# • ### WolframModelSignatureForm

Give the formatted form of a signature specification for a Wolfram model rule or state

• ### WolframModelData

Retrieve information on a Wolfram model from the Registry of Notable Universes

• ### RandomWolframModel

Generate a random canonical Wolfram model rule with a particular signature

• ### WolframModelRuleForm

Represent a Wolfram model in x, y, … letter form

Display a Wolfram model description in an analog of traditional mathematical notation

• ### EnumerateWolframModelRules

Enumerate canonical Wolfram model rules with a particular signature

• ### CanonicalWolframModelRule

Attempt to find a canonical representation for a Wolfram model

• ### ConnectedWolframModelQ

Determine whether a Wolfram model rule is left-connected

• ### WolframModel

Generate evolutions of Wolfram model systems

• ### HypergraphNeighborhoods

Enumerate all the neighborhoods of a hypergraph up to a given distance

• ### WolframMark

Run the standard Wolfram Language benchmark

• ### HypergraphNeighborhoodVolumes

Find the volumes of successively larger neighborhoods around nodes in a hypergraph

• ### EnumerateRuleSignatures

Enumerate possible rule signatures for substitution systems, Wolfram models, etc

• ### WolframModelEvolutionObject

Represent the result of evolution of a Wolfram model

• ### RandomSubstitutionSystemRule

Generate a random string substitution rule

• ### IteratedFiniteAutomaton

Iteratively apply a transducer finite automaton

• ### WolframModelPlot

Generate a visual display of a hypergraph

• ### HypergraphPlot

Plot a hypergraph defined by a list of hyperedges

• ### IsingModelCA

Simulate the Ising model using a cellular automata

• ### HuffmanDecode

Decode data specified by a Huffman encoding

Find the adjacency matrix for vertices in a hypergraph

• ### ConnectedHypergraphQ

Determine whether a hypergraph is connected

• ### RaggedMeanAround

Compute MeanAround for corresponding elements in a collection of lists of potentially different lengths

• ### TagSystemRulePlot

Generate the rule icon for a tag system

• ### DateListPlotRanged

Plot a time series that includes shading to indicate ranges in the plotted value

• ### HuffmanCodeWords

Find optimal Huffman code words given a list of probabilities

• ### SequentialSubstitutionSystemRulePlot

Generate the rule icon for a sequential substitution system

• ### RandomHypergraph

Generate a random hypergraph

• ### FiniteStateIndicatorIcon

Give graphics to indicate the state of a finite-state system such as the head of a Turing machine

• ### BitBooleanFunction

Apply a Boolean function to corresponding bits in integers

• ### StringOverlapsQ

Test whether a string or strings have overlaps

• ### HypergraphToGraph

Convert a hypergraph to a graph with the same distance matrix

• ### HuffmanEncode

Find a Huffman encoding from a list

• ### OverlapFreeStringTuples

Find all overlap-free strings of a specified length

• ### MobileAutomatonRulePlot

Generate the rule icon for a mobile automaton

• ### SequentialSubstitutionSystem

Compute the evolution of a sequential substitution system

• ### FindEquationalModels

Find instances of a binary operator that satisfy equational constraints

• ### DottedArrayPlot

Plot an array of values, with dots at specified positions

• ### ProgressiveMaxPositions

Find the positions of the largest elements so far in a list

• ### SequentialSubstitutionSystemPlot

Visualization of the evolution of a sequential substitution system

• ### MobileAutomaton

Compute the evolution of a mobile automaton

• ### CyclicTagSystem

Compute the evolution of a cyclic tag system

• ### SequentialCellularAutomaton

Cellular automaton evolution with the order of each cell update specified

• ### StringOverlaps

Find substrings that overlap between strings

• ### MobileAutomatonPlot

Visualization of the evolution of a mobile automaton

• ### LogDifferences

Find logarithmic differences of elements in a list

• ### TorusGraph

Create a grid graph of any dimension with the topology of a torus

• ### TagSystem

Compute the evolution of a tag system

• ### BinaryCodedTernary

Self-delimiting number representation

• ### CausalConnectionGraph

Generate a graph giving the relations between regions of causally equivalent events in a causal graph

• ### FindWolframModelProof

Try to find a proof of equivalence between hypergraphs in a given multiway Wolfram model system

• ### WolframPhysicsProjectStyleData

Look up styles used in the Wolfram Physics Project

• ### GraphicsMetricGraph

Create a mesh representing a metric from a graphic

• ### DistanceLayeredGraph

Render a graph with vertices at heights based on their distance from the root

• ### GraphAntipodes

Find a pair of vertices that are a maximum distance apart on a graph

• ### CayleyNestGraph

Create a generalized Cayley graph from generators and relations

• ### EnumerateHypergraphs

Enumerate possible ordered hypergraphs with a given signature

• ### GraphReconstructedSurface

Embed a hypergraph into a surface

• ### GenerationalMultiwaySystem

Compute the evolution of a generational multiway system and many associated properties

• ### SubstitutionSystemPlot

Visualize the evolution of a one-dimensional neighbor-independent substitution system

• ### LayeredGraphPlot3D

Generate a layered 3D plot of a graph

• ### EnumerateSubstitutionSystemRules

Enumerate possible inequivalent string substitution rules with a given signature

• ### MultiwayFunctionSystem

Compute the evolution of a multiway system based on function evaluation over the integers

• ### GraphMinors

Enumerate the graph minors of a graph

• ### ModusPonensToEquational

Convert an axiom system from modus ponens to equational form

• ### PrioritizedSubstitutionSystem

Compute the evolution of a substitution system where replacements are specified by a priority list

• ### MultiwayEvolutionPlot

Plot the evolution of a multiway system

• ### GraphFunctionPlot

Plot the values of a function at the vertices of a graph

• ### StringTuples

Generate a list of all tuples of characters from a string

• ### SymbolNameTranslate

Get the translated name of a Wolfram Language symbol in a given language

• ### NewWLSession

Start a new Wolfram Language session

• ### FibonacciEncode

Fibonacci-digit encoding for a number

• ### InteractiveListSelector

Interactively select elements of a one-dimensional list

Find the distinct heads that occur in an expression and their corresponding arities

