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Perform analytic and numeric quantum computations
A Wolfram Language implementation of the area method for geometry
Build, visualize, analyze, and simulate compartmental models
Functions for making software monads
Replace all occurrences of an algebraic subexpression with a new symbol
Compute the indefinite integral of an algebraic function in terms of elementary functions
Compute the hypertrace of a given hypermatrix
Transform components of tensors with arbitrary rank with regard to their transformation behavior under any given mapping
Substitution tiling systems based on algebraic barycentric coordinates
Perform matrix operations over a finite field
Return a substitution tiling
Evaluate the Khatri-Rao product of matrices
Calculations on conformal geometric algebra
A paclet for linear algebra
Computational tools for Geometric Algebras
Calculate the Tracy–Singh product of two matrices
Evaluate the face-splitting product of matrices
A paclet for linear algebra and its applications
Steps in an automated proof of the correctness of Wolfram’s Axiom
Given a metric, convert between covariant and contravariant components of a tensor
Picard Numbers of Quintic Surfaces
Tools for Lie Algebras and Representation Theory
Get the polynomial degree of an algebraic number
Algebraically rewrite an expression by completing the square
Move back and forth from the squared space or square root space of an algebraic number field
Compute a partial fraction decomposition over the algebraic closure of the rationals
Linear codes provide an optimal way for transmitting blocks of data over noisy channels
Verifies the Binet–Cauchy algebraic identity in a given dimension
Determine the consistency equations required for a system of linear equations to have a solution
Compute the Galois group for a polynomial
Compute a Groebner basis and a conversion matrix from the input polynomials to the basis
Generate the tensor associated with the nth derivative of a vector field at a point
Evaluate products and sums of monomials in the Steenrod algebra for the prime 2 written in the Serre–Cartan basis
Inverse of the Boole function
Evaluate the logarithmic norm of a square matrix
Compute the immanant of a square matrix associated with an integer partition
Make an abstract model of a quiver (i.e. a directed multigraph) that forms the basis of an abstract category
Perform persistent homology on a point cloud dataset
Replace repeated subexpressions in an expression with new symbols
Homogenize a polynomial with respect to a given set of variables
Split a vector-valued piecewise function into a list of piecewise functions
Evaluate the matrix sign function
Represent the abstract product of an arbitrary collection of objects in an abstract category
Represent the abstract coproduct of an arbitrary collection of objects in an abstract category
Make an abstract model of a category (i.e. a collection of objects and morphisms obeying associativity and identity axioms)
Get the d-dimensional identity hypermatrix
Make an abstract model of a category equipped with a strictly associative and unital tensor product structure
Produce random causal graphs by sprinkling points into a spacetime with a specified algebraic curvature function
Compute the hyperdeterminant for a given hypermatrix (a multidimensional array of complex numbers)
Represent the abstract pullback of a collection of morphisms with common codomain in an abstract category
Represent the abstract pushout of a collection of morphisms with common domain in an abstract category
Generate a commutation matrix
Complete the square of a quadratic polynomial having any number of variables but with no mixed terms
Get the augmented matrix of the system of linear equations
Make an abstract model of a functor (i.e. a homomorphism between abstract categories)
Check whether a number is transcendental
Find a small solution to a system of linear equations over the integers
Get a dynamic plot of a univariate function along with supplemental algebraic and calculus-based properties of the function
Generate the tridiagonal companion matrix of a univariate polynomial
Compute the geometric mean of two matrices
Evaluate a matrix polynomial
Decompose a vector into a linear combination of a set of vectors
Calculate the bialternate product of two square matrices
Estimate the Hölder p-norm of a numerical matrix
Compute the Dixon resultant with respect to a set of polynomials and variables
Produce random spatial graphs by sprinkling points into a Riemannian manifold with a specified intrinsic algebraic curvature function
Create a block-diagonal matrix from submatrices
Compute the Smith decomposition of a matrix of univariate polynomials
Compute the ordered Schur decomposition of a matrix
Compute the projection matrix for a given vector space
Compute the polar decomposition of a matrix
Compute the sign and natural logarithm of the determinant of a matrix
Compute properties of the row space of a matrix
Compute the angle between two subspaces
Compute properties of the column space of a matrix
Add row and column dividing lines to MatrixForm
Evaluate the inverse of a tridiagonal matrix
Evaluate the boundary curve of the field of values of a matrix
Calculate the symmetric Kronecker product of two matrices
Get a cofactor of a matrix
Show the Gershgorin disks of a square matrix
Find the topological boundary of a simplex or simplicial complex
Compute the minimal polynomial of a square matrix
Generate an n-sized centering matrix
Count the roots to a system of polynomials
Get the dual part of a dual number
A paclet for applications of dimensional analysis in physics and the engineering sciences
Compute the Weyr decomposition of a square matrix
Find the limiting ingredient in something similar to a chemical reaction
