Associations »

Association ( <|…|> ) — an association between keys and values

Key — indicate a key within a part specification

Keys   ▪ Values   ▪ Lookup   ▪ KeySort   ▪ KeyUnion

Merge — combine elements that have common keys

Counts , CountsBy — associate values with the number of times they occur

GroupBy — group values by collecting those sharing a criterion ("map reduce")

JoinAcross — combine lists of associations that match ("SQL join")

PositionIndex — build an index of positions at which values occur

Templates »

StringTemplate   ▪ FileTemplate   ▪ XMLTemplate   ▪ NotebookTemplate

TemplateObject — general symbolic template

TemplateExpression — an arbitrary expression evaluated when the template is applied

TemplateApply   ▪ TemplateSequence   ▪ TemplateSlot   ▪ TemplateIf   ▪ TemplateWith   ▪ ...

Entities »

EntityValue — get values for properties of entities

Entity — represent a particular entity in the world

EntityProperty   ▪ EntityProperties   ▪ CommonName   ▪ CanonicalName   ▪ EntityTypeName   ▪ ...

Finding Elements »

SelectFirst , FirstCase , FirstPosition — find the first element satisfying a criterion

MaximalBy , MinimalBy — find elements that maximize, minimize a criterion

Testing Expressions »

AllTrue , AnyTrue , NoneTrue — apply a test multiple times across a list

IntersectingQ , DisjointQ , SubsetQ — compare elements of two sets

BooleanQ

Entities »

EntityValue — get values for properties of entities

Entity — represent a particular entity in the world

EntityProperty   ▪ EntityProperties   ▪ CommonName   ▪ CanonicalName   ▪ EntityTypeName   ▪ ...

Machine Learning »

Classify — classify data into categories using a built-in classifier or learning from examples

Predict — predict values from data using a built-in predictor or learning from examples

ClassifierFunction   ▪ PredictorFunction   ▪ ClassifierMeasurements   ▪ PredictorMeasurements

WDF (Wolfram Data Framework) »

SemanticImport — import a file to give WDF

Interpreter — specify how to convert a string to WDF

"Date"   ▪ "City"   ▪ "Number"   ▪ "PhoneNumber"   ▪ "URL"   ▪ ...

ThermodynamicData — properties of thermodynamic substances

Formulas »

FormulaData — give the equations for a specific formula

FormulaLookup — look up formula names based on specific criteria

QuantityVariable — represent a physical quantity

QuantityVariableIdentifier   ▪ QuantityVariablePhysicalQuantity   ▪ QuantityVariableDimensions   ▪ QuantityVariableCanonicalUnit

Currency

CurrencyConvert — convert between different currencies

InflationAdjust — current and historical inflation adjustments

DatedUnit — associate a specific date with a unit

Broad Support for Time Series Processing »

TimeSeries — series consisting of time-value pairs

EventSeries — special time series with no interpolation between samples

TemporalData — general collection of time series

Basic Operations

TimeSeriesWindow — give the time series in the specified time window

TimeSeriesInsert — insert time-value pairs into a time series

TimeSeriesRescale   ▪ TimeSeriesResample   ▪ TimeSeriesShift   ▪ TimeSeriesThread   ▪ TimeSeriesMap   ▪ TimeSeriesMapThread   ▪ RegularlySampledQ   ▪ MinimumTimeIncrement

Filtering & Aggregating Time Series

MovingMap — apply a function to a moving overlapping window

TimeSeriesAggregate — apply a function to a moving non-overlapping window

Differences   ▪ Accumulate   ▪ MovingAverage   ▪ MovingMedian   ▪ ...

LowpassFilter   ▪ HighpassFilter   ▪ MeanFilter   ▪ ...

Time Series Process Modeling »

TimeSeriesModelFit — automatically fit a time series model

TimeSeriesForecast   ▪ CorrelationFunction   ▪ PowerSpectralDensity   ▪ ...