• ### ResourceSubmissions

Retrieve a list of submissions to the Wolfram Resource System

• ### MultiwaySystem

Compute the evolution of a multiway system and many associated properties

• ### CellularAutomatonFromNumber

Convert numbers specifying a cellular automaton into an explicit list of rules

• ### BlockCellularAutomaton

Evolve a block cellular automaton

• ### CellularAutomatonNumber

Convert an explicit list of rules specifying a cellular automaton into the corresponding rule number

• ### ResourceFunctionSearch

Search the Wolfram Resource System for specified resource functions

• ### CategoryResourceFunctions

List all of the Wolfram Function Repository resources in a category

• ### GraphNeighborhoodVolumes

Find the volumes of successively larger neighborhoods around nodes in a graph

• ### DepthLeafCountSort

Sort expressions by depth and leaf count

• ### TuringMachineFromNumber

Convert numbers specifying a Turing machine into an explicit list of rules

• ### CompressCloudObject

Compress the contents of a cloud object that contains a Wolfram Language expression

• ### MarkdownTableString

Convert Wolfram Language data into Markdown-friendly table strings

• ### ComputationalEssayTemplate

Open a computational essay template with tools for streamlined essay writing and publishing

• ### RunOnQuit

Set an evaluation to run when the Wolfram Language kernel session is terminated

• ### MultiwayTuringMachine

Simulate a nondeterministic Turing machine evolution as a multiway system

• ### Spotlight

Access the Spotlight feature in macOS from within the Wolfram Language

• ### SameInstanceQ

Determine if two Wolfram Language expressions come from the same instance

• ### FindFiniteModels

Finds finite models consistent with the set of relations

• ### FindEquationalCounterexample

Try to find a counterexample to an equational hypothesis in a given system of axioms

• ### MultiwayMonoid

Simulate an arbitrary (potentially commutative) monoid as a multiway system

• ### MultiwayGroup

Simulate an arbitrary (potentially abelian) group as a multiway system

• ### VisualizeSpanningCharacters

Display a table of all horizontal or vertical spanning characters used by the current Wolfram Notebook front end

• ### CloudResourceFunction

Access functions deployed to your own or another user’s Wolfram Cloud account that are not in the official Function Repository

• ### PiTopConnect

Provide Wolfram Language–based access to the pi-top Maker Architecture available for the pi-top 

• ### FindListProof

Try to find a proof of equivalence between lists in a given multiway system

• ### MultiwaySemigroup

Simulate an arbitrary (potentially commutative) semigroup as a multiway system

• ### FindStringProof

Try to find a proof of equivalence between strings in a given multiway system

• ### MultiwayOperatorSystem

Simulate the evaluation of a formal operator expression as a multiway system

• ### CatchFailure

Catches any Failure object thrown by an enclosed ThrowFailure evaluation

• ### ContextDependencies

Determine how symbols in a first context depend on symbols in a second context

• ### NFourierTrigSeries

Find a numerical approximation for a trigonometric Fourier series expansion of a function

• ### DynamicCellularAutomaton

Generate a cellular automaton evolution with initial conditions chosen by a click

• ### MachineIntegerQ

Check if a number falls into the range of machine-sized integers for your computer

• ### WishartDistribution

Represent the Wishart distribution

• ### BesselSimplify

Simplify Bessel functions in expression

• ### MultivariateMeanDeviation

Find the scalar mean of the Euclidean distances between the multivariate data points and their mean

• ### ReplaceAllUnheld

Apply replacement rules to evaluated parts of expression

• ### TakeLarger

Take values larger than a threshold in a list or association

• ### AssociationPartition

Partition an association into a list of associations

• ### TwinPrimes

Get the pairs of primes that differ by 2

• ### VarianceRatioCI

Estimate the confidence interval of the ratio of the population variances

• ### NLimit

Find the limiting value of an expression numerically

• ### ProvablePrimeQ

Certify a number as provably prime

• ### KSetPartitions

Give all possible ways to partition a set into a given number of subsets, ignoring order of blocks and within blocks

• ### SexyPrimes

Get the pairs of primes that differ by 6

• ### RationalInterpolation

Find a rational interpolation of a function

• ### ToInversionVector

Get the inversion vector of a permutation written as a list

• ### InversionVectorQ

Check if a list is the inversion vector of a permutation written as a list

• ### DerangementQ

Test whether the permutation list is completely scrambled

• ### ButcherTreeCount

Get a list of the number of Butcher trees through a given order

• ### ToPrompterNotebook

Create a slide show prompter from a notebook

• ### PythonPackageUninstall

Uninstall a Python package

• ### NFourierTransform

Find a numerical approximation for a Fourier transform

• ### NInverseFourierCosTransform

Find a numerical approximation for an inverse Fourier cosine transform

• ### PolyLogSimplify

Simplify polylogarithms in an expression

• ### EasterSunday

Find the date of Easter Sunday for a given year

• ### NSeries

Find a numerical approximation of a series expansion of a function

• ### TakeAfter

Take elements after a specified element in an expression

• ### SetPartitions

Give all possible ways to partition a set into blocks, ignoring the order of blocks and order within blocks

• ### ShuffleOrder

Determine how many shuffles restore the list of specified size to its original order

• ### EasterSundayGreekOrthodox

Find the date of Easter Sunday according to the Greek Orthodox Church

• ### ThrowFailure

Throw a Failure object to the nearest enclosing CatchFailure

• ### EulerEquations

Get the Euler–Lagrange differential equations derived from a given functional

• ### SimplexMedian

Get the simplex median of the elements of a matrix

• ### InterpolatingFunctionDomain

Obtain the domain of an interpolating function object

• ### TotalVariation

Get the total variation of a matrix

• ### BinarySearchBy

Find the position of a target value within an array sorted after applying a function

Represent the distribution of a quadratic form with a multivariate normal

• ### InverseFourierCoefficient

Find a function with a given Fourier exponential series

• ### TuringMachineCausalGraph

Generate a causal graph of the Turing machine evolution

• ### NInverseFourierSinTransform

Find a numerical approximation for an inverse Fourier sine transform

• ### IntegerPartitionQ

Check whether the argument is a weakly decreasing list of positive integers

• ### FRatioCI

Estimate the confidence interval based on an F-ratio distribution

Compute a matrix of well depth values representing a quadratic-residue diffuser

• ### MultivariateMedianDeviation

Find the median Euclidean distance from the median of the elements of multivariate data