Compute the full QR decomposition of a matrix
Compute the rational Cholesky decomposition of a matrix
Compute the Takagi decomposition of a complex-symmetric matrix
Compute the Aasen decomposition of a Hermitian matrix
Expand elliptic functions in an expression
Compute a full rank decomposition of a matrix
Determine whether a set of vectors is linearly independent
Compute the bidiagonal decomposition of a numerical matrix
Find row and column effects in a data matrix by repeatedly subtracting the median
Determine if a linear system has a solution
A memory efficient form of solving linear systems modulo 2
Compute a function of a square matrix
Write a quadratic expression as a sum of squares by eliminating its mixed terms and then completing squares
Compute the Hermite decomposition of a matrix of univariate polynomials
Obtain the canonical bases for selected spaces of matrices and functions
Simulate the evaluation of a formal operator expression as a multiway system
Construct and aggregate subexpressions with descending and ascending operators
Represent a metric tensor (field) for a Riemannian or pseudo-Riemannian manifold
A memory efficient form of computing the null space of a matrix modulo 2
Convert a Hermitian-definite matrix pencil into a matrix with the same eigenvalues
Determine whether an expression represents a linear function of a given set of variables
Compute the LU decomposition of a matrix with different pivoting methods
Compute the Gaussian Hessenberg decomposition of a matrix
Plot order condition trees for Runge-Kutta method
Generate the comrade matrix corresponding to an orthogonal polynomial series
Compute the Popov decomposition of a matrix of univariate polynomials
Generate the Sylvester matrix of two univariate polynomials
A software monad for Sparse Matrix Recommender (SMR) workflows
Represent the Einstein curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold
Get the total degree of a polynomial in any number of variables
Generate the Venn diagram associated to a logical expression or collection of sets
Give the incomplete partial fraction decomposition of a rational function
Symmetric tridiagonal matrix for Gaussian quadrature
Simulate an arbitrary (potentially commutative) semigroup as a multiway system
Represent the Ricci curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold
Simulate an arbitrary (potentially abelian) group as a multiway system
Simulate an arbitrary (potentially commutative) monoid as a multiway system
Compute the nullity of a matrix
Returns the coefficient matrix of a system of equations
Determine if the span of one list of vectors is contained in the span of a second list of vectors
Functionally compose a Boolean expression
Compute the Pfaffian of an antisymmetric (skew-symmetric) matrix
Determine whether two lists of vectors span the same subspace
Compute the skew-tridiagonal decomposition of an antisymmetric matrix
Get the positions of the columns that are pivot columns of a matrix
Find a basis for the subspace spanned by a list of vectors
Find a basis for the sum of a list of subspaces of ℝ^n
Return a basis for the subspace spanned by the columns of a matrix
Get a matrix with a 1 in a selected position and 0s elsewhere
Find the null values and vectors for the pencil of a set of square matrices
Project a vector onto a subspace
Find a basis for the intersection of subspaces of ℝ^n
Return a basis for the subspace spanned by the rows of the matrix
A partial fraction decomposition with the Extension option
Represent the Riemann curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold
Plot a list of vectors in the plane
Compute the degree of a polynomial in any number of variables
Give the quadrature conditions for Runge-Kutta methods
Give the column-simplifying conditions for Runge-Kutta methods
Give the row-simplifying conditions for Runge-Kutta methods
Visualize the Eigenvectors of a 2 x 2 or 3 x 3 matrix
A generalized sigmoidal interpolating polynomial
List equations for Runge-Kutta methods
Determine the constant term in an expression
Find a rational interpolation of a function defined parametrically
Find an economized rational approximation to a function
Interpolate data using Akima's method or modifications of it
Import a sparse matrix from the SuiteSparse matrix collection
Return a pseudorandom unimodular matrix
Compute the pseudoquotient and pseudoremainder with respect to a given variable for a pair of polynomials
Represent a canonical decomposition of the metric for a Riemannian or pseudo-Riemannian manifold via the ADM formalism
Determine whether a given Riemannian or pseudo-Riemannian manifold is a solution to the vacuum Einstein field equations
Interactively fold a tree
Represent a stress-energy tensor (field) over a Riemannian or pseudo-Riemannian manifold
Determine whether a given stress-energy tensor (field) is a solution to the Einstein field equations
Determine whether an expression represents a quadratic function of a given set of variables
Find the determinant of the covariance matrix
Get the total variation of a matrix
The complement of the union and intersection of lists, with duplicates deleted
Find the coordinate vector of a vector with respect to a basis
Return a pseudorandom vector of a given type and size
Find an independently verifiable certificate proving that a polynomial system has no solutions
Classify and plot any polynomial of degree two or less in three or fewer variables
Compute the directional derivative of a function
Determine whether a given bit in an integer is set to one
Give the totals of the entries on the rising diagonals of a square matrix
A memory efficient form of Gaussian elimination to row echelon form modulo 2
Generate the generalized Fiedler companion matrix of a univariate polynomial
Create a triangular set decomposition for a given list of polynomials and variables