Date & Time

DateObject   ▪ TimeObject

DateFormat   ▪ CalendarConvert   ▪ TimeZoneConvert

New in Image Processing & Analysis »

BarcodeImage , BarcodeRecognize — generate and recognize 1D or 2D barcodes

ConformImages — make a list of images that have conforming properties

RemoveBackground — separate and remove background from an image

DominantColors — improvements and new options to find a list of dominant colors

RandomColor   ▪ ColorDistance   ▪ ChromaticityPlot

ConstantImage   ▪ LinearGradientImage   ▪ RadialGradientImage

ImageCollage   ▪ LocalAdaptiveBinarize   ▪ GrowCutComponents   ▪ ImageApplyIndexed   ▪ ImageSaliencyFilter   ▪ SavitzkyGolayMatrix

Use more functions for processing and analyzing 3D images

ComponentMeasurements   ▪ SelectComponents

ImageRotate   ▪ ImageTransformation   ▪ ImagePerspectiveTransformation

EdgeDetect   ▪ CrossingDetect   ▪ ContourDetect   ▪ CornerFilter

HistogramTransform   ▪ HistogramTransformInterpolation

FourierDCTFilter

LABColor , LUVColor , XYZColor — use CIE color spaces for styles and color functions

Maps & Cartography »

GeoGraphics — construct maps and geographic images from primitives and directives

GeoPath   ▪ GeoStyling

Specialized Plots

NumberLinePlot — plot numbers, intervals, and predicates on a number line

MandelbrotSetPlot — plot the Mandelbrot set over a region

JuliaSetPlot — plot the Julia set for a function

Enhanced Legends

PlotLegends — improved legends using dashing, thickness, plot markers, and label styles

ArrayPlot — improved automatic legends

MatrixPlot — improved automatic legends

Legended — improved placement of multiple legends and wider support as a wrapper for data

ListLogPlot   ▪ ListLogLinearPlot   ▪ ListLogLogPlot   ▪ QuantilePlot   ▪ ProbabilityPlot   ▪ ProbabilityScalePlot

Enhanced Units

Create financial plots from data with units

CandlestickChart   ▪ KagiChart   ▪ PointFigureChart   ▪ RenkoChart   ▪ LineBreakChart

PlotTheme — specify an overall theme for visualizations

Geometric Computation »

Geometric computation framework for modeling and computing with geometric regions.

Plane Geometry »

SSSTriangle   ▪ ArcLength   ▪ Area   ▪ ...

Solid Geometry »

Tetrahedron   ▪ Volume   ▪ RegionMember   ▪ ...

Properties and Measures »

RegionNearest — find the nearest point in a region

RegionMeasure   ▪ RegionCentroid   ▪ RegionDistance   ▪ ...

Solvers over Regions »

Integrate , NIntegrate — integrate over regions

NDSolve — solve partial differential equations over regions

Solve   ▪ NSolve   ▪ Minimize   ▪ NMinimize   ▪ ...

Special Regions »

Ball — a ball given by center and radius

Simplex   ▪ Hexahedron   ▪ InfiniteLine   ▪ ...

Formula Regions

ImplicitRegion — a region given by combinations of inequalities and equalities

ParametricRegion — a region given by parametric functions

Mesh Regions »

MeshRegion — a region specified by a collection of mesh cells

BoundaryMeshRegion — a region boundary specified by a collection of mesh cells

HighlightMesh   ▪ MeshCellStyle   ▪ MeshCellLabel   ▪ ...

Data Regions »

DelaunayMesh — a Delaunay triangulation mesh constructed from points

VoronoiMesh   ▪ ConvexHullMesh   ▪ ...

Region Converters »

DiscretizeGraphics , BoundaryDiscretizeGraphics — discretize 2D or 3D graphics

DiscretizeRegion , BoundaryDiscretizeRegion — discretize a region

Derived Regions »

RegionUnion — the union of regions

TransformedRegion — a region as the image of a transformation

RegionIntersection   ▪ BooleanRegion   ▪ RegionBoundary   ▪ ...

