPR_Hypergeometric0F1Regularized

FEXPR_Hypergeometric1F1

FEXPR_Hypergeometric1F1Regularized

FEXPR_Hypergeometric1F2

FEXPR_Hypergeometric1F2Regularized

FEXPR_Hypergeometric2F0

FEXPR_Hypergeometric2F1

FEXPR_Hypergeometric2F1Regularized

FEXPR_Hypergeometric2F2

FEXPR_Hypergeometric2F2Regularized

FEXPR_Hypergeometric3F2

FEXPR_Hypergeometric3F2Regularized

FEXPR_HypergeometricU

FEXPR_HypergeometricUStar

FEXPR_HypergeometricUStarRemainder

FEXPR_IdentityMatrix

FEXPR_Im

FEXPR_Implies

FEXPR_IncompleteBeta

FEXPR_IncompleteBetaRegularized

FEXPR_IncompleteEllipticE

FEXPR_IncompleteEllipticF

FEXPR_IncompleteEllipticPi

FEXPR_IndefiniteIntegralEqual

FEXPR_Infimum

FEXPR_Infinity

FEXPR_IntegersGreaterEqual

FEXPR_IntegersLessEqual

FEXPR_Integral

FEXPR_Intersection

FEXPR_Interval

FEXPR_IsEven

FEXPR_IsHolomorphicOn

FEXPR_IsMeromorphicOn

FEXPR_IsOdd

FEXPR_IsPrime

FEXPR_Item

FEXPR_JacobiP

FEXPR_JacobiSymbol

FEXPR_JacobiTheta

FEXPR_JacobiThetaEpsilon

FEXPR_JacobiThetaPermutation

FEXPR_JacobiThetaQ

FEXPR_KeiperLiLambda

FEXPR_KhinchinConstant

FEXPR_KroneckerDelta

FEXPR_KroneckerSymbol

FEXPR_LCM

FEXPR_LaguerreL

FEXPR_LambertW

FEXPR_Lamda

FEXPR_Lamda_

FEXPR_LandauG

FEXPR_Lattice

FEXPR_LeftLimit

FEXPR_LegendreP

FEXPR_LegendrePolynomialZero

FEXPR_LegendreSymbol

FEXPR_Length

FEXPR_LerchPhi

FEXPR_Less

FEXPR_LessEqual

FEXPR_Limit

FEXPR_LiouvilleLambda

FEXPR_List

FEXPR_Log

FEXPR_LogBarnesG

FEXPR_LogBarnesGRemainder

FEXPR_LogGamma

FEXPR_LogIntegral

FEXPR_Logic

FEXPR_LowerGamma

FEXPR_Matrices

FEXPR_Matrix

FEXPR_Matrix2x2

FEXPR_Max

FEXPR_Maximum

FEXPR_MeromorphicDerivative

FEXPR_MeromorphicLimit

FEXPR_Min

FEXPR_Minimum

FEXPR_Mod

FEXPR_ModularGroupAction

FEXPR_ModularGroupFundamentalDomain

FEXPR_ModularJ

FEXPR_ModularLambda

FEXPR_ModularLambdaFundamentalDomain

FEXPR_MoebiusMu

FEXPR_Mul

FEXPR_MultiZetaValue

FEXPR_NN

FEXPR_Neg

FEXPR_Not

FEXPR_NotElement

FEXPR_NotEqual

FEXPR_NumberE

FEXPR_NumberI

FEXPR_Omega

FEXPR_Omega_

FEXPR_One

FEXPR_OpenClosedInterval

FEXPR_OpenComplexDisk

FEXPR_OpenInterval

FEXPR_OpenRealBall

FEXPR_Or

FEXPR_Otherwise

FEXPR_PSL2Z

FEXPR_Parentheses

FEXPR_PartitionsP

FEXPR_Path

FEXPR_Phi

FEXPR_Phi_

FEXPR_Pi

FEXPR_Pol

FEXPR_Poles

FEXPR_PolyLog

FEXPR_Polynomial

FEXPR_PolynomialDegree

FEXPR_PolynomialFractions

FEXPR_PolynomialRootIndexed

FEXPR_PolynomialRootNearest

FEXPR_Polynomials

FEXPR_Pos

FEXPR_Pow

FEXPR_Prime

FEXPR_PrimePi

FEXPR_PrimeProduct

FEXPR_PrimeSum

FEXPR_Primes

FEXPR_PrimitiveDirichletCharacters

FEXPR_PrimitiveReducedPositiveIntegralBinaryQuadraticForms

FEXPR_Product

FEXPR_ProjectiveComplexNumbers

FEXPR_ProjectiveRealNumbers

FEXPR_Psi

FEXPR_Psi_

FEXPR_QQ

FEXPR_QSeriesCoefficient

FEXPR_QuotientRing

FEXPR_RR

FEXPR_Range

FEXPR_Re

FEXPR_RealAbs

FEXPR_RealAlgebraicNumbers

FEXPR_RealBall

FEXPR_RealDerivative

FEXPR_RealInfinities

FEXPR_RealLimit

FEXPR_RealSignedInfinities

FEXPR_RealSingularityClosure

FEXPR_Repeat

FEXPR_Residue

FEXPR_RiemannHypothesis

FEXPR_RiemannXi

FEXPR_RiemannZeta

FEXPR_RiemannZetaZero

FEXPR_RightLimit

FEXPR_Rings

FEXPR_RisingFactorial

FEXPR_Root

FEXPR_RootOfUnity

FEXPR_Row

