Wolfram Research

Category

Symbolic & Numeric Computation

195 items

  • Adjugate

    Give the adjugate matrix of a square matrix

  • AkimaInterpolation

    Interpolation and smooth curve fitting based on local procedures

  • ANOVA

    Perform an analysis of variance

  • AntidiagonalTotals

    Give the totals of the entries on the rising diagonals of a square matrix

  • ArcCosDegree

    Compute the inverse cosine of a number and return a result in degrees

  • ArcCotDegree

    Compute the inverse cotangent of a number and return a result in degrees

  • ArcCscDegree

    Compute the inverse cosecant of a number and return a result in degrees

  • ArcSecDegree

    Compute the inverse secant of a number and return a result in degrees

  • ArcSinDegree

    Compute the inverse sine of a number and return a result in degrees

  • ArcsineLawRandomnessTest

    Uses the arcsine law to assess the randomness of a sequence of zeros and ones

  • ArcTanDegree

    Compute the inverse tangent of a number and return a result in degrees

  • AreaBetweenCurves

    Find the area between two plane curves

  • Asymptotes

    Compute the asymptotes to a given curve in two dimensions

  • AugmentedMatrix

    Get the augmented matrix of the system of linear equations

  • BilliardPolygon

    Show the trajectory of a ball bouncing in a regular n-sided polygon

  • BinaryCodedTernary

    Self-delimiting number representation

  • BinaryIteratedLog

    Implements the binary iterated logarithm function

  • BinaryRunRandomnessTest

    Conducts a runs–based test on a sequence of zeros and ones

  • BisectionMethodFindRoot

    Determine the root of an equation using the bisection method

  • BitFlip

    Flip an individual bit in an integer (0 to 1 and 1 to 0)

  • BitStringLinearSolve

    A memory efficient form of solving linear systems modulo 2

  • BitStringNullSpace

    A memory efficient form of computing the null space of a matrix modulo 2

  • BitStringRowReduce

    A memory efficient form of Gaussian elimination to row echelon form modulo 2

  • BoolEval

    Fast vectorized evaluation of array inequalities

  • ButcherTreeCount

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

  • ButcherTreeQ

    Determine if a Butcher tree is in valid functional syntax

  • ButcherTrees

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

  • ButcherTreeSimplify

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

  • ChebyshevPsi

    Calculate the value of the second Chebyshev function ψ(x)

  • ChebyshevTheta

    Calculate the value of the first Chebyshev function θ(x)

  • ChiSquareCI

    Estimate the confidence interval based on a Chi-squared distribution

  • ChiSquareRandomnessTest

    Tests a sequence of 0s and 1s or a set of random reals between 0 and 1 for equidistribution and returns a p-value

  • ClausenCl

    Compute the Clausen functions

  • CoefficientMatrix

    Returns the coefficient matrix of a system of equations

  • CofactorMatrix

    Give the matrix of cofactors for a given input matrix

  • ColumnSpace

    Compute properties of the column space of a matrix

  • ColumnSpaceBasis

    Return a basis for the subspace spanned by the columns of a matrix

  • CommonDivisors

    Find the common divisors of two or more integers

  • CommonMultiples

    Finds the common multiples of two or more integers

  • CompleteSquare

    Algebraically rewrite an expression by completing the square

  • CompleteTheSquare

    Complete the square of a quadratic polynomial having any number of variables but with no mixed terms

  • ComplexRootQ

    Determine if a given number is an integer complex root of another number

  • ComplexRoots

    Get the full list of complex nth roots of a number

  • ConditionedMultinormalDistribution

    Calculate conditional and marginal distributions of the multivariate normal distribution

  • ConstantTerm

    Determine the constant term in an expression

  • CoordinateVector

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

  • CoprimeIntegerList

    Return a list of positive integers coprime to a given integer

  • CosDegree

    Compute the cosine of an angle given in degrees

  • CotDegree

    Compute the cotangent of an angle given in degrees

  • CscDegree

    Compute the cosecant of an angle given in degrees

  • CurvaturePlot

    Plot a curve defined by its curvature

  • CUSUMMaxRandomnessTest

    Conducts a cumulative sum–based randomness test that creates a test statistic from the maximum value that a cumulative sums random walk achieves