Inactive Operators

Inactive — new inactive operator for working with formal operations

Inactivate — inactivate parts of expressions

Activate   ▪ IgnoringInactive

Enhanced Calculus

DSolveValue , RSolveValue — new functions that can directly return functions of solutions

DSolve — now solves delay differential and hybrid differential equations

Sum — new algorithms for functional telescoping, multiple sums, and special functions

Product — new algorithms for functional telescoping

DifferenceDelta — new results for differences of special functions

DiscreteRatio — new results for ratios of special functions

Enhanced Algebraic Computation

NSolve — new homotopy-based algorithm for fast solution of polynomial systems

Reduce , Solve , FindInstance — new fast solving over the reals

Function Properties

FunctionPeriod — find the period of functions over the reals, integers, and complexes

FunctionDomain — find the domain of a function

FunctionRange — find the range of a function

Vector Analysis

ArcLength — length

ArcCurvature — curvature

FrenetSerretSystem — generalized curvatures and associated basis

Linear Algebra »

PositiveSemidefiniteMatrixQ — new and improved matrix predicates

NormalMatrixQ   ▪ OrthogonalMatrixQ   ▪ SquareMatrixQ   ▪ ...

New Special Functions

LogisticSigmoid — the logistic function

CantorStaircase — the Cantor ternary function

MinkowskiQuestionMark   ▪ ScorerHi   ▪ ScorerGi   ▪ FresnelF   ▪ FresnelG   ▪ RiemannXi   ▪ DirichletBeta   ▪ DirichletEta   ▪ DirichletLambda   ▪ Fibonorial   ▪ AlternatingFactorial   ▪ FareySequence

Nonlinear Control Systems »

AffineStateSpaceModel — affine model and

FeedbackLinearize — linearization through nonlinear feedback and state transformation

AsymptoticOutputTracker — tracker with state feedback

NonlinearStateSpaceModel   ▪ FullInformationOutputRegulator   ▪ ...

Probability & Statistics

AutocorrelationTest — test for autocorrelation in data

Time Series Processes »

TimeSeriesModelFit — automatic fitting, diagnostics, and forecasting for time series

ARCHProcess , GARCHProcess — new classes of time series processes

ARProcess , ARMAProcess — full support for vector processes

MAProcess   ▪ SARMAProcess   ▪ FARIMAProcess

Markov Processes

HiddenMarkovProcess — hidden Markov process with discrete or continuous emissions

FindHiddenMarkovStates — hidden state decoding (Viterbi decoding etc.)

Parametric Processes »

TransformedProcess — transformations of random processes

WhiteNoiseProcess — new and improved capabilities for parametric processes

PoissonProcess   ▪ WienerProcess   ▪ GeometricBrownianMotionProcess   ▪ ...

Templates »

StringTemplate   ▪ FileTemplate   ▪ XMLTemplate   ▪ NotebookTemplate

TemplateObject — general symbolic template

TemplateExpression — an arbitrary expression evaluated when the template is applied

TemplateApply   ▪ TemplateSequence   ▪ TemplateSlot   ▪ TemplateIf   ▪ TemplateWith   ▪ ...

WDF (Wolfram Data Framework) »

SemanticImport — import a file to give WDF

Interpreter — specify how to convert a string to WDF

"Date"   ▪ "City"   ▪ "Number"   ▪ "PhoneNumber"   ▪ "URL"   ▪ ...

Graphs & Networks

MultigraphQ — framework-wide support for multigraphs

MixedGraphQ — framework-wide support for mixed (directed and undirected) graphs

FindSpanningTree — find a spanning tree (or spanning forest) of a graph

VertexContract   ▪ EdgeContract   ▪ LinkRankCentrality

Visualization

Graph3D — generate 3D layouts for graphs

PerformanceGoal — performance improvements for all graph visualization

GraphLayout — additional planar embedding "TutteEmbedding"

Paths & Connectivity

FindPath — find all paths between two vertices

FindVertexIndependentPaths   ▪ FindEdgeIndependentPaths

KVertexConnectedComponents   ▪ KEdgeConnectedComponents   ▪ KVertexConnectedGraphQ   ▪ KEdgeConnectedGraphQ

Tours & Cycles

FindShortestTour — new and improved capabilities for tours and cycles

FindCycle — find all cycles

FindFundamentalCycles   ▪ EdgeCycleMatrix

Isomorphisms

FindGraphIsomorphism — find several isomorphism mappings between graphs

GraphAutomorphismGroup — the group of all ways to remap vertex indexes

CanonicalGraph — canonical form for graphs

Relations

TransitiveClosureGraph — the transitive closure or reachability graph

TransitiveReductionGraph — the transitive reduction or Hasse diagram

Polynomials

TuttePolynomial — new graph polynomials

ChromaticPolynomial   ▪ FlowPolynomial

LABColor , LUVColor , XYZColor — use colors defined in CIE color spaces

New in Image Processing & Analysis »