FEXPR_RowMatrix

FEXPR_SL2Z

FEXPR_Same

FEXPR_Sec

FEXPR_Sech

FEXPR_SequenceLimit

FEXPR_SequenceLimitInferior

FEXPR_SequenceLimitSuperior

FEXPR_Ser

FEXPR_Set

FEXPR_SetMinus

FEXPR_Sets

FEXPR_ShowExpandedNormalForm

FEXPR_Sigma

FEXPR_Sigma_

FEXPR_Sign

FEXPR_SignExtendedComplexNumbers

FEXPR_Sin

FEXPR_SinIntegral

FEXPR_Sinc

FEXPR_SingularValues

FEXPR_Sinh

FEXPR_SinhIntegral

FEXPR_SloaneA

FEXPR_Solutions

FEXPR_SpecialLinearGroup

FEXPR_Spectrum

FEXPR_SphericalHarmonicY

FEXPR_Sqrt

FEXPR_SquaresR

FEXPR_Step

FEXPR_StieltjesGamma

FEXPR_StirlingCycle

FEXPR_StirlingS1

FEXPR_StirlingS2

FEXPR_StirlingSeriesRemainder

FEXPR_Sub

FEXPR_Subscript

FEXPR_Subset

FEXPR_SubsetEqual

FEXPR_Subsets

FEXPR_Sum

FEXPR_Supremum

FEXPR_SymmetricPolynomial

FEXPR_Tan

FEXPR_Tanh

FEXPR_Theta

FEXPR_Theta_

FEXPR_True

FEXPR_Tuple

FEXPR_Tuples

FEXPR_Undefined

FEXPR_Union

FEXPR_UniqueSolution

FEXPR_UniqueZero

FEXPR_UnitCircle

FEXPR_Unknown

FEXPR_UnsignedInfinity

FEXPR_UpperGamma

FEXPR_UpperHalfPlane

FEXPR_WeierstrassP

FEXPR_WeierstrassSigma

FEXPR_WeierstrassZeta

FEXPR_Where

FEXPR_XGCD

FEXPR_XX

FEXPR_Xi

FEXPR_Xi_

FEXPR_ZZ

FEXPR_Zero

FEXPR_ZeroMatrix

FEXPR_Zeros

FEXPR_alpha

FEXPR_alpha_

FEXPR_beta

FEXPR_beta_

FEXPR_chi

FEXPR_chi_

FEXPR_delta

FEXPR_delta_

FEXPR_ell

FEXPR_ell_

FEXPR_epsilon

FEXPR_epsilon_

FEXPR_eta

FEXPR_eta_

FEXPR_gamma

FEXPR_gamma_

FEXPR_iota

FEXPR_iota_

FEXPR_kappa

FEXPR_kappa_

FEXPR_lamda

FEXPR_lamda_

FEXPR_mu

FEXPR_mu_

FEXPR_nu

FEXPR_nu_

FEXPR_omega

FEXPR_omega_

FEXPR_phi

FEXPR_phi_

FEXPR_pi

FEXPR_pi_

FEXPR_rho

FEXPR_rho_

FEXPR_sigma

FEXPR_sigma_

FEXPR_tau

FEXPR_tau_

FEXPR_theta

FEXPR_theta_

FEXPR_varphi

FEXPR_varphi_

FEXPR_vartheta

FEXPR_vartheta_

FEXPR_xi

FEXPR_xi_

FEXPR_zeta

FEXPR_zeta_

Instances

FlintExpression FEXR_Builtin

Defined in Data.Number.Flint.Calcium.Fexpr.Instances

Methods

toFexpr :: FEXR_Builtin -> IO Fexpr

Enum FEXR_Builtin

Defined in Data.Number.Flint.Calcium.Fexpr.Builtin

Methods

succ :: FEXR_Builtin -> FEXR_Builtin

pred :: FEXR_Builtin -> FEXR_Builtin

toEnum :: Int -> FEXR_Builtin

fromEnum :: FEXR_Builtin -> Int

enumFrom :: FEXR_Builtin -> [FEXR_Builtin]

enumFromThen :: FEXR_Builtin -> FEXR_Builtin -> [FEXR_Builtin]

enumFromTo :: FEXR_Builtin -> FEXR_Builtin -> [FEXR_Builtin]

enumFromThenTo :: FEXR_Builtin -> FEXR_Builtin -> FEXR_Builtin -> [FEXR_Builtin]

Show FEXR_Builtin

Defined in Data.Number.Flint.Calcium.Fexpr.Builtin

Methods

showsPrec :: Int -> FEXR_Builtin -> ShowS

show :: FEXR_Builtin -> String

showList :: [FEXR_Builtin] -> ShowS

Eq FEXR_Builtin

Defined in Data.Number.Flint.Calcium.Fexpr.Builtin

Methods

(==) :: FEXR_Builtin -> FEXR_Builtin -> Bool

(/=) :: FEXR_Builtin -> FEXR_Builtin -> Bool

Ord FEXR_Builtin

Defined in Data.Number.Flint.Calcium.Fexpr.Builtin

Methods

compare :: FEXR_Builtin -> FEXR_Builtin -> Ordering

(<) :: FEXR_Builtin -> FEXR_Builtin -> Bool

(<=) :: FEXR_Builtin -> FEXR_Builtin -> Bool

(>) :: FEXR_Builtin -> FEXR_Builtin -> Bool

(>=) :: FEXR_Builtin -> FEXR_Builtin -> Bool

max :: FEXR_Builtin -> FEXR_Builtin -> FEXR_Builtin

min :: FEXR_Builtin -> FEXR_Builtin -> FEXR_Builtin