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Every public built-in function in Mathilda, grouped by category. Each page follows the same shape: Description (the function's docstring), Examples (verified against the current build), Implementation notes, Implementation status, and References.

1129 functions across 38 categories. Use the search box (press /) to jump to any function.

Categories

Algebra

AlgebraicIntegerQ AlgebraicNumber AlgebraicNumberDenominator AlgebraicNumberNorm AlgebraicNumberPolynomial AlgebraicNumberTrace Apart Cancel Coefficient CoefficientList Collect Decompose Denominator Discriminant Expand ExpandDenominator ExpandNumerator Factor FactorSquareFree FactorTerms FactorTermsList GroebnerBasis HornerForm IrreduciblePolynomialQ MinimalPolynomial NumberFieldIntegralBasis Numerator PolynomialExtendedGCD PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialRemainder PowerExpand Resultant RootReduce SubresultantPolynomials Subresultants ToNumberField Together Variables

Arithmetic

Abs Accumulate Accuracy Arg Binomial Ceiling Complex ComplexExpand Conjugate Differences DigitCount DigitSum Divide Factorial Factorial2 FactorialPower Fibonacci Floor FractionalPart FromDigits Im IntegerDigits IntegerExponent IntegerLength IntegerPart IntegerString ListGradient LucasL MantissaExponent Minus Mod N NonCommutativeMultiply Plus Power Precision Quotient QuotientRemainder Rational Rationalize Ratios Re ReIm RealDigits RealExponent Round SetAccuracy SetPrecision Sign Sqrt Subtract Times Total

Assignment and Rules

AddTo Clear ClearAll CompoundExpression Decrement DivideBy DownValues Increment OptionValue Options OwnValues PreDecrement PreIncrement Protect Remove Replace ReplaceAll ReplaceAt ReplaceList ReplaceRepeated Rule RuleDelayed Set SetDelayed SetOptions SubtractFrom TagSet TagSetDelayed TagUnset TimesBy Unprotect Unset UpSet UpSetDelayed

Bitwise operations

BitLength

Calculus

Curl D DSolve Derivative DifferenceDelta Div Dt FindRoot Grad Integrate Laplacian Limit Maximize Minimize PolynomialQuotientRemainder Product Residue SubresultantPolynomialRemainders Sum

Comparisons

Equal Greater GreaterEqual Inequality Less LessEqual SameQ Unequal UnsameQ

Control Flow

$Epilog $Post $Pre $PrePrint $PreRead $RecursionLimit Boole Break Catch Check Compile CompileDiagnostics CompilePrint ConditionalExpression Continue Do Equivalent For Goto If Implies Label Message Piecewise Quiet Return Switch Throw TrueQ Which While Xor

Data Structures

Append Apply ApplyTo AssociateTo Association AssociationComap AssociationMap AssociationQ AssociationThread Cases Catenate Count CountDistinct CountDistinctBy Counts CountsBy Delete DeleteCases DeleteDuplicates DeleteDuplicatesBy DeleteMissing Discard Drop First FoldList Gather GatherBy GroupBy Insert Join JoinAcross Key KeyComplement KeyDrop KeyExistsQ KeyFreeQ KeyIntersection KeyMap KeyMemberQ KeySelect KeySort KeySortBy KeyTake KeyUnion KeyValueMap KeyValuePattern Keys Last LengthWhile Lookup Map MapAt Max Mean Median Merge Min MinMax Missing MissingQ Most Normal Part Partition Pick Position PositionIndex Prepend Rest Select Sort SortBy SparseArray Splice StandardDeviation SubsetQ Take TakeWhile Tally Transpose Values Variance

Elementary Functions

ArcCos ArcSin ArcTan Chop Clip Cos Cosh Cot Csc Exp ExpToTrig Log Log10 Log2 Ramp Sec Sin Sinh Tan Tanh TrigExpand TrigFactor TrigReduce TrigToExp UnitBox UnitStep