BarcodeImage , BarcodeRecognize — generate and recognize 1D or 2D barcodes

ConformImages — make a list of images that have conforming properties

RemoveBackground — separate and remove background from an image

DominantColors — improvements and new options to find a list of dominant colors

RandomColor   ▪ ColorDistance   ▪ ChromaticityPlot

ConstantImage   ▪ LinearGradientImage   ▪ RadialGradientImage

ImageCollage   ▪ LocalAdaptiveBinarize   ▪ GrowCutComponents   ▪ ImageApplyIndexed   ▪ ImageSaliencyFilter   ▪ SavitzkyGolayMatrix

Use more functions for processing and analyzing 3D images

ComponentMeasurements   ▪ SelectComponents

ImageRotate   ▪ ImageTransformation   ▪ ImagePerspectiveTransformation

EdgeDetect   ▪ CrossingDetect   ▪ ContourDetect   ▪ CornerFilter

HistogramTransform   ▪ HistogramTransformInterpolation

FourierDCTFilter

Geometric Computation »

Geometric computation framework for modeling and computing with geometric regions.

Plane Geometry »

SSSTriangle   ▪ ArcLength   ▪ Area   ▪ ...

Solid Geometry »

Tetrahedron   ▪ Volume   ▪ RegionMember   ▪ ...

Properties and Measures »

RegionNearest — find the nearest point in a region

RegionMeasure   ▪ RegionCentroid   ▪ RegionDistance   ▪ ...

Solvers over Regions »

Integrate , NIntegrate — integrate over regions

NDSolve — solve partial differential equations over regions

Solve   ▪ NSolve   ▪ Minimize   ▪ NMinimize   ▪ ...

Special Regions »

Ball — a ball given by center and radius

Simplex   ▪ Hexahedron   ▪ InfiniteLine   ▪ ...

Formula Regions

ImplicitRegion — a region given by combinations of inequalities and equalities

ParametricRegion — a region given by parametric functions

Mesh Regions »

MeshRegion — a region specified by a collection of mesh cells

BoundaryMeshRegion — a region boundary specified by a collection of mesh cells

HighlightMesh   ▪ MeshCellStyle   ▪ MeshCellLabel   ▪ ...

Data Regions »

DelaunayMesh — a Delaunay triangulation mesh constructed from points

VoronoiMesh   ▪ ConvexHullMesh   ▪ ...

Region Converters »

DiscretizeGraphics , BoundaryDiscretizeGraphics — discretize 2D or 3D graphics

DiscretizeRegion , BoundaryDiscretizeRegion — discretize a region

Derived Regions »

RegionUnion — the union of regions

TransformedRegion — a region as the image of a transformation

RegionIntersection   ▪ BooleanRegion   ▪ RegionBoundary   ▪ ...

Broad Support for Time Series Processing »

TimeSeries — series consisting of time-value pairs

EventSeries — special time series with no interpolation between samples

TemporalData — general collection of time series

Basic Operations

TimeSeriesWindow — give the time series in the specified time window

TimeSeriesInsert — insert time-value pairs into a time series

TimeSeriesRescale   ▪ TimeSeriesResample   ▪ TimeSeriesShift   ▪ TimeSeriesThread   ▪ TimeSeriesMap   ▪ TimeSeriesMapThread   ▪ RegularlySampledQ   ▪ MinimumTimeIncrement

Filtering & Aggregating Time Series

MovingMap — apply a function to a moving overlapping window

TimeSeriesAggregate — apply a function to a moving non-overlapping window

Differences   ▪ Accumulate   ▪ MovingAverage   ▪ MovingMedian   ▪ ...

LowpassFilter   ▪ HighpassFilter   ▪ MeanFilter   ▪ ...

Time Series Process Modeling »

TimeSeriesModelFit — automatically fit a time series model

TimeSeriesForecast   ▪ CorrelationFunction   ▪ PowerSpectralDensity   ▪ ...