Represent the Christoffel symbols for (the Levi-Civita connection over) a Riemannian or pseudo-Riemannian manifold
Approximate a numerical matrix as sum of Kronecker products
A minimal PythonObject configuration for the SciPy package
Determine if a matrix represents a consistent system of linear equations
Decompose a Riemannian or pseudo-Riemannian manifold into a union of discrete hypersurfaces
Determine whether an expression represents a rational function of a given set of variables
Represent a quaternion object
Calculate a partial trace of a matrix
Tests whether a matrix is an antidiagonal matrix
Generate an orthonormal basis from a given 3D vector
Creates an antidiagonal matrix by given the antidiagonal
Determine whether a given ADM decomposition is a solution to the vacuum ADM equations
Evaluate the Carleman matrix of a function
Construct an interpolating polynomial approximation of a function using the Padua points
Convert coefficients of a series with respect to one orthogonal polynomial basis into another
Compute the weight of a Butcher tree
Compute the generic invariant of a group
Get characteristics of Butcher trees, such as the height, width, order, density and number of labelings
Get a list of terms in the Taylor series expansion of the error for Runge–Kutta methods
Use Stauduhar's method for Galois groups of polynomials
Get the full list of complex nth roots of a number
Find a rational interpolation of a function
Numerically evaluate the gradient of a function summed over the eigenvalues of a matrix, with respect to matrix parameters
Generate a matrix from a list such that no row or column contains the same element twice
Return the Christoffel symbol for a given metric
Fast vectorized evaluation of array inequalities
Evaluate the divided difference of a polynomial
Compute a reduced basis for a set of vectors, along with a unimodular matrix that converts from the vectors to the reduced basis
Normalizes the values of an Association
Estimate the level of difficulty for a given sudoku puzzle
Represent the extrinsic curvature tensor field for a Riemannian submanifold
Create a binary matrix with a rotated, ellipse-shaped region of 1s
Compute the shape operator on a surface
Get the polynomial with coefficients giving the number of nonisomorphic graphs for a given number of vertices
Find a permutation that minimizes a matrix sum
Convert a unit quaternion to an equivalent rotation matrix
Give the antidiagonal of a matrix
Compute the first order correlation matrix from an original correlation matrix
Symmetrically reorder the rows and columns of a square matrix
Replace the diagonal of an arbitrary matrix with zeros
Convert TensorContract expressions into an equivalent form using Dot and Tr
Generate the conditions under which a list of symbolic expressions has a particular ordering or set of orderings with respect to an operation
Given tensors and their indices, sum over repeated indices
Evaluate the Stieltjes-Jacobi polynomial
Find equations describing a linear recurrence corresponding to an input sequence
Generate the axis-angle representation of a three-dimensional rotation matrix
Decompose a matrix into two non-negative matrix factors
Find a unimodular conversion matrix corresponding to a lattice Gramian matrix
Get a magic square for any dimension
General contraction of levels of an array
Display symbolic tensor expressions as a diagram
Find an instance of n-dimensional vectors that produce a specified distance matrix
Evaluate Dirac matrices in any dimension
Closed form of cos(2π/p) where p is a Fermat prime (3, 5, 17, 257, 65537) a la Gauss
Generate a cubic B-spline curve that passes through given points
Solve the linear least absolute value problem
Solve for a given quantity in a geometric scene
Build a matrix containing which biomolecular sequence positions can bond
Get the irreducible group representation of SU(2) for a given angular momentum
Compute and visualize the roots of fractional (noninteger) derivatives of polynomials
Compute the control points of a Bézier curve that interpolates a given set of points
Append a column to the right of a matrix
Evaluate the Cayley-Menger matrix of a simplex
Return uniformly distributed random rotations in quaternion form
Construct all potential bond lists from a folding matrix associated with a biomolecular sequence
Classifies and plots any polynomial of degree two or less in two or fewer variables
Calculate the ray transfer matrix of a Gaussian optical system
Decompose a matrix into Independent Component Analysis matrix factors
Quickly cluster a point cloud by recursive separation
Support arithmetic operations for pairs of Eisenstein integers
Florentine families network in the early 15th century
Classification of Steiner Surfaces
Various simple matrix decompositions algorithms and support functions
Compute the indefinite integral of a rational function
Interactively construct a tree
Generate the orthogonal polynomial Vandermonde matrix corresponding to a given vector
Generate the companion matrix for the Newton interpolating polynomial of a given set of points
Convert a rotation matrix to an equivalent unit quaternion
Get a rational univariate representation for a general polynomial system
Make a diagrammatic representation of a linear map in the ZX-calculus
Convert a ZX-diagram into a pure quantum discrete state
Convert a ZX-diagram into a discrete quantum operator
Convert a discrete quantum operator into a ZX-diagram
Convert a pure quantum discrete state into a ZX-diagram
Compute the dimension of a polynomial ideal
Compute an approximate GCD to a pair of polynomials with approximate coefficients
Prove or disprove a closed first-order formula in the theory of univariate mixed trigonometric polynomials
Compute the half-GCD of a pair of integers