Wolfram/LLMFunctions

Language model and other API based machine learning functions for the WL

  WolframChemistry/MoleculeFingerprints

Compute and compare molecule fingerprints

  TheRealCStover/Trigonometry

A collection of lesser-known circular and hyperbolic trig functions and their inverses

  StianRamsnes/MaXrd

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

  PeterBurbery/WordCloud

Word cloud functionality

  JaneShenGunther/TCGADataTool

TCGA Data Tool retrieves TCGA cancer datasets easily from the NCI GDC and TCIA portals

  VariationalD

Get the variational derivative of a functional

  VariationalBound

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

  TotalVariation

Get the total variation of a matrix

  NVariationalBound

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

  Orbital Variations and Insolation Database

Dataset of insolation values at different latitudes from 5000000 cal yr BP (-4998050 CE) to 0 cal yr BP (1950 CE)

  Wolfram/Lambda

Tools for the lambda calculus

  FernandoDuarte/Itovsn3

A Mathematica package for Symbolic Ito calculus

  WolframAlphaMath/SpecialFunctionsAndCalculus

Compute MeijerG forms of functions, fractional-order integro-derivatives, integral transforms and more

  Generate Constants of Integration & Summation

  Quantum Natural Gradient Descent via Variational Quantum Eigensolver

Optimize a variational quantum circuit using quantum natural gradient descent through VQE

  TwilightTimes

Compute the starting times for variations of twilight

  GainRescale

Apply a flatter or steeper variation in the middle of an interval

  MakeZXDiagram

Make a diagrammatic representation of a linear map in the ZX-calculus

  FractionalD

Calculate a fractional derivative

  EulerEquations

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

  AngleBetweenPlanes

Compute the angle between two planes in R^3

  FunctionDifferentiability

Find the conditions for which a single-variable, real-valued function is differentiable

  CoplanarQ

Determine whether a set of points lies in a plane

  CollinearQ

Determine whether a set of points lie on a line

  FindCombinatorProof

Attempt to find a proof of a theorem in combinatory logic using a given combinatory calculus

  FractionalIntegrate

Calculate fractional integrals

  FunctionConcavity

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

  ChebyshevQuadratureAbscissas

Get a numerically sorted list of abscissas for Chebyshev equal-weight quadrature

  Stable Diffusion V1

Generate photorealistic images

  MultinormalKLDivergence

Compute the Kullback–Leibler divergence between two multinormal distributions

  CurveAnalysis

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

  PossiblyDifferentiableQ

Determine whether a single-variable, real-valued function is differentiable

  NewtonCotesWeights

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

  FiniteDifferenceStencil

Compute the finite difference stencil for a specified set of variables and their derivatives

  GlobalMaxima

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

  ProductRule

Represent the derivative of a product, explicitly displaying the terms

  ChainRule

See how to apply the chain rule for derivatives

  SumRule

See how to apply the sum rule for derivatives

  QuotientRule

See how to apply the quotient rule for derivatives to an expression

  ProductD

Evaluate the product derivative of a function

  FejerQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for Fejér quadrature

  FractionalDTimeSeries

Calculate the fractional difference of a time series

  MonotonicFunctionQ

Check if a function is monotonic

  StrictlyMonotonicFunctionQ

Check if a function is strictly monotonic

  PowerRule

See how to apply the power rule for derivatives to an expression

  TangentPlane

Find the tangent plane of a function at a point

  ClenshawCurtisQuadratureWeights

Get a numerically sorted list of abscissa-weight pairs for Clenshaw-Curtis quadrature

  ProductIntegrate

Evaluate the product integral of a function

  NewtonCotesError

Find the error in the Newton–Cotes quadrature formula

  GaussianQuadratureWeights

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

  FunctionMonotonicity

Compute the regions on which an expression is monotonic

  HyperellipticODE

Get a physicist's constructive proof of Fuchs's theorem on hyperelliptic curves

  DihedralODE

Find the ordinary differential equation constraining periods of certain symmetrical curves

  GaussianQuadratureMatrix

Symmetric tridiagonal matrix for Gaussian quadrature

  DerivativeSignCharts

Get a grid of sign charts for a function and its first and second derivatives

  IntegrateRational

Compute the indefinite integral of a rational function

  MeanValueTheoremQuiz

Generate a quiz to assess understanding of the mean value theorem for derivatives

  DAVIDGeneEnrichmentAnalysis

Retrieve a functional enrichment analysis on a gene list from the DAVID genetic website

  EnsemblCrossReference

Look up Ensembl identifiers or external symbols and provide cross references in other databases

  IntegralApproximationPlot3D

Compute and plot an approximation to the integral of a function of two variables over a rectangle

  Quantum Natural Gradient Descent via Block Diagonalization

Optimize a variational quantum circuit using quantum natural gradient descent through block diagonalization