Date & Time

DateObject   ▪ TimeObject

DateFormat   ▪ CalendarConvert   ▪ TimeZoneConvert

Astronomical Computation »

Sunrise , Sunset — time of sunrise, sunset for any location and date

SunPosition   ▪ MoonPosition   ▪ MoonPhase   ▪ ...

PlanetData — static and dynamic properties of solar system planets

PlanetaryMoonData   ▪ CometData   ▪ ...

StarData — positions and properties of all stars in standard catalogs

ConstellationData   ▪ GalaxyData   ▪ ...

SatelliteData — properties and real-time computed positions of artificial satellites

DeepSpaceProbeData — planetary and deep space probes

Maps & Cartography »

GeoGraphics — create maps based on detailed worldwide geographic information

GeoListPlot — plot points or regions on maps

GeoRegionValuePlot — create geographic heat maps

GeoPosition — a position on the Earth

GeoVisibleRegion   ▪ GeoVisibleRegionBoundary   ▪ DayNightTerminator   ▪ ...

GeoStyling — styling for rendering any region ("OutlineMap", "StreetMap", "ReliefMap", ...)

GeoBackground   ▪ GeoZoomLevel   ▪ GeoScaleBar   ▪ ...

GeoProjection — projection to use ("Mercator", "Equirectangular", "Robinson", ...)

GeoGridLines   ▪ GeoGridLinesStyle

Entity — countries, cities, and other geographic entities, entered e.g. using

AdministrativeDivisionData   ▪ OceanData   ▪ ...

MountainData   ▪ BuildingData   ▪ AirportData   ▪ UniversityData   ▪ ...

Physics & Chemistry »

ElementData — bulk, atomic, chemical, etc. properties of all chemical elements

ChemicalData — structural, physical, and other properties of chemical compounds

ThermodynamicData   ▪ ParticleData   ▪ ...

FormulaData   ▪ PhysicalSystemData   ▪ ...

Astronomical Computation »

Sunrise , Sunset — time of sunrise, sunset for any location and date

SunPosition   ▪ MoonPosition   ▪ MoonPhase   ▪ ...

PlanetData — static and dynamic properties of solar system planets

PlanetaryMoonData   ▪ CometData   ▪ ...

StarData — positions and properties of all stars in standard catalogs

ConstellationData   ▪ GalaxyData   ▪ ...

SatelliteData — properties and real-time computed positions of artificial satellites

DeepSpaceProbeData — planetary and deep space probes

Connected Devices »

DeviceOpen — open a connection to a device

FindDevices — attempt to find devices available on a particular machine

DeviceRead   ▪ DeviceWrite   ▪ DeviceExecute   ▪ DeviceExecuteAsynchronous   ▪ ...

Nonlinear Control Systems »

AffineStateSpaceModel — affine model and

FeedbackLinearize — linearization through nonlinear feedback and state transformation

AsymptoticOutputTracker — tracker with state feedback

NonlinearStateSpaceModel   ▪ FullInformationOutputRegulator   ▪ ...

New in Image Processing & Analysis »

BarcodeImage , BarcodeRecognize — generate and recognize 1D or 2D barcodes

ConformImages — make a list of images that have conforming properties

RemoveBackground — separate and remove background from an image

DominantColors — improvements and new options to find a list of dominant colors

RandomColor   ▪ ColorDistance   ▪ ChromaticityPlot

ConstantImage   ▪ LinearGradientImage   ▪ RadialGradientImage

ImageCollage   ▪ LocalAdaptiveBinarize   ▪ GrowCutComponents   ▪ ImageApplyIndexed   ▪ ImageSaliencyFilter   ▪ SavitzkyGolayMatrix

Use more functions for processing and analyzing 3D images

ComponentMeasurements   ▪ SelectComponents

ImageRotate   ▪ ImageTransformation   ▪ ImagePerspectiveTransformation

EdgeDetect   ▪ CrossingDetect   ▪ ContourDetect   ▪ CornerFilter

HistogramTransform   ▪ HistogramTransformInterpolation

FourierDCTFilter

Connected Devices »

DeviceOpen — open a connection to a device

FindDevices — attempt to find devices available on a particular machine

DeviceRead   ▪ DeviceWrite   ▪ DeviceExecute   ▪ DeviceExecuteAsynchronous   ▪ ...