Expression Information

$MachineEpsilon $MachinePrecision $MaxMachineNumber $MaxNumber $MinMachineNumber $MinNumber $Version $VersionNumber Activate AtomQ Attributes ByteCount ClearAttributes ComposeList Composition Definition Evaluate EvenQ Flat FreeQ FullForm Hash Hold HoldAll HoldAllComplete HoldComplete HoldForm Identity Inactive Information InputForm IntegerQ LeafCount ListQ MachineNumberQ MatrixQ MaxMemoryUsed MemberQ MemoryInUse Names Negative NonNegative NonPositive NumberForm NumberQ NumericQ OddQ OneIdentity Orderless Positive PossibleZeroQ Print ReleaseHold Row Sequence SequenceHold SetAttributes StandardForm StringQ Symbol TeXForm ToExpression ToString Trace TraditionalForm Unevaluated UpValues ValueQ VectorQ

File I/O

Close Export FileBaseName FileExistsQ FileExtension FileNameJoin FileNameSplit FilePrint FileSize Get Import LoadModule OpenAppend OpenRead OpenWrite Put PutAppend Read ReadList SetStreamPosition StreamPosition Streams Write WriteString

Fourier Transforms

Fourier FourierDCT FourierDST InverseFourier ListConvolve ListCorrelate

Functional Programming

AllTrue AnyTrue Distribute FirstCase FixedPoint FixedPointList Fold Function InterpolatingFunction InterpolatingPolynomial Interpolation ListInterpolation MapAll MapIndexed MapThread MaximalBy MinimalBy Nest NestList NestWhile NestWhileList NoneTrue ReverseSort ReverseSortBy Scan SelectFirst Slot SlotSequence TakeLargest TakeLargestBy TakeSmallest TakeSmallestBy Thread Through

Computational geometry

Area ConvexHullRegion Perimeter RegionCentroid RegionMember

Graphics

Animate ArrayPlot BarChart CMYKColor ComplexPlot ComplexPlot3D ContourPlot DensityPlot Histogram ListPlot Manipulate ParametricPlot ParametricPlot3D Plot Plot3D PolarAxes PolarPlot Show StreamPlot VectorPlot

Graphs

AcyclicGraphQ AdjacencyGraph AdjacencyList AdjacencyMatrix BetweennessCentrality BipartiteGraphQ CanonicalGraph CirculantGraph ClosenessCentrality CompleteGraph CompleteGraphQ CompleteKaryTree ConnectedComponents ConnectedGraphQ CycleGraph DegreeCentrality DirectedGraph DirectedGraphQ EccentricityCentrality EdgeAdd EdgeBetweennessCentrality EdgeConnectivity EdgeCount EdgeCoverQ EdgeDelete EdgeIndex EdgeList EdgeQ EdgeRules EdgeWeight EdgeWeightedGraphQ EigenvectorCentrality EmptyGraphQ EulerianGraphQ FindClique FindCycle FindEdgeCover FindEdgeCut FindEulerianCycle FindGraphIsomorphism FindHamiltonianCycle FindHamiltonianPath FindIndependentEdgeSet FindIndependentVertexSet FindKClique FindMaximumFlow FindMinimumCut FindPath FindShortestPath FindSpanningTree FindVertexColoring FindVertexCover FindVertexCut GlobalClusteringCoefficient Graph GraphAutomorphismGroup GraphCenter GraphComplement GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphIntersection GraphPeriphery GraphPlot GraphQ GraphRadius GraphTriangleCount GraphUnion GridGraph HITSCentrality HamiltonianGraphQ HararyGraph HypercubeGraph IncidenceMatrix IndependentEdgeSetQ IndependentVertexSetQ IndexGraph IsomorphicGraphQ KaryTree KatzCentrality KirchhoffMatrix LineGraph LocalClusteringCoefficient LoopFreeGraphQ MeanClusteringCoefficient MeanGraphDistance MixedGraphQ NeighborhoodGraph PageRankCentrality PathGraph PathGraphQ PetersenGraph PlanarGraphQ RandomGraph ReverseGraph SimpleGraphQ StarGraph StronglyConnectedComponents Subgraph TopologicalSort TreeGraphQ TuranGraph UndirectedGraph UndirectedGraphQ VertexAdd VertexConnectivity VertexCount VertexCoverQ VertexDegree VertexDelete VertexEccentricity VertexInDegree VertexIndex VertexList VertexOutDegree VertexQ VertexReplace WeaklyConnectedComponents WeightedAdjacencyMatrix WeightedGraphQ WheelGraph

