Skip to content

Documentation Center

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.

700 functions across 32 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 FromDigits Im IntegerDigits IntegerExponent IntegerLength IntegerString LucasL MantissaExponent N Plus Power Precision Rational Rationalize Ratios Re ReIm RealDigits RealExponent Round SetAccuracy SetPrecision Sign Sqrt Subtract Times Total

Assignment and Rules

AddTo Clear ClearAll CompoundExpression Decrement DownValues Increment OptionValue Options OwnValues PreDecrement PreIncrement Protect Remove Replace ReplaceAll ReplaceAt ReplaceList ReplaceRepeated Rule RuleDelayed Set SetDelayed SetOptions SubtractFrom Unprotect Unset

Calculus

D Derivative DifferenceDelta Dt FindMaximum FindMinimum FindRoot Integrate 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 ConditionalExpression Continue Do For Goto If Label Piecewise Return Switch Throw TrueQ Which While

Data Structures

Append Apply AssociateTo Association AssociationMap AssociationQ AssociationThread Cases Count Counts CountsBy Delete DeleteCases DeleteDuplicates DeleteDuplicatesBy DeleteMissing Drop First FoldList 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 Sec Sin Sinh Tan Tanh TrigExpand TrigFactor TrigReduce TrigToExp 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 MemberQ Names Negative NonNegative NonPositive NumberQ NumericQ OddQ OneIdentity Orderless Positive PossibleZeroQ Print ReleaseHold Sequence SequenceHold SetAttributes Symbol TeXForm ToExpression ToString Trace Unevaluated ValueQ VectorQ

File I/O

FileBaseName FileExistsQ FileExtension FileNameJoin FileNameSplit FilePrint Get LoadModule Put PutAppend

Fourier Transforms

Fourier FourierDCT FourierDST InverseFourier ListConvolve ListCorrelate

Functional Programming

AllTrue AnyTrue Distribute FirstCase FixedPoint FixedPointList Fold Function InterpolatingFunction 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 BarChart CMYKColor ComplexPlot ComplexPlot3D ContourPlot DensityPlot Histogram ListPlot ParametricPlot ParametricPlot3D Plot Plot3D PolarAxes PolarPlot Show StreamPlot VectorPlot

Graphs

Graph GraphQ

Linear Algebra

ConjugateTranspose Cross DesignMatrix Det DiagonalMatrix DiagonalMatrixQ Dot Eigenvalues Eigenvectors FindIntegerNullVector Fit HankelMatrix 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 Permutations Range Rescale Table Tuples UnitVector

Mathematical Constants

Catalan Degree E EulerGamma Glaisher GoldenAngle GoldenRatio I Khinchin Pi

Number Theory

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

ND NIntegrate NLimit NProduct NResidue NRoots NSeries NSolve NSum

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 With

Simplification

$Assumptions $SimplifyDebug Assuming Element Simplify SimplifyCount TransformationFunctions

Solutions of Equations

Cubics Eliminate GeneratedParameters InverseFunctions Quartics 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

Commonest ExponentialMovingAverage MovingAverage MovingMedian Quartiles RootMeanSquare

String Operations

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

Structural Manipulation

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

Time and Date

AbsoluteTime RepeatedTiming TimeConstrained Timing

Other & Advanced

$PlotLegendData $PlotResample $StreamColorBar AdjacencyGraph AdjacencyList AdjacencyMatrix AiryAiPrime AiryBiPrime AspectRatio BarSpacing BesselJZero Black Blue Brown ChartLabels ChartStyle CompleteGraph ConnectedComponents ConnectedGraphQ ContourLabels ContourShading ContourStyle Contours Cyan CycleGraph DataType DirectedGraphQ EdgeCount EdgeList FindShortestPath FindSpanningTree FourierParameters Frame FrameStyle FrameTicks FresnelC FresnelS GraphDistance GraphPlot Gray Green HoldFirst HoldRest ImageSize IncidenceMatrix LightBlue LightBrown LightCyan LightGray LightGreen LightMagenta LightOrange LightPink LightPurple LightRed LightYellow Lighting List Magenta NDArrayQ Orange PathGraph Pink PolynomialSqrt Purple RandomGraph RatCanonPrototype Reap Red ScalingFunctions Sow StringExpression StronglyConnectedComponents VectorPoints VectorScale VectorStyle 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