• ### GrayCode

Find the Gray code for an integer

• ### EllipsoidQuantile

Find ellipsoidal location statistics

• ### ButcherRowConditions

Give the row-simplifying conditions for Runge–Kutta methods

• ### PhiNumberSystem

Get a list of powers of the golden ratio which sum to a given integer

• ### ButcherPhi

Compute the weight of a Butcher tree

• ### OSMImport

Import OSM (OpenStreetMap) data from XML files or the OSM API

• ### NFourierCoefficient

Find a numerical approximation for a Fourier exponential series coefficient of a function

Give the quadrature conditions for Runge–Kutta methods

• ### EconomizedRationalApproximation

Find an economized rational approximation to a function

• ### MultivariateKurtosis

Find the kurtosis coefficient for multivariate data

• ### GammaSimplify

Simplify gamma functions in expression

• ### ReflectPoints

Reflect a set of points using a line or plane defined by two or three points

• ### NormalCI

Estimate the confidence interval based on a normal distribution

• ### PrimeQCertificateCheck

Test if a certificate can be used for ascertaining the primality or compositeness of a number

• ### PairwiseScatterPlot

Construct a scatter plot matrix

• ### ButcherTreeQ

Determine if a Butcher tree is in valid functional syntax

• ### ChiSquareCI

Estimate the confidence interval based on a Chi-squared distribution

• ### PlouffeP

Get the value of the Plouffe P function

• ### GeneralMiniMaxApproximation

Find a mini-max approximation of a function defined parametrically

• ### NFourierSequenceTransform

Find a numerical approximation to the Fourier sequence transform

• ### SyntaxHighlight

Syntax-highlight a code string

• ### EchoPerformance

Print the timing and memory used to evaluate an expression

• ### TakeSmaller

Take values smaller than a threshold in a list or association

• ### NFourierSeries

Find a numerical approximation for an exponential Fourier series expansion of a function

• ### TetrahedronEdgeAngles

Given edgelengths of a tetrahedron, return the dihedral angles opposite those edges

• ### NDerivative

Find a numerical approximation to a function derivative near the specified point

• ### NInverseFourierCoefficient

Find a numerical approximation for a function with a given Fourier exponential series

• ### NInverseFourierTransform

Find a numerical approximation for the inverse Fourier transform

• ### AssociationKeyFlatten

Flatten keys in a nested association

• ### Derangements

Give all the ways the numbers 1, 2, …, n can be scrambled completely

• ### Monus

Truncate negative numbers in the result of subtraction

• ### NotebookHistoryDialog

Explore history of changes in the currently open notebooks

• ### CousinPrimes

Get the pairs of primes that differ by 4

• ### RungeKuttaOrderConditions

List equations for Runge–Kutta methods

• ### ButcherPlot

Plot order condition trees for Runge–Kutta method

• ### NewtonCotesError

Find the error in the Newton–Cotes quadrature formula

• ### ANOVA

Perform an analysis of variance

• ### DyckWords

Give all possible ways to form proper brackets

• ### UlamSequence

Starting with the third term, give the least integer expressible uniquely as the sum of two distinct earlier terms

• ### ButcherPrincipalError

Get a list of terms in the Taylor series expansion of the error for Runge–Kutta methods

• ### ZetaSimplify

Simplify zeta functions in expressions

• ### VariationalBound

Find the values of parameters of a trial function that extremize a functional

• ### FromInversionVector

Construct the permutation list corresponding to the given inversion vector

• ### EveryOther

Split a list into two sublists gathering every other element of the list

• ### GeneralRationalInterpolation

Find a rational interpolation of a function defined parametrically

• ### ZeckendorfRepresentation

Give the 0–1 list that indicates the unique nonconsecutive Fibonacci numbers that sum to the non-negative integer input

• ### VariationalD

Get the variational derivative of a functional

• ### PolyGammaSimplify

Simplify polygamma functions in an expression

• ### CircularWinder

Create a rotatable arrow handle

• ### TakeBefore

Take elements before the specified element in an expression

• ### BinCountAssociation

Collect histogram data in an association of bin intervals and bin heights

• ### StrictIntegerCompositions

Generate the zero-free compositions of a positive integer

• ### StudentTCI

Estimate the confidence interval based on Student t distribution

• ### InterpolatingFunctionData

Extract data from an InterpolatingFunction object

• ### PermutationInvolutionQ

Test whether a permutation equals its inverse

• ### Spirograph

Plot a spirograph

• ### PermutationAscents

Give the indices of a permutation where there is an immediate ascent

• ### SetOutputFormCellLabels

Set up custom cell labels for a formatting function

Get a list of abscissa-weight pairs based on the Gaussian quadrature

• ### CellInformation

Retrieve information about selected cells in notebook

• ### PythonVersion

Display the Python version installed on your machine

• ### NFourierSinTransform

Find a numerical approximation for a Fourier sine transform

• ### JewishNewYear

Find the date of the Jewish New Year

• ### ButcherTreeData

Get characteristics of Butcher trees, such as the height, width, order, density and number of labelings

• ### LargestPrimeGap

Give the greatest gap between the primes up to the argument

• ### ConjugatePartition

Switch the rows and columns of a partition

• ### PermutationCyclesGraph

A graph representing cycles and fixed points of a permutation

• ### HexagonalGridGraph

Generate a graph corresponding to a hexagonal grid

• ### NVariationalBound

Search numerically for the values of parameters of a trial function that extremize a functional

• ### MultivariateTrimmedMean

Find the mean of multivariate data after removing outermost points

• ### PolynomialTotalDegree

Get the total degree of a polynomial in any number of variables

Find the error in the Gaussian quadrature approximation of a function’s integral

• ### EllipsoidQuartiles

Find the ellipsoidal loci of the quartiles of matrix

• ### StemLeafPlot

Construct a stem-and-leaf diagram

• ### GeneralizedVariance

Find the determinant of the covariance matrix

• ### PythonPackageInformation

Display information for a Python package

• ### DuplicatesList

Give the elements that appear more than once in the input list

• ### BinarySearch

Find the position of a target value within a sorted array

• ### NFourierSinCoefficient

Find a numerical approximation for a Fourier sine coefficient of a function

• ### TriangleEdgeAngles

Given edge lengths of a triangle, return the angles opposite those edges

• ### RaggedDigitsPlot

Plot an array of digits, allowing them to be ragged on the left

• ### RationalFunctionQ

Determine whether an expression represents a rational function of a given set of variables

