Wolfram Resource System

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Search the Wolfram Resource System

Paclet Resource: Wolfram/QuantumFramework

Perform analytic and numeric quantum computations

Paclet Resource: Wolfram/GitLink

Integrate git functionality into the Wolfram Language

Paclet Resource: WolframChemistry/ProteinVisualization

Functions for protein visualizations

Paclet Resource: WolframChemistry/ChemistryFunctions

Wolfram Language functions for Chemistry

Paclet Resource: StianRamsnes/MaXrd

Symmetry data and utilities related to crystallography and X-ray scattering

Paclet Resource: RobertNachbar/CompartmentalModeling

Build, visualize, analyze, and simulate compartmental models

Paclet Resource: PeterBurbery/RecreationalMathematics

This paclet is for recreational mathematics and math puzzles

Paclet Resource: PeterBurbery/MixedGraphs

A collection of mixed graph functionality

Paclet Resource: KlausSutner/Automata

Automata theory package

Paclet Resource: AntonAntonov/TriesWithFrequencies

Functions for creation and manipulation of tries (prefix trees) with frequencies

Paclet Resource: AntonAntonov/QuantileRegression

Quantile regression functions

Paclet Resource: AntonAntonov/MosaicPlot

Mosaic plots for datasets and lists of records

Paclet Resource: AntonAntonov/MonadicQuantileRegression

Software monad for Quantile Regression workflows

Paclet Resource: AntonAntonov/JavaTriesWithFrequencies

WL interface to Tries with frequencies implemented in Java

Paclet Resource: AntonAntonov/DimensionReducers

Dimension reduction algorithms

Function Resource: IncompletePFD

Give the incomplete partial fraction decomposition of a rational function

Function Resource: ExtendedApart

A partial fraction decomposition with the Extension option

Function Resource: IntegratePFD

Integrate a rational function using partial fraction decomposition

Function Resource: ApartAll

Compute a partial fraction decomposition over the algebraic closure of the rationals

Function Resource: EgyptianFraction

Compute Egyptian fractions using different methods

Function Resource: MatrixPartialTrace

Calculate a partial trace of a matrix

Function Resource: UpperTriangularDecomposition

Find an upper triangular form and conversion matrix for a given matrix

Function Resource: FractionIndicator

Visualize fractional values with minimal styling

Function Resource: FractionMod

Get a congruent integer for a given fraction and modulus

Function Resource: PivotedLUDecomposition

Compute the LU decomposition of a matrix with different pivoting methods

Function Resource: PartialOrderGraphQ

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

Function Resource: FractionPieChart

Visualize fractions and mixed numbers using pie charts

Function Resource: SequenceOverlapFraction

Compute the overlap fraction between two strings or biosequences

Function Resource: PolarDecomposition

Compute the polar decomposition of a matrix

Function Resource: BidiagonalDecomposition

Compute the bidiagonal decomposition of a numerical matrix

Function Resource: CPDecomposition

Compute the canonical polyadic (CP) decomposition of a tensor

Function Resource: LDLDecomposition

Find the LDL decomposition of a Hermitian matrix

Function Resource: TuckerDecomposition

Compute the Tucker decomposition of a tensor

Function Resource: WeyrDecomposition

Compute the Weyr decomposition of a square matrix

Function Resource: TakagiDecomposition

Compute the Takagi decomposition of a complex-symmetric matrix

Function Resource: AasenDecomposition

Compute the Aasen decomposition of a Hermitian matrix

Paclet Resource: LawrenceWinkler/MatrixDecomposition

Various simple matrix decompositions algorithms and support functions

Function Resource: PopovDecomposition

Compute the Popov decomposition of a matrix of univariate polynomials

Function Resource: ADMDecomposition

Represent a canonical decomposition of the metric for a Riemannian or pseudo-Riemannian manifold via the ADM formalism