  • DiagonalizeQuadratic

    Write a quadratic expression as a sum of squares by eliminating its mixed terms and then completing squares

  • DigitSum

    Find the sum of digits in the positional representation of an integer

  • DiracMatrix

    Dirac matrices in any dimensions

  • DiscreteIntegralPlot

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

  • EconomizedRationalApproximation

    Find an economized rational approximation to a function

  • EffectivePrecision

    Get the effective precision of an expression

  • EgyptianFraction

    Compute Egyptian fractions using different methods

  • EinsteinSolid

    Make a simulation of the Einstein solid

  • EllipsoidProbability

    Find the cumulative probability within the specified elliptic domain

  • EllipsoidQuantile

    Find ellipsoidal location statistics

  • EllipsoidQuartiles

    Find the ellipsoidal loci of the quartiles of matrix

  • Erfci

    Set up a symbol to give an error message when called with an unexpected number of arguments

  • EulerEquations

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

  • EvenFunctionQ

    Determine whether an expression is an even function of the given variable or variables

  • FormatFactorization

    Express an integer factorization as it would be seen in a factorization table

  • FractionalBrownianMotion2D

    Generate a fractional Brownian surface

  • FRatioCI

    Estimate the confidence interval based on an F-ratio distribution

  • FromNegabinary

    Recover an integer from negabinary representation

  • FunctionDiscontinuities

    Compute the discontinuities of a function of a single variable

  • FunctionParity

    Determine the parity of a function (whether it is even or odd) with respect to one or more variables

  • GammaSimplify

    Simplify gamma functions in expression

  • GeneralizedVariance

    Find the determinant of the covariance matrix

  • GeneralMiniMaxApproximation

    Find a mini-max approximation of a function defined parametrically

  • GeneralRationalInterpolation

    Find a rational interpolation of a function defined parametrically

  • GrayCode

    Find the Gray code for an integer

  • HappyNumberQ

    Test whether an integer is a happy number

  • HasDefinitionsQ

    Check if a symbol has definitions associated with it

  • HeronFormula

    Compute the area of a triangle from the edge lengths

  • HessianDeterminant

    Compute the Hessian determinant of a function with respect to a list of variables

  • HessianMatrix

    Compute the Hessian matrix of a function with respect to a list of variables

  • HexStringToReal

    Convert a hexadecimal string to a real number

  • InactiveFactorInteger

    Compute the prime factorization of an integer and return it in an inactivated form

  • IncompletePFD

    Give the incomplete partial fraction decomposition of a rational function

  • InflectionPoints

    Find the inflection points of a function of one variable

  • IntegerPartitionQ

    Check whether the argument is a weakly decreasing list of positive integers

  • IntegralApproximationPlot

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

  • Intercepts

    Compute the intercepts of a function with the coordinate axes

  • IntersectionBasis

    Find a basis for the intersection of subspaces of ℝ^n

  • IntervalComplement

    Calculate the complement of intervals

  • Intrinsic3DCurve

    Plot intrinsic curves in 3D

  • InverseFourierCoefficient

    Find a function with a given Fourier exponential series

  • IteratedLog

    Determine the iterated logarithm of an input

  • JacobianDeterminant

    Compute the Jacobian determinant of a vector function with respect to a list of variables

  • JacobianMatrix

    Compute the Jacobian matrix of a vector function with respect to a list of variables

  • LatinSquare

    Generate a matrix from a list such that no row or column contains the same element twice

  • LinearConstraints

    Determine the consistency equations required for a system of linear equations have a solution

  • LinearFunctionQ

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

  • Loess

    Smooth noisy data using local regression

  • Logit

    The logit function from probability

  • LogSumExpLayer

    Neural network layer that implements the LogSumExp operation on any level

  • MachineIntegerQ

    Check if a number falls into the range of machine-sized integers for your computer

  • MagicSquare

    Get a magic square for odd dimension

  • MappedTransformedDistribution

    Transform a statistical distribution by applying the same function to all of its arguments