• ### NewtonCotesWeights

Get the abscissa–weight pairs of the elementary Newton–Cotes formula

• ### NResidue

Find a numerical approximation of a residue of an expression around the specified point

• ### ButcherTreeSimplify

Get the butcher trees through a given order that are not reduced by Butcher’s quadrature or row- or column-simplifying conditions

• ### EulerianNumber

Get the number of permutations with a given number of ascents

• ### MinSumPermutation

Find a permutation that minimizes a matrix sum

• ### FlameChart

Visualize data as a flame chart

• ### NFourierCosCoefficient

Find a numerical approximation for a Fourier cosine coefficient of a function

Crop uniform values from the edges of an array

• ### EllipsoidProbability

Find the cumulative probability within the specified elliptic domain

• ### MiniMaxApproximation

Find a mini-max approximation of a function

• ### ComputationalSystemRules

Find explicit sets of rules for computational systems

• ### ButcherTrees

Get a list of the trees for any Runge-Kutta method of a given order

• ### PythonPackageInstall

Install a Python package

Checks hyperlinks in an expression, webpage, or notebook, on your computer or in the cloud

• ### PythonPackageList

List Python packages available on your machine

• ### PerforatePolygons

Make a hole in the middle of a polygon

• ### TwoSidedPValue

Find the probability of the absolute value of the test statistic being at least as extreme as the given value

• ### SendMailFromNotebook

Send mail messages defined by sections in a notebook

• ### Quaternion

Represent a quaternion object

• ### NInverseFourierSequenceTransform

Find a numerical approximation to the inverse Fourier sequence transform of a periodic function

Plot a 3D relief representing a quadratic-residue diffuser

• ### NotebookHistoryData

Collect history of changes in the currently open notebooks

• ### NFourierCosTransform

Find a numerical approximation for a Fourier cosine transform

• ### ButcherColumnConditions

Give the column-simplifying conditions for Runge–Kutta methods

• ### MeanDifferenceCI

Estimate the confidence interval of the difference between the population means

• ### FileFormatQ

Test if a file is in the specified format

• ### Cofactor

Get a cofactor of a matrix

• ### FerrersDiagram

Display the Ferrers diagram of a partition with dots

• ### SelectAtoms3D

Interactively select atom indices from a 3D molecule plot

• ### FromAtomicNumber

Find the element for a given atomic number.

• ### Excise

Remove enclosed arguments

• ### ChemicalNameToSMILES

Convert a chemical name into a SMILES identifier string

• ### SignificantDigits

Determine the number of significant digits in a number

• ### AtomicNumber

Find the atomic number for a given element

• ### NestedLookup

Look up a set of keys in order to get deeper parts of an association or list of rules

• ### IntegrateByParts

Get an inactive expression representing an integration by parts

• ### InactiveFactorInteger

Compute the prime factorization of an integer and return it in an inactivated form

• ### FermatPrime

Find the nth Fermat number that is also a prime number

• ### HasDefinitionsQ

Check if a symbol has definitions associated with it

• ### BinarySerializeWithDefinitions

Serialize an expression along with any dependent definitions

• ### ExpressionBag

A data structure meant for accumulating items efficiently

Evaluate an expression when a package is first loaded

• ### ToAssociations

Recursively replace lists of rules with associations

Save a notebook to a file that is formatted to maximize readability when viewing changes in version control systems

• ### GaloisGroupProperties

Compute the Galois group for a polynomial

• ### FunctionDiscontinuities

Compute the discontinuities of a function of a single variable

• ### RatioSimplify

Simplify a list as if it were a ratio

• ### Logit

The logit function from probability

• ### MonitoredTestReport

Generate a TestReportObject with dynamic progress

• ### EvenFunctionQ

Determine whether an expression is an even function of the given variable or variables

• ### ReapAssociation

Equivalent to Reap, but returns an association with tags as keys

• ### HyperbolaProperties

Get an association of the properties of a given hyperbola

• ### CloseCellGroups

Close cell groups in a notebook by style

• ### EnlargeBoundingBox

Increase a bounding box by a fractional amount

• ### ClockHandsAngles

Compute the angle between the hands of a clock

• ### ArcTanDegree

Compute the inverse tangent of a number and return a result in degrees

• ### SymbolDependencies

Get a list of symbols that an expression depends on

• ### NthDigit

Compute the digit in a given place of the positional representation of a number

• ### OrderedGraphModelPlot

Plots ordered trivalent graphs

• ### SinDegree

Compute the sine of an angle given in degrees

• ### GetKeyValuePattern

Create a suitable KeyValuePattern from an example association

• ### SystemNotifier

Create a system tray icon that can be used to issue system notifications

• ### MersennePrime

Find the nth Mersenne prime

• ### MockTheta

Implement the Ramanujan mock theta functions

• ### CheckMatch

Verify that an evaluation output matches a given pattern and produces no errors

• ### PopulationVariance

Compute the population variance for a set of data

• ### RelativePath

Create a file path relative to a given directory

• ### RatioEqual

Check if two lists are equal as ratios

• ### HoldArguments

Construct a function from another function that holds certain arguments

• ### DiagonalIntersectionsCount

Find the number of intersections of the diagonals of a regular polygon

• ### HessianMatrix

Compute the Hessian matrix of a function with respect to a list of variables

• ### KatakanaQ

Test if a string is composed of katakana characters

• ### DeficientNumberQ

Check whether an input is a deficient number

• ### FindPythonExecutable

Automatically attempt to find a Python executable on the current machine

• ### ShowDefinitions

Get a browsable, hyperlinked definition of a symbol

• ### DefinitionData

Store full definitions for a symbol in a compact object

• ### BytesToQuantity

Convert a byte count to a quantity of bytes in an appropriate unit

• ### SymbolDependencyGraph

Create a graph of symbol dependencies

• ### AutocompleteSearchQuery

Generate suggested text for autocompletion of a search query

• ### FromCharacterName

Get a string character from its name

• ### LongestCommonPrefix

Find the longest common contiguous prefix of a set of strings or lists

• ### ProportionsBy

Get the proportion of times that each distinct element appears in a list when evaluated with a given function

• ### ChannelMessages

Send relevant data to a channel object when a message occurs

• ### AssociationNotebook

Create a structured notebook containing data from an association

• ### ProcessRunningQ

Check if a process, session or task is currently active

• ### NibbleArray

An array of nibbles (four-bit values)