Hypergraphs

ConnectedHypergraphQ FindMinimumTransversal HyperedgeConnectedComponents HyperedgeDistance HyperedgeSizes Hypergraph HypergraphCliqueExpansion HypergraphConnectedComponents HypergraphCorank HypergraphDistance HypergraphDual HypergraphEdgeAdd HypergraphEdgeDelete HypergraphLineGraph HypergraphPlot HypergraphQ HypergraphRank HypergraphRestriction HypergraphStarExpansion HypergraphToGraph HypergraphVertexAdd HypergraphVertexDelete RandomHypergraph Subhypergraph TransversalHypergraph UniformHypergraphQ

Image Processing

AlphaChannel Binarize BoxMatrix Closing ColorConvert ColorQuantize ColorReplace CornerFilter DerivativeFilter Dilation DistanceTransform EdgeDetect Erosion FindThreshold GaussianFilter GaussianMatrix GradientFilter HistogramTransform Image Image3D Image3DQ ImageAdjust ImageAssemble ImageChannels ImageCompose ImageConvolve ImageCorners ImageCorrelate ImageCrop ImageData ImageDimensions ImageLevels ImagePad ImageQ ImageReflect ImageResize ImageRotate ImageType LocalAdaptiveBinarize MeanFilter MedianFilter MorphologicalComponents Opening Pruning RandomImage RemoveAlphaChannel SetAlphaChannel Thinning

Linear Algebra

CharacteristicPolynomial ConjugateTranspose Cross DesignMatrix Det Diagonal DiagonalMatrix DiagonalMatrixQ Dot Eigenvalues Eigenvectors FindIntegerNullVector Fit HankelMatrix HermiteDecomposition HermitianMatrixQ HilbertMatrix IdentityMatrix Inner Inverse JordanDecomposition LUDecomposition LatticeReduce LeastSquares LinearSolve MatrixPower MatrixRank NDArray NegativeDefiniteMatrixQ Norm Normalize NullSpace Outer PositiveDefiniteMatrixQ PseudoInverse QRDecomposition RowReduce SchurDecomposition SingularValueDecomposition SquareMatrixQ SymmetricMatrixQ ToeplitzMatrix Tr UpperTriangularMatrixQ VandermondeMatrix

Lists and Iteration

Array ArrayPad ArrayReshape ConstantArray CosineDistance EditDistance EuclideanDistance FindClusters HammingDistance ManhattanDistance Nearest Nothing Permutations Range Rescale Riffle SquaredEuclideanDistance Subdivide Table Tuples UnitVector

Machine Learning

Classify DimensionReduce DimensionReduction LearnDistribution LinearModelFit PDF Predict PrincipalComponents RandomVariate SmoothKernelDistribution Standardize

Mathematical Constants

Catalan Degree E EulerGamma Glaisher GoldenAngle GoldenRatio I Khinchin Pi

Number Theory

ChineseRemainder ContinuedFraction CoprimeQ DirichletCharacter Divisible DivisorSigma Divisors EulerPhi ExtendedGCD FactorInteger FromContinuedFraction GCD IntegerPartitions JacobiSymbol LCM LiouvilleLambda MoebiusMu MultiplicativeOrder NextPrime PartitionsP PartitionsQ PowerMod Prime PrimeNu PrimeOmega PrimePi PrimeQ PrimitiveRoot PrimitiveRootList SquareFreeQ

Numerical Calculus

FindMaximum FindMinimum ND NDSolve NIntegrate NLimit NMaximize NMinimize NProduct NResidue NRoots NSeries NSolve NSum

Packed arrays

FromNDArray FromPackedArray PackedArrayQ ToNDArray ToPackedArray

Pattern Matching

Blank BlankNullSequence BlankSequence Default FirstPosition HoldPattern Longest MatchQ Optional Repeated RepeatedNull Shortest

Power Series

Series SeriesCoefficient SeriesData

Random Number Generation

RandomChoice RandomComplex RandomInteger RandomReal RandomSample SeedRandom

Scoping Constructs

$Context $ContextPath Begin BeginPackage Block Context End EndPackage Module Unique With

Simplification

$Assumptions $SimplifyDebug Assuming Element Refine Simplify SimplifyCount TransformationFunctions

Solutions of Equations

Cubics CylindricalDecomposition Eliminate Exists FindInstance ForAll GeneratedParameters InverseFunctions LogicalExpand NotElement Quartics Reduce Resolve Root RootSum Solve SolveAlways ToRadicals VerifySolutions

