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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.

864 functions across 35 categories. Use the search box (press /) to jump to any function.

Categories

Algebra

Apart Cancel Coefficient CoefficientList Collect Decompose Denominator Discriminant Expand ExpandDenominator ExpandNumerator Factor FactorSquareFree FactorTerms FactorTermsList GroebnerBasis HornerForm IrreduciblePolynomialQ MinimalPolynomial Numerator PolynomialExtendedGCD PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialRemainder PowerExpand Resultant RootReduce SubresultantPolynomials Subresultants 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 LucasL MantissaExponent Mod N 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 TimesBy Unprotect Unset

Calculus

Curl D Derivative DifferenceDelta Div Dt FindRoot Grad Integrate Laplacian Limit 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 Compile CompileDiagnostics CompilePrint ConditionalExpression Continue Do Equivalent For Goto If Implies Label Piecewise Return Switch Throw TrueQ Which While Xor

Data Structures

Append Apply AssociateTo Association AssociationMap AssociationQ AssociationThread Cases Count Counts CountsBy Delete DeleteCases DeleteDuplicates DeleteDuplicatesBy DeleteMissing Drop First FoldList Gather GatherBy GroupBy Join KeyDrop KeyExistsQ KeyFreeQ KeyMap KeyMemberQ KeySelect KeySort KeySortBy KeyTake KeyUnion KeyValueMap KeyValuePattern Keys Last LengthWhile Lookup Map MapAt Max Mean Median Merge Min MinMax Most Position PositionIndex Prepend Rest Select Sort SortBy StandardDeviation Take TakeWhile Tally Values Variance

Elementary Functions

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

Expression Information

$MachineEpsilon $MachinePrecision $MaxMachineNumber $MaxNumber $MinMachineNumber $MinNumber $Version $VersionNumber AtomQ Attributes ByteCount ClearAttributes ComposeList Composition Evaluate EvenQ Flat FreeQ FullForm Hold HoldAll HoldAllComplete HoldComplete HoldForm Identity 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 StringQ Symbol TeXForm ToExpression ToString Trace Unevaluated ValueQ VectorQ

File I/O

Export FileBaseName FileExistsQ FileExtension FileNameJoin FileNameSplit FilePrint Get Import LoadModule Put PutAppend

Fourier Transforms

Fourier FourierDCT FourierDST InverseFourier ListConvolve ListCorrelate

Functional Programming

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

Graphics

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

Graphs

Graph GraphQ

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 LUDecomposition LatticeReduce LeastSquares LinearSolve MatrixPower MatrixRank NDArray NegativeDefiniteMatrixQ Norm Normalize NullSpace Outer PositiveDefiniteMatrixQ PseudoInverse QRDecomposition RowReduce SingularValueDecomposition SquareMatrixQ SymmetricMatrixQ ToeplitzMatrix Tr UpperTriangularMatrixQ VandermondeMatrix

Lists and Iteration

Array 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 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 ToNDArray ToPackedArray

Pattern Matching

Blank BlankNullSequence BlankSequence Default HoldPattern Longest MatchQ Optional Repeated RepeatedNull Shortest

Power Series

Normal 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 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 CosIntegral CoshIntegral Erf Erfc Erfi EulerE ExpIntegralEi Gamma HarmonicNumber HurwitzZeta Hyperfactorial Hypergeometric0F1 Hypergeometric1F1 Hypergeometric2F1 HypergeometricPFQ InverseErf InverseErfc LegendreP LerchPhi LogGamma LogIntegral Pochhammer PolyGamma PolyLog ProductLog QPochhammer SinIntegral Sinc SinhIntegral StieltjesGamma Zeta

Statistics

CentralMoment Commonest Correlation Covariance ExponentialMovingAverage Kurtosis Moment MovingAverage MovingMedian Quartiles RootMeanSquare Skewness

String Operations

Characters RegularExpression StringCases StringContainsQ StringCount StringDrop StringEndsQ StringExtract StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPadLeft StringPadRight StringPart StringPartition StringPosition StringRepeat StringReplace StringReplacePart StringReverse StringRiffle StringSplit StringStartsQ StringTake StringTrim

Structural Manipulation

ArrayFlatten Catenate Complement Dimensions ExpandAll Exponent Extract FactorList Flatten FlattenAt Head Insert Intersection Length Level Order OrderedQ Ordering PadLeft PadRight Part Partition RankedMax RankedMin Reverse RotateLeft RotateRight Span Split Transpose Union UpTo

Time and Date

AbsoluteTime AbsoluteTiming RepeatedTiming TimeConstrained Timing

Other & Advanced

$AutoArrayPacking $AutoCompilation $PlotLegendData $PlotResample $RaylibVerbose $StreamColorBar AccuracyGoal AdjacencyGraph AdjacencyList AdjacencyMatrix AiryAiPrime AiryBiPrime AspectRatio BarSpacing BesselJZero Black Blue Brown ChartLabels ChartStyle ClassifierFunction CompleteGraph ComplexQ ConnectedComponents ConnectedGraphQ ContourLabels ContourShading ContourStyle Contours Cyan CycleGraph DataType DimensionReducerFunction DirectedGraphQ EdgeCount EdgeList ExactNumberQ FindShortestPath FindSpanningTree FourierParameters Frame FrameStyle FrameTicks FresnelC FresnelS GraphDistance GraphPlot Gray Green HoldFirst HoldRest ImageSize IncidenceMatrix InexactNumberQ Interval IntervalIntersection IntervalMemberQ IntervalUnion LearnedDistribution LightBlue LightBrown LightCyan LightGray LightGreen LightMagenta LightOrange LightPink LightPurple LightRed LightYellow Lighting List MachineIntegerQ Magenta Modulus NDArrayQ NormalDistribution Orange OrderlessPatternSequence PathGraph PatternSequence Pick Pink PolynomialSqrt PrecisionGoal PredictorFunction Purple RandomGraph RatCanonPrototype RationalQ Reap Red ScalingFunctions Sow SplitBy StringExpression StronglyConnectedComponents Subsets UniformDistribution VectorPoints VectorScale VectorStyle Verbatim VertexConnectivity VertexCount VertexDegree VertexInDegree VertexList VertexOutDegree WeaklyConnectedComponents White 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