• ### ResourceFunctionDefinitionViewer

View the definitions of a resource function along with its dependencies

• ### SimplexBoundary

Find the topological boundary of a simplex or simplicial complex

• ### ResourceFunctionSymbols

Get a list of the symbols used in the definition of a resource function

• ### CircleProperties

Get an association of the properties of a given circle

• ### SetUnless

Initialize a value unless it already satisfies a given condition

Determine whether an expression represents a quadratic function of a given set of variables

• ### TanDegree

Compute the tangent of an angle given in degrees

• ### PopulationStandardDeviation

Compute the population standard deviation for a set of data

• ### StringTemplateInput

Automatically format a string into boxes for documentation purposes

• ### AssociationMapAt

Similar to MapAt but with improved behavior for nested expressions involving associations

• ### ComplexToPolar

Get a complex number in polar form or polar exponential form

• ### InflectionPoints

Find the inflection points of a function of one variable

• ### ChessPGNDisplay

Dynamically display chess games from a Portable Game Notation (PGN) string or file

• ### SupplementaryAngle

Compute the geometric supplement to a given angle

• ### SubstitutionSystemCausalEvolution

Generate a representation of causal structure in substitution system evolution

• ### CreatePackageEventHandler

Create an event handler that evaluates an expression when a package is loaded

• ### SequenceToProduct

Turn a sequence of expressions into a symbolic product

• ### ColumnSpace

Compute properties of the column space of a matrix

• ### ByteArrayPlot

Visualize the contents of binary data

Display an expression in a format intended to maximize readability

• ### CoprimeIntegerList

Return a list of positive integers coprime to a given integer

Delete adjacent duplicates from a list

• ### ComplementaryAngle

Compute the geometric complement to a given angle

• ### ComplexRootQ

Determine if a given number is an integer complex root of another number

• ### ArcSecDegree

Compute the inverse secant of a number and return a result in degrees

• ### RowSpace

Compute properties of the row space of a matrix

• ### StringFunction

Use functions meant for lists on strings

• ### CriticalPoints

Find the critical points of a univariate function

• ### ArcCotDegree

Compute the inverse cotangent of a number and return a result in degrees

• ### UnionTo

Equivalent to Union but redefines the first argument to the result

• ### GetBoxPositions

Get positions of all boxes in a notebook

• ### LinearCombination

Decompose a vector into a linear combination of a set of vectors

• ### Kurvendiskussion

Get a dynamic plot of a univariate function along with supplemental information, known in the German language as a Kurvendiskussion

• ### LinearFunctionQ

Determine whether an expression represents a linear function of a given set of variables

• ### ExpressionLineDiff

Highlight the changes between two expressions

• ### LocalExtrema

Compute the local extrema of an expression with respect to the given variables

• ### UnevaluatedAssociation

Construct an association without evaluating any of the keys or values

• ### ImplicitD

Compute the derivative y’ as a function of x from an implicit equation in those variables

• ### SameAsQ

An operator form of SameQ

• ### EnsureFilePath

Create the parent directories necessary to fill out a given file path

• ### IteratedLog

Determine the iterated logarithm of an input

• ### ClosestPrime

Find the prime integer closest to a number

• ### RightTriangleQ

Determine whether a list of side lengths can form a right triangle

• ### DirectoryBlock

Temporarily change the current directory for an evaluation and ensure that it is restored when evaluation is completed

• ### TableQ

Similar to ArrayQ, except it allows for ragged collections of nested lists

• ### Proportions

Get the proportion of times that each distinct element appears in a list

• ### FloydSteinbergDithering

Apply Floyd–Steinberg dithering to an image

• ### SupplementaryAngleDegree

Compute the geometric supplement to a given angle using degrees

• ### PatternBindings

Pick named elements of a pattern

• ### JapaneseTextTokenizer

Separate a piece of Japanese text into grammatical parts

• ### ClickToCopy

Make an expression that is copied to the clipboard when clicked

• ### MoveMouse

Move the mouse cursor to a specified location

• ### OnceUnlessFailed

Equivalent to using Once, but will only cache results if evaluation was successful

• ### EvaluationTiming

Get a full timing report for functions evaluated during an evaluation

• ### RepeatingDecimalToRational

Find a rational number equivalent to a real number with repeating digits

• ### StringToBoxes

Convert a string into boxes as if it were typed into a notebook

• ### FunctionOverview

Get information about a real-valued univariate function

• ### MonotonicFunctionQ

Check if a function is monotonic

• ### Nullity

Compute the nullity of a matrix

• ### HiraganaQ

Test if a string is composed of hiragana characters

• ### GetUnboundSymbols

Get all the non-local symbols that appear in an expression

• ### ResetDirectoryStack

Reset the value of Directory[] and DirectoryStack[]

• ### IdealCoinTossStatistics

Compute the probabilities and statistics associated with tossing a coin

• ### SuperperfectNumberQ

Check whether a number is a superperfect number

• ### Erfci

Set up a symbol to give an error message when called with an unexpected number of arguments

• ### RegularPolygonDiagonals

Find the number of diagonals of a regular polygon

• ### ReplaceContext

Transform an expression by replacing all symbols in one context with symbols of the same name in another context

• ### StringSplitAfter

Split a string after each substring matching a string pattern

• ### ManipulatePlot

Generate a plot in which the plot ranges and function parameters can be manipulated dynamically

• ### CurveFitReport

Display information related to fitting of a set of data

Add a toolbar for formatting function documentation to a notebook

• ### SimplexMeasure

Get the measure of a simplex or simplicial complex

• ### PascalsTriangle

Display a given number of rows in Pascal's triangle

• ### FindImageBoundingBoxes

Calculate the bounding rectangles of elements in a binary image

• ### SystemShellRun

Run a command on the current system shell

• ### CopyDefinitions

Copy the definitions of one symbol to another

• ### OddFunctionQ

Determine whether an expression is an odd function of the given variable or variables

• ### EpidemicModel

Generate an interactive tool for visualizing various compartment based epidemiological models

• ### StandardSimplex

Get the standard simplex for a specified dimension

• ### FunctionParity

Determine the parity of a function, even or odd, with respect to one or more variables

Generate an HTTP response that prompts the browser to download as a given file name