  IntegratePFD

Integrate a rational function using partial fraction decomposition

  ODENormalForm

Transform a differential equation into normal form

  SignChart

Get a number line diagram with information about where a function is positive, negative, zero or discontinuous

  HarmonicConjugate

Compute the harmonic conjugate of a function

  ZXDiagramToQuantumDiscreteState

Convert a ZX-diagram into a pure quantum discrete state

  ZXDiagramToQuantumDiscreteOperator

Convert a ZX-diagram into a discrete quantum operator

  QuantumDiscreteOperatorToZXDiagram

Convert a discrete quantum operator into a ZX-diagram

  QuantumDiscreteStateToZXDiagram

Convert a pure quantum discrete state into a ZX-diagram

  MetricTensor

Represent a metric tensor (field) for a Riemannian or pseudo-Riemannian manifold

  ButcherPlot

Plot order condition trees for Runge-Kutta method

  EnhancedGrad

Grad enhanced to evaluate using limits and at several points

  WeakPathGraphs

Create path graphs between two vertices in a graph where the paths are constructed without consideration of the direction of the edges

  ModifiedGaussianQuadratureWeights

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

  EinsteinTensor

Represent the Einstein curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

  RicciTensor

Represent the Ricci curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

  RungeKuttaMethod

Solve differential equations using the Runge-Kutta method

  LogContract

Contracts sums of logarithms into a single logarithm

  ApartAll

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

  NewtonMethod

Approximate the root of a function using Newton’s method

  SequenceLimit

Numerically estimate the limit of a sequence of values

  ExtendedApart

A partial fraction decomposition with the Extension option

  RiemannTensor

Represent the Riemann curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold

  FractionalOrderD

Compute the fractional derivative of an expression

  Spectrogram of a Synthesized Violin

  ButcherQuadratureConditions

Give the quadrature conditions for Runge-Kutta methods

  ButcherColumnConditions

Give the column-simplifying conditions for Runge-Kutta methods

  ButcherRowConditions

Give the row-simplifying conditions for Runge-Kutta methods

  TwistedSurface

Generate a surface twisting a curve

  StrophoidCurve

Compute a strophoid curve

  RungeKuttaOrderConditions

List equations for Runge-Kutta methods

  ComplexD

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

  SecondFundamentalFormCoefficients

Compute the coefficients of the second fundamental form

  RecognizeSeries

Recognize functions by their power series expansions

  ADMDecomposition

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

  SolveVacuumEinsteinEquations

Determine whether a given Riemannian or pseudo-Riemannian manifold is a solution to the vacuum Einstein field equations

  StressEnergyTensor

Represent a stress-energy tensor (field) over a Riemannian or pseudo-Riemannian manifold

  SolveEinsteinEquations

Determine whether a given stress-energy tensor (field) is a solution to the Einstein field equations

  QuadraticFunctionQ

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

  QuadricSurfacePlot

Classify and plot any polynomial of degree two or less in three or fewer variables

  DirectionalD

Compute the directional derivative of a function

  Intrinsic3DCurve

Plot intrinsic curves in 3D

  NewtonMethodPlot

Plot the function together with a graphical display of the Newton iterations approximating its root

  ChristoffelSymbols

Represent the Christoffel symbols for (the Levi-Civita connection over) a Riemannian or pseudo-Riemannian manifold

  DiscreteHypersurfaceDecomposition

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

  Dynamics of Simple Harmonic Motion in a Mass-Spring System

Explore the mass-spring system from equations to animations

  RationalFunctionQ

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

  FirstFundamentalFormCoefficients

Compute the coefficients of the first fundamental form of a surface

  AreaElement

Compute the area element for a surface

  GaussianCurvature

Compute the Gaussian curvature of a surface

  RichardsonExtrapolate

Calculate an accelerated version of a symbolic sequence

  ThieleExpansion

Expand a function into a Thiele continued fraction

  PerpendicularSurface

Compute the perpendicular surface of a curve

  GaussianQuadratureError

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

  Erfci

Evaluate the integral of the complementary error function

  CesaroEquation

Compute the Cesàro equation for a planar curve

  SolveVacuumADMEquations

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

  CarlemanMatrix

Evaluate the Carleman matrix of a function

  ButcherPhi

Compute the weight of a Butcher tree

  ButcherTreeQ

Determine if a Butcher tree is in valid functional syntax

  ButcherTreeData

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

  ButcherPrincipalError

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

  DiscreteIntegralPlot

Plot and find the area of a region determined by a list of points, the x axis and the type of boundary

  NEigenvalueSumGradient

Numerically evaluate the gradient of a function summed over the eigenvalues of a matrix, with respect to matrix parameters