Special Functions

AiryAi AiryBi BarnesG BernoulliB BesselI BesselJ BesselK BesselY Beta ChebyshevT ChebyshevU CosIntegral CoshIntegral DirichletL EllipticE EllipticF EllipticK EllipticPi Erf Erfc Erfi EulerE ExpIntegralE ExpIntegralEi FresnelC FresnelS FunctionExpand Gamma HarmonicNumber HermiteH HurwitzZeta Hyperfactorial Hypergeometric0F1 Hypergeometric1F1 Hypergeometric2F1 HypergeometricPFQ HypergeometricU InverseErf InverseErfc LaguerreL LegendreP LegendreQ LerchPhi LogGamma LogIntegral MeijerG Pochhammer PolyGamma PolyLog ProductLog QPochhammer SinIntegral Sinc SinhIntegral StieltjesGamma StruveH WhittakerM WhittakerW Zeta

Statistics

CentralMoment Commonest Correlation Covariance ExponentialMovingAverage InterquartileRange Kurtosis MeanDeviation MedianDeviation Moment MovingAverage MovingMedian Quantile Quartiles RootMeanSquare Skewness

String Operations

Alphabet Capitalize CharacterRange Characters Decapitalize DigitQ FromCharacterCode LetterQ LowerCaseQ RegularExpression StringCases StringContainsQ StringCount StringDelete StringDrop StringEndsQ StringExtract StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPadLeft StringPadRight StringPart StringPartition StringPosition StringRepeat StringReplace StringReplaceList StringReplacePart StringReverse StringRiffle StringRotateLeft StringRotateRight StringSplit StringStartsQ StringTake StringTakeDrop StringTrim ToCharacterCode ToLowerCase ToUpperCase UpperCaseQ

Structural Manipulation

ArrayFlatten CoefficientRules Complement Dimensions ExpandAll Exponent Extract FactorList FactorSquareFreeList Flatten FlattenAt FromCoefficientRules Head Intersection Length Level MonomialList Order OrderedQ Ordering PadLeft PadRight PolynomialReduce RankedMax RankedMin Reverse RotateLeft RotateRight Span Split Union UpTo

Time and Date

$TimeUnit AbsoluteTime AbsoluteTiming DateList Pause RepeatedTiming SessionTime TimeConstrained TimeUsed Timing UnixTime

Other & Advanced

$AutoArrayPacking $AutoCompilation $PlotLegendData $PlotResample $RaylibVerbose $StreamColorBar AccuracyGoal AiryAiPrime AiryBiPrime AspectRatio BarSpacing BesselJZero Black Blue BooleanQ Brown Byte Character ChartLabels ChartStyle ClassifierFunction CoefficientArrays ComplexQ ContourLabels ContourShading ContourStyle Contours Cyan DataType DimensionReducerFunction EndOfFile ExactNumberQ Expression File FourierParameters Frame FrameStyle FrameTicks Gray Green HoldFirst HoldRest ImageSize InexactNumberQ InputStream Interval IntervalIntersection IntervalMemberQ IntervalUnion LearnedDistribution LightBlue LightBrown LightCyan LightGray LightGreen LightMagenta LightOrange LightPink LightPurple LightRed LightYellow Lighting List MachineIntegerQ Magenta Modulus NDArrayQ NormalDistribution NullRecords NullWords Number Orange OrderlessPatternSequence OutputStream PDEClassify PatternSequence Pink PolynomialSqrt PrecisionGoal PredictorFunction Purple RatCanonPrototype RationalQ Real Reap Record RecordSeparators Red ScalingFunctions Sow SplitBy String StringExpression Subsets SymbolName TokenWords UniformDistribution VectorPoints VectorScale VectorStyle Verbatim White Word WordSeparators Yellow

FLINT context

FLINTPolynomialGCD](flint/PolynomialGCD.md) [FLINTResultant FLINTFactor](flint/Factor.md) [FLINTFactorSquareFree FLINTDet](flint/Det.md) [FLINTInverse FLINTLinearSolve](flint/LinearSolve.md) [FLINTRowReduce FLINTMatrixRank](flint/MatrixRank.md) [FLINTZeta FLINTHurwitzZeta](flint/HurwitzZeta.md) [FLINTPolyGamma FLINTStieltjesGamma`

Alphabetical index