• ### AbundantNumber

Gives the nth abundant number

• ### WolfieSay

Have Wolfie say an expression

• ### StringPrepend

Prepend a string to another string

• ### SuggestPlotRange

Get a variable range against which to plot a given function

• ### ShoeSizeToLength

Determine the length of a shoe given its size within any of a variety of sizing systems

• ### ReplaceAt

Replace parts of an expression using replacement rules and a part specification

• ### CommonDivisors

Find the common divisors of two or more integers

• ### HighlightText

Highlight parts of text according to a given pattern

• ### AreaBetweenCurvesIntegral

Compute the integral describing the area between two plane curves

• ### OsculatingCircleProperties

Compute the defining properties of the osculating circle for a curve at a point

• ### CubehelixColorFunction

Generate color functions using the "cubehelix" method

• ### StrictlyMonotonicFunctionQ

Check if a function is strictly monotonic

• ### ArcLengthIntegral

Generate an inactive integral or sum of integrals used for computing the arc length of an expression with given bounds

• ### AbundantNumberQ

Check whether an input is an abundant number

• ### RandomPartChoice

Choose random parts of an expression

• ### SubstitutionSystemCausalGraph

Generate a causal graph from a substitution system using standard updating order

• ### DynamicEnabledButton

Create a button that is automatically disabled when clicked and enabled when it finishes running its code

• ### IsContinuousFunction

Determine whether a function is continuous

• ### PossibleNameQ

Test if an expression corresponds to a valid symbol name

• ### JacobianMatrix

Compute the Jacobian matrix of a vector function with respect to a list of variables

• ### BinaryIteratedLog

Get the binary iterated logarithm of a positive number

• ### LinearlyIndependent

Determine whether a set of vectors is linearly independent

• ### LocalMinima

Compute the local minima of an expression with respect to the given variables

• ### PrintAsCellObject

Equivalent to Print, except returns a CellObject corresponding to the printed notebook cell

• ### KanjiQ

Test if a string is composed of kanji characters

• ### FullSymbolName

Return a fully qualified name of a symbol regardless of current context settings

• ### StationaryPoints

Compute the stationary points of a function of one or more variables

• ### StringAppend

Append a string to another string

• ### RegularHyperbolicTilingGraph

Create a graph of a regular hyperbolic tiling

• ### TangentLine

Compute properties of the tangent line to a curve at a given point

• ### SessionInformation

Get an association containing various session-related information

• ### BinetFibonacci

Generalize the Fibonacci numbers for complex inputs using Binet's Fibonacci formula

• ### SetTo

Use as an operator form of Set

• ### SimplexOrientation

Get the orientation of a simplex

• ### Intercepts

Compute the intercepts of a function with the coordinate axes

• ### ImportPGN

Import a PGN file or string as an association of structured chess data

• ### ToCompressedBoxes

Generate boxes corresponding to the printed form of an expression that are compressed where possible

• ### SameExpressionShapeQ

Check if expressions have the same shape

• ### ResourceFunctionMessage

Print a labeled message from ResourceFunction with contexts hidden

• ### RootSymbol

Recursively take the head of an expression

• ### AppendSequence

Append multiple items to an expression at once

• ### UniqueContext

Provide a new context that contains no symbols

• ### SequenceToSum

Turn a sequence of expressions into a symbolic sum

• ### LocalMaxima

Compute the local maxima of an expression with respect to the given variables

• ### CurveIntersection

Find the points of intersection of two curves

• ### CollinearQ

Determine whether a set of points lie on a line

• ### ComplementaryAngleDegree

Compute the geometric complement to a given angle using degrees

• ### FormatAsResourceFunction

Format a symbol as a ResourceFunction in outputs

• ### CompressWithDefinitions

Compress an expression, along with any needed definitions, so that it can be used in another session

• ### SVGImport

Import an SVG file as a graphics object

• ### CoplanarQ

Determine whether a set of points lies in a plane

• ### ReplaceAllOutside

Similar to ReplaceAll, but parts of the expression can be ignored by providing a pattern

• ### BirdSay

Have a bird say an expression

• ### CurveFitOverview

Get an association of information related to fitting a set of data

• ### CompleteSquare

Algebraically rewrite an expression by completing the square

• ### GetDefinitions

Use Get without modifying the \$ContextPath

• ### FunctionMonotonicity

Compute the regions on which an expression is monotonic

• ### EchoGroup

Echo a label and make any echoes that occur within a body indented

• ### IsTranscendentalNumber

Check whether a number is transcendental

• ### CloseOtherNotebooks

Close all other open notebooks

• ### DeficientNumber

Compute the nth deficient number

• ### InteractiveConicPlot

Display an interactive plot with all relevant information for a given conic section

• ### AreaBetweenCurves

Find the area between two plane curves

• ### KeyIndex

Create an association indexed by a given key from a list of associations

• ### CoinTossSimulator

Dynamically simulate tossing a coin

• ### CotDegree

Compute the cotangent of an angle given in degrees

• ### PoincarePolynomial

Compute the Poincaré polynomial for a simplicial complex

• ### ArcCscDegree

Compute the inverse cosecant of a number and return a result in degrees

• ### DiagonalizeMatrix

Get the diagonalized matrix of a given matrix

• ### EchoTiming

Print the timing for an evaluation and return the result

• ### SplitByPatterns

Split a list into sublists that match the same pattern from an ordered list of patterns

• ### InverseBoole

Inverse of the Boole function

• ### ArcCosDegree

Compute the inverse cosine of a number and return a result in degrees

• ### JoinMap

Map a function over a list and join the result

• ### FunctionConcavity

Compute the regions on which an expression is concave up or down

• ### RegularPolygonRegionCount

Find the number of regions partitioned by the diagonals of a regular polygon

• ### CscDegree

Compute the cosecant of an angle given in degrees

• ### HessianDeterminant

Compute the Hessian determinant of a function with respect to a list of variables

• ### ImportGravatarImage

Import an avatar image from the Gravatar service

• ### SpeechBubble

Decorate an expression with a speech bubble frame

• ### ContextModule

Temporarily set \$Context and \$ContextPath to a unique empty context for an evaluation

• ### SecDegree

Computes the secant of an angle given in degrees

• ### CommonMultiples

Find the common multiples of two or more integers

• ### LargestPrimeFactor

Find the largest prime factor of a given integer

• ### TangentPlane

Find the tangent plane of a function at a point

• ### InheritedBlock

Similar to Block, except values of local symbols are not cleared when entering the block