  IntegralApproximationPlot

Compute and plot the approximation to the integral of a function on an interval

  ButcherTrees

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

  CurvaturePlot

Plot a curve defined by its curvature

  ChainD

Get the derivative with respect to a function

  FactorialSeriesExpansion

Expand a function into a factorial series

  GMM-3 Mars Gravity Map

Goddard Mars Model 3 map of the gravity field of Mars

  AbstractStrictMonoidalCategory

Make an abstract model of a category equipped with a strictly associative and unital tensor product structure

  Pose-Aware Face Recognition in the Wild Nets Trained on CASIA WebFace Data

Represent a facial image as a vector

  NLimit

Find the limiting value of an expression numerically

  NResidue

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

  BrioschiCurvature

Compute the Gaussian curvature for a metric

  PolynomialDividedDifference

Evaluate the divided difference of a polynomial

  NInverseFourierCosTransform

Find a numerical approximation for an inverse Fourier cosine transform

  NSeries

Find a numerical approximation of a series expansion of a function

  ButcherTreeCount

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

  ButcherTreeSimplify

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

  NDerivative

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

  ImplicitCurvature

Compute the implicit curvature of a curve

  UnitNormal

Compute the unit normal of a surface

  TotalSignedCurvature

Compute the total signed curvature of a curve

  AssociationNormalize

Normalizes the values of an Association

  CurvatureTorsionPlot3D

Plot a curve defined by its curvature and torsion

  NInverseFourierCoefficient

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

  InverseFourierCoefficient

Find a function with a given Fourier exponential series

  Modes of a Pentagon Drum

Compute and plot eigenmodes of a polygon drum

  Mass Accretion in Cataclysmic Variable Stars

Compute and visualize the impact point of stellar mass transfer streams onto accretion disks using event detection

  ExtrinsicCurvatureTensor

Represent the extrinsic curvature tensor field for a Riemannian submanifold

  UnwindingNumber

Evaluate the unwinding number

  ShapeOperator

Compute the shape operator on a surface

  CurveAberrancy

Compute the aberrancy of a plane curve

  LommelS

Evaluate the Lommel function

  AberrancyCurve

Compute the curve of aberrancy of a plane curve

  ArcTanIntegral

Evaluate the inverse tangent integral

  FindMinimumPlot

Visualize the function evaluations done by FindMinimum

  MovingOrthonormalFrame

Compute the moving orthonormal frame of a surface

  RicciCurvature

Compute the components of the Ricci curvature for a metric

  RuledSurfacePlot

Plot a ruled surface

  StieltjesJacobiE

Evaluate the Stieltjes-Jacobi polynomial

  ResNet-101 Trained on Augmented CASIA-WebFace Data

Represent a facial image as a vector

  PursuitCurvePlot

Plot a predator-prey pursuit curve

  NInverseLaplaceTransform

Find the numerical approximation for the inverse Laplace transform

  FractionalDPolynomialRoots

Compute and visualize the roots of fractional (noninteger) derivatives of polynomials

  Solve Poisson's Equation Over an Interactively Changing Region

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

  Numerical Solution to the Telegraph Equation in 1D

  FEMAddOnsInstall

Install or update the finite element FEMAddOns paclet

  PDE over a 3D Space Shuttle Region

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

  Solve a Nonlinear Model of Fluid Flow

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

  Solve PDEs with Events over Regions

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

  Kepler-11 Light Curve Data

Light curve data for planetary system Kepler-11

  Analyze Random Walks from Video

Track randomly moving particles and classify their trajectories

  Sample Data: Leukaemia NW England

Locations of leukaemia in N.W. England from 1982 to 1998, annotated with age, gender, deprivation index, and subject type marks

  NCBIGenomicSNPData

Retrieve information on reference SNPs from the NCBI database

  CombinatorEncode

Encode an SK combinator expression into a list of 0s and 1s

  TensorCoordinateTransform

Transform components of tensors with arbitrary rank with regard to their transformation behavior under any given mapping

  TensorIndexJuggling

Given a metric, convert between covariant and contravariant components of a tensor

  CoordinateMappingData

Calculate characteristic properties for a generalized mapping between two coordinate systems

  Sample Data: Meuse River

Annotated locations of soil samples along the Dutch bank of the Meuse River north of Maastricht

  BernoulliBTree

Generate a binary tree representation of Bernoulli numbers by Woon's method

  TensorPureFunction

Get a pure function whose argument is a vector or a matrix for a given tensor

  RandomBinaryTree

Generate a random binary tree

  ScalarPureFunction

Get a pure function whose argument is a vector for a given multivariable scalar function

  MatrixGeometricMean

Compute the geometric mean of two matrices

  ReadabilityScore

Calculate the readability of a text using a standard formula

  Parameter Trajectories for Quantum Natural Gradient Descent

Compare quantum natural gradient descent and regular gradient descent

  StringsToVectors

Convert a set of text strings to numeric vectors