Riemann tensor | Wolfram Resource System

Wolfram/QuantumFramework

Perform analytic and numeric quantum computations

WolframExternalFunctions/GSLLink

GSLLink is a package that provides a link to the GNU Scientific Library (GSL) from the Wolfram Language

AntonAntonov/DataReshapers

Data reshaping functions

RiemannTensor

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

RiemannSum

Compute information related to a Riemann sum

BowenPing/STensor

Provide a STensor object for abstract indices tensor computation

InactiveRiemannSumToIntegral

Determine an integral corresponding to a Riemann sum

TensorDiagram

Display symbolic tensor expressions as a diagram

FromTensor

Convert TensorContract expressions into an equivalent form using Dot and Tr

ToTensor

Convert an expression involving ArrayDot, Dot, Transpose, Tr and MatrixPower into an equivalent expression using TensorContract

RiemannSphereComplexPlot

A 3D rotatable Riemann sphere version of ComplexPlot

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

MetricTensor

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

AdjacencyTensor

Compute the adjacency tensor of an arbitrary hypergraph

KirchhoffTensor

Compute the Kirchhoff tensor (Laplacian) of an arbitrary hypergraph

GyrationTensor

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

IdentityTensorReduce

Simplify expressions containing a symbolic identity tensor

TensorPureFunction

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

RiemannSurfacePlot3D

Plot Riemann surfaces of compositions of elementary functions

StressEnergyTensor

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

TensorCoordinateTransform

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

ExtrinsicCurvatureTensor

Represent the extrinsic curvature tensor field for a Riemannian submanifold

TensorIndexJuggling

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

QuantumTensorProduct

Compute the tensor product of quantum bases, states or operators

QuantumTensorAutomaton

A quantum cellular automaton model that evolves the tensor product of a collection of initial qubits using arbitrary compositions of unitary operators for a finite number of steps

VerbTense

Find the tenses of verbs and verb phrases in a given text

SO3TensorCommutators

Compute SO(3) representation tensor commutators and anti-commutators

RicciScalar

Compute the Ricci scalar for a metric

RicciCurvature

Compute the components of the Ricci curvature for a metric

PresentTenseRephrase

Rewrite text into the present tense

WolframRicciCurvatureTensor

Compute projections of the Wolfram–Ricci curvature tensor of a graph and many associated properties

Quantum Circuit Diagrams and Graphs

Visualize quantum circuits with custom labels and layout

EinsteinSummation

Given tensors and their indices, sum over repeated indices

DiscreteIntegralPlot

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

SolveEinsteinEquations

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

ArrayContract

General contraction of levels of an array

NumericalIntegralApproximation

Determine the value of an integral using a numerical method

AssociationOuter

Compute the generalized outer product of lists and get an association keyed by arguments

AdjacencyHypergraph

Compute the hypergraph with a specified adjacency tensor

TuckerDecomposition

Compute the Tucker decomposition of a tensor

ImportSafetensors

Import a safetensors binary file

KirchhoffHypergraph

Compute the hypergraph with a specified Kirchhoff tensor (Laplacian)

IntegralApproximationPlot

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

ADMDecomposition

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

DeBruijnNewmanH

Compute the values of the function from which the de Bruijn–Newman constant is defined

ChristoffelSymbol

Return the Christoffel symbol for a given metric

SolveVacuumEinsteinEquations

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

AbstractStrictMonoidalCategory

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

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

SolveVacuumADMEquations

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

ArrayContractThread

General contraction of levels of the outer product of arrays

HyperTr

Compute the hypertrace of a given hypermatrix

IntegralApproximationPlot3D

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

HarmonicConjugate

Compute the harmonic conjugate of a function

CPDecomposition

Compute the canonical polyadic (CP) decomposition of a tensor

DensityMatrixToStateMultipole

Represent matrix elements via density state multipoles (statistical tensors)

StateMultipoleToDensityMatrix

Represent state multipoles (statistical tensors) via density matrix elements

InverseStereographicProjection

Compute the parametrization of a curve projected onto the unit sphere

ElasticData

Compute elastic properties of a material with a specified elastic tensor (stiffness matrix)

ThirdPersonRephrase

Rewrite text into a third-person point of view

MaterialsProjectData

Get material properties from the Materials Project database

DVectorField

Generate the tensor associated with the nth derivative of a vector field at a point

CoordinateMappingData

Calculate characteristic properties for a generalized mapping between two coordinate systems

LieART/LieART

Tools for Lie Algebras and Representation Theory

FractionalOrderD

Compute the fractional derivative of an expression

TableQ

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

SecondFundamentalFormCoefficients

Compute the coefficients of the second fundamental form

MatrixPartialTrace

Calculate a partial trace of a matrix

IdentityHypermatrix

Get the d-dimensional identity hypermatrix

ZXDiagramToQuantumDiscreteOperator

Convert a ZX-diagram into a discrete quantum operator

QuantumDiscreteOperatorToZXDiagram

Convert a discrete quantum operator into a ZX-diagram

QuaternionToRotationMatrix

Convert a unit quaternion to an equivalent rotation matrix

HyperDet

Compute the hyperdeterminant for a given hypermatrix (a multidimensional array of complex numbers)

AbstractPullback

Represent the abstract pullback of a collection of morphisms with common codomain in an abstract category

AbstractFunctor

Make an abstract model of a functor (i.e. a homomorphism between abstract categories)

AbstractProduct

Represent the abstract product of an arbitrary collection of objects in an abstract category

AbstractCoproduct

Represent the abstract coproduct of an arbitrary collection of objects in an abstract category

AbstractPushout

Represent the abstract pushout of a collection of morphisms with common domain in an abstract category

CRVZSum

Evaluate an alternating sum using the Cohen-Rodriguez Villegas-Zagier method

BernoulliBTree

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

Quantum Natural Gradient Descent via Block Diagonalization

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

Quantum Natural Gradient Descent via Variational Quantum Eigensolver

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

Parameter Trajectories for Quantum Natural Gradient Descent

Compare quantum natural gradient descent and regular gradient descent

Search the Wolfram Resource System