• ### CofactorMatrix

Give the matrix of cofactors for a given input matrix

• ### WindowsSystemData

Get information from the current Windows system about running processes, hardware, security settings and more

• ### FunctionCorners

Find the corners of a curve

• ### SerializeWithDefinitions

Serialize an expression along with any needed definitions so that it can be used in another session

• ### ToFullString

Create a string of the FullForm of an expression with fully qualified symbol names

• ### OpenCellGroups

Open cell groups in a notebook by style

• ### LocalEvaluate

Synchronously evaluate an expression in a separate kernel

• ### JacobianDeterminant

Compute the Jacobian determinant of a vector function with respect to a list of variables

• ### TraceInteractive

Trace an evaluation with an interface that allows interactive debugging

• ### AbortOnMessage

Abort an evaluation as soon as a message is generated

• ### PrintDefinitionCases

Find definitions for symbols in a context using a pattern, getting highlighted occurrences of it

• ### FoldRightList

Compute a right-associated fold returning the list of intermediate results

• ### BlockProtected

Modify definitions of protected symbols and ensure that their attributes are restored

• ### FuriganaForm

Show kana with a piece of Japanese text that indicates the pronunciation of kanji

• ### SelectPositions

A function like Select that returns positions instead of values

• ### NeedsDefinitions

Equivalent to Needs, but does not modify the \$ContextPath

• ### StringSplitBefore

Split a string before each substring matching a string pattern

• ### GlobalMinima

Compute the global minima of an expression with respect to the given variables

• ### FoldRight

Compute a right-associated fold

• ### CompileColorFunction

Compile a color function for improved performance in colorizing images

• ### JoinTo

Equivalent to Join, but redefines the first argument to the result

• ### MultiplicationTable

Generate a multiplication table for a range of integers, optionally using modular arithmetic

• ### CurveAnalysis

Get a dynamic plot of a univariate function along with supplemental algebraic and calculus-based properties of the function

• ### FailOnMessage

Stop an evaluation when a message is encountered and return a given failure expression

• ### LengthToShoeSize

Find the appropriate shoe size in a given system for a wearer given a last/foot length

Compute the quadratic residues of an integer

• ### ColorToHex

Convert a color to a hex string

• ### EllipseProperties

Get an association of the properties of a given ellipse

• ### GlobalMaxima

Compute the global maxima of an expression with respect to the given variables

• ### PatternSort

Sort a list of patterns according to their precedence

• ### Asymptotes

Compute the asymptotes to a given curve in two dimensions

• ### DigitSum

Find the sum of digits in the positional representation of an integer

• ### VersionOrder

Compare two version numbers to determine their order

• ### FunctionCusps

Find the cusps of a curve

• ### TwinPrime

Find the nth twin prime

• ### SecondsToQuantity

Convert a number representing seconds to a quantity of time in an appropriate unit

• ### AssociationKeyDeflatten

Deflatten the keys in a flat association to create a nested association

• ### ArcSinDegree

Compute the inverse sine of a number and return a result in degrees

• ### BettiNumbers

Compute the Betti numbers for a simplicial complex

• ### MapCases

Map a function at parts of an expression that match a given pattern

• ### KleinBottleGraph

Create a grid graph in the shape of a Klein bottle

• ### IntersectionPlot

Plot two curves and highlight their points of intersection

• ### SwapSymbolValues

Swap values of symbols using a temporary variable

• ### SelectByCurrentValue

Efficiently select from a list of front end objects

• ### CloudPutByHash

CloudPut to a location determined by the hash of an expression

• ### NestedCatch

Propagate a Throw upward to the outermost NestedCatch

• ### KeyReplace

Replace keys in an association

• ### EchoIf

A curried form of Echo that can be useful in certain debugging situations

• ### SubstitutionSystemCausalPlot

Generate a plot illustrating causal features of substitution system evolution

• ### FrontEndObjectQ

Determine if an expression is a valid front end object

• ### FunctionJectivity

Determine the injectivity and surjectivity of a function

• ### PrimitiveRootOfUnityList

Get the set of primitive nth roots of unity

• ### ReferenceAngle

Compute the reference angle to a given input angle

• ### SetContextStyle

Set the auto-style options for a given context

• ### SimpleListAnimate

Create an animation from a list of expressions

• ### Inline

Insert the values of symbols into an expression before evaluation

• ### MessagedQ

Test if a message is issued during an evaluation

• ### ReferenceAngleDegree

Compute the reference angle to a given input angle using degrees

• ### GlobalExtrema

Compute the global extrema of an expression with respect to the given variables

• ### ClipboardContent

Get the contents of the clipboard as an expression

• ### MultisetSupport

Determine the support for a multiset

• ### MultisetUnion

Perform the union operation on multisets

• ### MultisetSokalSneathDissimilarity

Compute the Sokal–Sneath dissimilarity of two multisets

• ### ImportNewickString

Import a string in Newick format

• ### AkimaSpline

Smooth curve interpolation based on local procedures for a multiple-valued curve (x(u), y(u))