Function Resource: FullRankDecomposition

Compute a full rank decomposition of a matrix

Function Resource: OrderedSchurDecomposition

Compute the ordered Schur decomposition of a matrix

Function Resource: FullQRDecomposition

Compute the full QR decomposition of a matrix

Function Resource: RationalCholeskyDecomposition

Compute the rational Cholesky decomposition of a matrix

Function Resource: GallaiEdmondsDecomposition

The Gallai–Edmonds decomposition of a graph

Function Resource: QuadtreeImageDecomposition

Quadtree decomposition of an image

Function Resource: SkewTridiagonalDecomposition

Compute the skew-tridiagonal decomposition of an antisymmetric matrix

Function Resource: PolynomialHermiteDecomposition

Compute the Hermite decomposition of a matrix of univariate polynomials

Function Resource: PolynomialSmithDecomposition

Compute the Smith decomposition of a matrix of univariate polynomials

Function Resource: GaussianHessenbergDecomposition

Compute the Gaussian Hessenberg decomposition of a matrix

Function Resource: IntegerSpectralDecomposition

Determine the spectral decomposition of an integer in a modular number system

Function Resource: DiscreteHypersurfaceDecomposition

Decompose a Riemannian or pseudo-Riemannian manifold into a union of discrete hypersurfaces

Function Resource: SkewLTLDecomposition

Tridiagonalize an antisymmetric (skew-symmetric) matrix using the Parlett-Reid algorithm

Example Resource: What Fraction of Possible Letter Sequences Are Words?

Function Resource: ComplexTogether

Combine the real and imaginary parts of complex numbers into a single fraction

Example Resource: Compute the Product of a Matrix and Vector using a Quantum Circuit

Function Resource: MixedNumberForm

Represent an improper fraction in mixed form

Function Resource: Unthread

A partial inverse for Thread

Function Resource: MaximalSubsets

Prune non-maximal subsets from a list of subsets

Function Resource: MinimalSubsets

Prune non-minimal subsets from a list of subsets

Function Resource: ReplaceAllUnheld

Apply replacement rules to evaluated parts of expression

Function Resource: RemoveSubintervals

Remove intervals that are wholly contained in other intervals

Example Resource: Trotterization Quantum Circuit

Construct a circuit for the Suzuki-Trotter decomposition of an exponential product of operators

Function Resource: ThieleExpansion

Expand a function into a Thiele continued fraction

Function Resource: FareyRange

Generate a list of fractions with a bounded denominator

Function Resource: Mediant

Compute the mediant of a list of non-negative rationals

Function Resource: RoundedPercentageAllocation

Split a value into list of rounded numbers according to a list of target proportions

Function Resource: DirectedGraphTransferMatrix

Obtain partial probabilities of random walks on a directed graph

Function Resource: TapeDiagram

Visualize fractions, integers and multiplication using tape diagrams

Function Resource: AssessmentTree

Create a tree of AssessmentFunction expressions to traverse during assessment

Function Resource: SimplifyRepeatedSubexpressions

Replace repeated subexpressions in an expression with new symbols

Function Resource: CalkinWilfTree

Generate a complete binary tree of positive fractions

Function Resource: DirectionalD

Compute the directional derivative of a function

Function Resource: TapeMeasureNumberLinePlot

Show a length on a tape measure and give the closest ruler fractions

Function Resource: FindFirstNumberInstance

Find the first number that matches a certain requirement

Function Resource: SternBrocotTree

Generate a complete binary search tree of positive fractions

Function Resource: RecurringDecimalForm

Display a number in decimal form so that recurring digit sequences are highlighted and displayed only once

Function Resource: FactorSemiprime

Fast integer factorization of a certain class of semiprimes

Function Resource: SternBrocot

Get the position of a fraction or vice-versa in the Stern–Brocot sequence

Function Resource: IncrementalParallelSelect

Incrementally select elements in parallel from a list or infinite range that satisfy a predicate

Example Resource: Solve PDEs with Events over Regions

Model thermostat-controlled heat generation in a room with three insulated walls and a glass front

Function Resource: CalkinWilf

Get the position of a fraction or vice-versa within the Calkin–Wilf sequence

Example Resource: Solve Poisson's Equation Over an Interactively Changing Region

Manipulate the boundary conditions interactively for a solution to Poisson's equation over a rectangle