Linear Algebra »

PositiveSemidefiniteMatrixQ — new and improved matrix predicates

NormalMatrixQ   ▪ OrthogonalMatrixQ   ▪ SquareMatrixQ   ▪ ...

New Special Functions

LogisticSigmoid — the logistic function

CantorStaircase — the Cantor ternary function

MinkowskiQuestionMark   ▪ ScorerHi   ▪ ScorerGi   ▪ FresnelF   ▪ FresnelG   ▪ RiemannXi   ▪ DirichletBeta   ▪ DirichletEta   ▪ DirichletLambda   ▪ Fibonorial   ▪ AlternatingFactorial   ▪ FareySequence

Vector Analysis

ArcLength — length

ArcCurvature — curvature

FrenetSerretSystem — generalized curvatures and associated basis

Enhanced Calculus

DSolveValue , RSolveValue — new functions that can directly return functions of solutions

DSolve — now solves delay differential and hybrid differential equations

Sum — new algorithms for functional telescoping, multiple sums, and special functions

Product — new algorithms for functional telescoping

DifferenceDelta — new results for differences of special functions

DiscreteRatio — new results for ratios of special functions

Probability & Statistics

AutocorrelationTest — test for autocorrelation in data

Time Series Processes »

TimeSeriesModelFit — automatic fitting, diagnostics, and forecasting for time series

ARCHProcess , GARCHProcess — new classes of time series processes

ARProcess , ARMAProcess — full support for vector processes

MAProcess   ▪ SARMAProcess   ▪ FARIMAProcess

Markov Processes

HiddenMarkovProcess — hidden Markov process with discrete or continuous emissions

FindHiddenMarkovStates — hidden state decoding (Viterbi decoding etc.)

Parametric Processes »

TransformedProcess — transformations of random processes

WhiteNoiseProcess — new and improved capabilities for parametric processes

PoissonProcess   ▪ WienerProcess   ▪ GeometricBrownianMotionProcess   ▪ ...

Wolfram Predictive Interface »

String Completion — autocomplete string arguments

File Name Completion — autocomplete file names and paths

Color Chooser — choose a color from an interface

Function Template Tooltip — show function templates by clicking a tooltip

URL Manipulation »

URLEncode — convert a string to use URL-style percent encoding

URLDecode — convert to Unicode from URL-style percent encoding

URLBuild   ▪ URLParse   ▪ URLShorten   ▪ ...

Database Connections and Resources »

SQLConnectionOpenQ — client validity test for SQL connection

SQLConnectionUsableQ — server validity test for SQL connection

Connected Devices »

DeviceOpen — open a connection to a device

FindDevices — attempt to find devices available on a particular machine

DeviceRead   ▪ DeviceWrite   ▪ DeviceExecute   ▪ DeviceExecuteAsynchronous   ▪ ...

Cloud Functions & Deployment »

CloudObject — a handle to an expression or other content in the cloud

CloudGet — get an expression from the cloud

CloudPut — put an expression into the cloud, creating a new cloud object if necessary

CloudSave — save definitions associated with a symbol to the cloud

CloudImport   ▪ CloudExport   ▪ ...

Cloud Evaluation

CloudEvaluate — evaluate an expression in the cloud

CloudFunction — a pure function to be evaluated in the cloud

Deploying to the Cloud

CloudDeploy — deploy code or content to be accessed externally in the cloud

APIFunction — symbolic representation of an API to be deployed

FormFunction — symbolic representation of a form to be deployed

ExternalBundle — representation of a directory of objects

ExportForm   ▪ ResponseForm   ▪ HTTPResponse   ▪ ...

Creating Embeddable Content

EmbedCode — HTML etc. code for external embedding of cloud content

Content Management

Permissions   ▪ CloudDirectory   ▪ ...

URL Manipulation »

URLEncode — convert a string to use URL-style percent encoding

URLDecode — convert to Unicode from URL-style percent encoding

URLBuild   ▪ URLParse   ▪ URLShorten   ▪ ...