• ### MultisetComplement

Perform the complement operation on multisets

• ### ComplexRoots

Get the full list of complex nth roots of a number

• ### MultisetInclusionQ

Test whether or not one multiset is included in another multiset

• ### AkimaInterpolation

Interpolation and smooth curve fitting based on local procedures

• ### NewickDendrogram

Render a Newick tree as a dendrogram

• ### MultisetDiceDissimilarity

Compute the Dice dissimilarity of two multisets

• ### MultisetJaccardDissimilarity

Compute the Jaccard dissimilarity of two multisets

• ### MultisetSum

Perform the sum operation on multisets

• ### MultisetProduct

Perform the product operation on multisets

• ### Tetartoid

Get a tetartoid given three values

• ### MultisetCardinality

Determine the cardinality for a multiset

• ### MultisetIntersection

Perform the intersection operation on multisets

• ### DirectionalD

Compute the directional derivative of a function

• ### CanalSurface

Compute the parametrization of a canal surface

• ### StereographicProjection

Compute the stereographic projection from the unit sphere to a plane

• ### TangentialAngle

Compute the tangential angle of a curve

• ### TranslationSurface

Compute a translation surface parametrization

• ### ParallelSurface

Compute the parallel surface of a surface

• ### TwistedSurface

Generate a surface twisting a curve

• ### VariableSectionTube

Compute the parametrization of a tube of variable section

• ### PedalSurface

Compute a pedal surface

• ### ShapeOperator

Compute the shape operator on a surface

• ### FindRanges

Find continuous ranges in a list of integers

• ### SphericalCurve

Get curves defined over a sphere

• ### ParallelCurve

Compute parallel (offset) curves

• ### TangentVector

Compute the tangent vector of a curve

• ### PerpendicularSurface

Compute the perpendicular surface of a curve

• ### BinormalVector

Compute the binormal vector of a curve

• ### CurveTube

Convert a 3D curve into a parametrized tube

• ### ApproximatedCurve

Get an approximation to a parametric curve

• ### Cyclide

Compute expressions for Dupin cyclide surfaces

• ### TurningNumber

Compute the turning number of a curve

• ### FocalSet

Compute the focal set of a surface

• ### Geodesic

Compute the geodesics for a parametrized surface

• ### Curvature

Compute the curvature of a curve

• ### InversionSurface

Compute the inversion surface

• ### RollingCurve

Compute a rolling curve

• ### WeingartenMatrix

Compute the Weingarten matrix of a surface

• ### TotalSignedCurvature

Compute the total signed curvature of a curve

• ### InversionCurve

Compute the inversion of a curve

• ### FrenetSerretFrame

Plot the Frenet–Serret frame of a curve

• ### InverseStereographicProjection

Compute the parametrization of a curve projected onto the unit sphere

• ### GeneralizedHelicoid

Compute the generalized helicoid of a curve

• ### ImplicitCurvature

Compute the implicit curvature of a curve

• ### CesaroEquation

Compute the Cesàro equation for a planar curve

• ### NormalCurvature

Compute the normal curvature of a curve on a surface

• ### ParametricSurfaceTangentPlane

Compute the tangent plane of a parametric surface

• ### NormalVector

Compute the normal vector of a curve

• ### AsymptoticCurves

Compute the asymptotic curves of a parameterized surface

• ### DarbouxVector

Compute the Darboux vector field of a curve

• ### FirstFundamentalFormCoefficients

Compute the coefficients of the first fundamental form of a surface

• ### RiemannTensor

Compute the components of the Riemann tensor for a metric

• ### CurveTorsion

Compute the torsion of a curve

Compute the relative probability of finding a particle at a given distance from another particle

• ### AreaElement

Compute the area element for a surface

• ### GyrationTensor

Compute the gyration tensor and derived metrics quantifying the shape of particle distributions

• ### NaturalEquations

Compute the natural equations of a curve

• ### EnneperWeierstrass

Compute the Enneper-Weierstrass parametrization

• ### NegativePedalCurve

Compute the negative pedal curve

• ### FractalCellularTexture

Generate Worley's cellular texture

• ### GraphPolynomial

Get the polynomial with coefficients giving the number of nonisomorphic graphs for a given number of vertices

• ### NextPermutation

Get the next permutation in lexicographic order

• ### Mediant

Compute the mediant of a list of positive rationals

• ### NextIntegerPartition

Get the next partition of an integer in reverse lexicographic order

• ### GrayCodeKSubsets

Get k-subsets of a given set in minimum change order

• ### GrayCodeSubsets

Get subsets of a given set in minimum change order

• ### ReflexiveGraphQ

Test whether a graph is reflexive

• ### CycleLengthCountList

List the possible cycle length counts of permutations of a given length

• ### IntegerCompositions

Generate all compositions of an integer into the specified number of parts

• ### SwapOrderedPermutations

Construct a list of permutations so that successive permutations differ by exactly one transposition

• ### PermutationCountByCycleLength

Calculate the number of permutations of the specified cycle length counts

• ### NecklaceCount

Count the number of distinct necklaces made with beads of different colors

• ### PruferCodeToLabeledTree

Construct a labeled tree given its Prüfer code

• ### LabeledTreeToPruferCode

Find the Prüfer code associated with a labeled tree

• ### PermutationCountByInversions

Get the number of permutations having a specified length and number of inversions

• ### HasseDiagram

Construct a Hasse diagram of a poset

• ### NextIntegerComposition

Get the next composition of an integer in canonical order

• ### TransitiveGraphQ

Test whether the binary relation defined by edges of a graph is transitive

• ### NthGrayCodeSubset

Get the n-th Gray code subset of a list

• ### SubsetGroup

Compute a group induced by a permutation group on k-subsets

• ### NextSubset

Get the next subset of a given set in canonical order

• ### PermutationMajorIndex

Compute the major index of a permutation

• ### PartialOrderGraphQ

Test whether a graph is a partial order, that is, reflexive, antisymmetric and transitive

• ### NextLexicographicSubset

Get the next subset of a given set in lexicographic order

• ### BacktrackSearch

Solve computational problems using a generic backtracking algorithm

• ### NthSubset

Get the subset of a list for a given index

• ### VertexColoring

Assign colors to vertices of a graph so that no edge connects vertices of the same color

• ### PerfectGraphQ

Test whether a graph is perfect

• ### SpanningTreeCount

Count the number of labeled spanning trees in a graph

• ### DominatingIntegerPartitionQ

Find out if one partition of an integer dominates another

• ### GrayCodeSubsetIndex

Find the index of a subset in Gray code order

• ### GraphCount

Find the number of fundamentally different graphs of a specified size

• ### InversionCount

Count the number of pairs of out-of-order elements in a permutation

• ### IntervalGraph

Intersection graph of intervals

• ### JosephusPermutation

Find the solution of the Josephus problem

• ### PermutationGraph

Compute the permutation graph of a permutation

• ### ArticulationVertices

Find articulation vertices of a graph

• ### CycleLengthCounts

Count the number of cycles for all possible cycle lengths in a permutation

• ### NextKSubset

Get the lexicographic successor of a k-subset of a list

• ### InvolutionCount

Count the number of involutions

• ### Fibbinary

Get the fibbinary sequence

• ### Involutions

List permutations comprised only of cycles of size two or less

• ### LexicographicSubsets

List the subsets of a set in lexicographic order

• ### ApproximateVertexCover

Find a vertex cover not much larger than the minimal cover

• ### Shuffle

Rearrange elements of a list