Function Resource: ComplexD

Compute a partial derivative with respect to a complex variable or its conjugate

Function Resource: GeneralizedChaosGame

Create fractals with random partial jumps toward reference points

Function Resource: BacktrackSearch

Solve computational problems using a generic backtracking algorithm

Function Resource: RowSpace

Compute properties of the row space of a matrix

Function Resource: ColumnSpace

Compute properties of the column space of a matrix

Function Resource: SubspaceAngle

Compute the angle between two subspaces

Function Resource: SymbolicSort

Sort symbolic expressions using assumptions

Function Resource: PlanarPolygonFragmentation

Decompose a pair of polygons into disjoint fragments

Function Resource: RecognizeSeries

Recognize functions by their power series expansions

Function Resource: CoordinateVector

Find the coordinate vector of a vector with respect to a basis

Function Resource: BlockSubmatrices

Decompose a matrix into a comprehensive set of smaller matrices

Function Resource: LinearCombination

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

Function Resource: FareySunburst

Create a Farey sunburst

Function Resource: IndependentComponentAnalysis

Decompose a matrix into Independent Component Analysis matrix factors

Function Resource: NonNegativeMatrixFactorization

Decompose a matrix into two non-negative matrix factors

Function Resource: SolveVacuumADMEquations

Determine whether a given ADM decomposition is a solution to the vacuum ADM equations

Function Resource: FindNestedTransientRepeat

Decompose a nested iteration into its transient and repeating parts

Neural Net Resource: Scaled-YOLO V4 Trained on MS-COCO Data

Detect and localize objects in an image

Function Resource: DorlingCartogram

Create a non-overlapping cartogram type with visual equalization, partial topology preservation and no shape preservation

Neural Net Resource: YOLO V5 Trained on MS-COCO Data

Detect and localize objects in an image

Function Resource: SolarEclipseIcon

Create a simple icon representing the appearance of a solar eclipse

Function Resource: LineFit

Fit a line to data points in n-dimensional space

Function Resource: TriangularSets

Create a triangular set decomposition for a given list of polynomials and variables

Function Resource: PrimitiveToPolygons

Decompose a graphics 3D primitive into polygons when possible

Example Resource: Numerical Solution to the Telegraph Equation in 1D

Function Resource: ConvexLayers2D

Calculate the convex layers of a set of 2D points

Example Resource: Compare Color Sets and Color Spaces

Look at color sets based on their spectral colors and the fraction each occupies in different color spaces

Example Resource: Modes of a Pentagon Drum

Compute and plot eigenmodes of a polygon drum

Example Resource: Cooling Effect of a Duct with a Cooling Liquid

Neumann heat flux values prescribe the flux over the boundary edge of an axisymmetric cross section of a pipe

Function Resource: DominatingIntegerPartitionQ

Determine if one integer partition dominates another

Example Resource: Testing the Redundancy of English

Find what fraction of the letters in a piece of English text can be removed, while still allowing the text to be read

Function Resource: ActuarialCommutation

Creates an Association containing values for the six standard commutation functions used in actuarial mathematics

Example Resource: PDE over a 3D Space Shuttle Region

Apply Finite Element method to solve PDEs over a 3D space shuttle region and visualize solutions

Function Resource: CurvedSpacetimeTriangulation

Produce causal graphs by dynamically triangulating a specified region of a (potentially curved) spacetime

Function Resource: FlatSpacetimeTriangulation

Produce causal graphs by dynamically triangulating a flat (Minkowski) spacetime

Example Resource: Solve a Nonlinear Model of Fluid Flow

Model the time-dependent flow around a cylinder with the transient Navier–Stokes equation

Function Resource: SequenceLimit

Numerically estimate the limit of a sequence of values

Example Resource: Magnetic Potential inside an Electric Motor

Find a fit for measured BH-curve data with a Gaussian model to solve a magnetostatic problem

Function Resource: NearestKroneckerProductSum

Approximate a numerical matrix as sum of Kronecker products

Paclet Resource: AntonAntonov/MonadicLatentSemanticAnalysis

Software monad for Latent semantic analysis

Example Resource: Model Energy Transport Dynamics

Solve Navier-Stokes equations coupled with a heat transfer equation over a rectangular region with cutout

Function Resource: ExtrinsicCurvatureTensor

Represent the extrinsic curvature tensor field for a Riemannian submanifold

Example Resource: Fokker–Planck Mass Transport Model

Example Resource: Solute Diffusion under Centrifugation

Model the Lamm equation in a sector of a disk

Example Resource: Smoluchowski Diffusion Equation

Model diffusion with a conservative mass transport equation

Example Resource: Numeric Cyclic Voltammetry

Solve a coupled reaction model

Neural Net Resource: Sketch-RNN Trained on QuickDraw Data

Generate hand-drawn sketches

Function Resource: HalfGCD

Compute the half-GCD of a pair of integers

Data Resource: Kepler-11 Light Curve Data

Light curve data for planetary system Kepler-11

Function Resource: FromNumberExpansion

Rational approximation of a real number using different kinds of commonly known series expansions

Function Resource: NumberExpansion

Express a number as an expansion using any of several methods

Function Resource: SimultaneousRationalize

Approximately rationalize a set of numbers to give a common denominator

Function Resource: OutShuffle

Perform an out shuffle on a list

Function Resource: InShuffle

Perform an in shuffle on a list

Function Resource: ProjectionMatrix

Compute the projection matrix for a given vector space

Function Resource: SignLogDet

Compute the sign and natural logarithm of the determinant of a matrix

Data Resource: Sample Data: Bronze Gradient Filter

Locations of bronze particles in a gradient filter annotated with radii (in millimeters) marks

Function Resource: DiagonalizeMatrix

Get the diagonalized matrix of a given matrix

Function Resource: LinearSolveModIntegers

Solve rational linear system modulo the integers

Function Resource: ComputeMatrixFunction

Compute a function of a square matrix

Function Resource: Pfaffian

Compute the Pfaffian of an antisymmetric (skew-symmetric) matrix

Function Resource: MatrixFieldOfValues

Evaluate the boundary curve of the field of values of a matrix

Function Resource: MatrixGeometricMean

Compute the geometric mean of two matrices

Function Resource: GershgorinDisks

Show the Gershgorin disks of a square matrix

Function Resource: LinearSolveMod

Solve a linear system with multiple moduli

Function Resource: FibonacciEncode

Fibonacci-digit encoding for a number

Function Resource: DistinctCompactBinaryHuffmanCode

Generate a tree or an association with properties for non-equivalent compact binary Huffman codes

Function Resource: MatrixMinimalPolynomial

Compute the minimal polynomial of a square matrix

Function Resource: PhylogeneticTreePlot

Plot a dendrogram for a set of genome nucleotide sequences

Function Resource: RandomUnimodularMatrix

Return a pseudorandom unimodular matrix

Function Resource: ExtractPlotImageData

Extract data from a plot image

Function Resource: PairwiseMultidimensionalScaling

Multidimensional scaling algorithm for embedding pairwise distances into a Cartesian space

Function Resource: SmallIntegerLinearSolve

Find a small solution to a system of linear equations over the integers

Function Resource: PlaneOfBestFit

Get the hyperplane that best fits a set of points

Function Resource: ModifiedGaussianQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for various modifications of Gaussian quadrature

Function Resource: OrthogonalLineFit

Find the best fitting line with respect to orthogonal distance

Function Resource: RandomSparseSPDMatrix

Create a random sparse symmetric positive definite matrix

Function Resource: GeneralizedDMSString

Convert an angle into a customizable degree-minute-second string

Function Resource: MultidimensionalScaling

Reduce a matrix of real values to low dimension using the principal coordinates analysis method

Function Resource: ApproximatePolynomialGCD

Compute an approximate GCD to a pair of polynomials with approximate coefficients

Function Resource: NSolveByMonodromy

Numerically solve for isolated roots of a square system of polynomial equations using monodromy