  • MatrixPencilSolve

    Find the null values and vectors for the pencil of a set of square matrices

  • MaximizeOverPermutations

    Find the permutation that maximizes a function

  • MeanDifferenceCI

    Estimate the confidence interval of the difference between the population means

  • MeanMedianLogNormalDistribution

    Create a lognormal distribution using mean and median as parameters instead of the conventional parameters

  • MiniMaxApproximation

    Find a mini-max approximation of a function

  • MinMaxRounded

    Get the minimum and maximum of a list rounded to a multiple

  • MortalityConvert

    Convert vector descriptions of mortality into another representation

  • MultiNonlinearModelFit

    Fit multiple datasets with multiple expressions that share parameters

  • MultivariateKurtosis

    Find the kurtosis coefficient for multivariate data

  • MultivariateMeanDeviation

    Find the scalar mean of the Euclidean distances between the multivariate data points and their mean

  • MultivariateMedianDeviation

    Find the median Euclidean distance from the median of the elements of multivariate data

  • MultivariateTrimmedMean

    Find the mean of multivariate data after removing outermost points

  • NDerivative

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

  • NewtonMethod

    Approximate the root of a function using Newton’s method

  • NewtonMethodPlot

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

  • NFourierCoefficient

    Find a numerical approximation for a Fourier exponential series coefficient of a function

  • NFourierCosCoefficient

    Find a numerical approximation for a Fourier cosine coefficient of a function

  • NFourierCosTransform

    Find a numerical approximation for a Fourier cosine transform

  • NFourierSequenceTransform

    Find a numerical approximation to the Fourier sequence transform

  • NFourierSeries

    Find a numerical approximation for an exponential Fourier series expansion of a function

  • NFourierSinCoefficient

    Find a numerical approximation for a Fourier sine coefficient of a function

  • NFourierSinTransform

    Find a numerical approximation for a Fourier sine transform

  • NFourierTransform

    Find a numerical approximation for a Fourier transform

  • NFourierTrigSeries

    Find a numerical approximation for a trigonometric Fourier series expansion of a function

  • NInverseFourierCoefficient

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

  • NInverseFourierCosTransform

    Find a numerical approximation for an inverse Fourier cosine transform

  • NInverseFourierSequenceTransform

    Find a numerical approximation to the inverse Fourier sequence transform of a periodic function

  • NInverseFourierSinTransform

    Find a numerical approximation for an inverse Fourier sine transform

  • NInverseFourierTransform

    Find a numerical approximation for the inverse Fourier transform

  • NInverseLaplaceTransform

    Find the numerical approximation for the inverse Laplace transform

  • NLimit

    Find the limiting value of an expression numerically

  • NormalCI

    Estimate the confidence interval based on a normal distribution

  • NResidue

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

  • NSeries

    Find a numerical approximation of a series expansion of a function

  • NthDigit

    Compute the digit in a given place of the positional representation of a number

  • Nullity

    Compute the nullity of a matrix

  • NVariationalBound

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

  • OddFunctionQ

    Determine whether an expression is an odd function of the given variable or variables

  • OEISSequence

    Return the list provided by the OEIS for a given OEIS sequence number

  • PolyGammaSimplify

    Simplify polygamma functions in an expression

  • PolyLogSimplify

    Simplify polylogarithms in an expression

  • PolynomialDegree

    Compute the degree of a polynomial in any number of variables

  • PolynomialHomogenize

    Homogenize a polynomial with respect to a given set of variables

  • PrimitiveRootOfUnityList

    Get the set of primitive nth roots of unity

  • ProjectOnSubspace

    Project a vector onto a subspace

  • QuadraticFormDistribution

    Represent the distribution of a quadratic form with a multivariate normal

  • QuadraticFunctionQ

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

  • QuadraticResidues

    Compute the quadratic residues of an integer

  • RandomRealPoint

    Randomly choose a point within a specified domain

  • RationalInterpolation

    Find a rational interpolation of a function

  • RealEuclideanDistance

    Get the Euclidean distance between two real vectors without using absolute value

  • RealToHexString

    Give a string representing the hexadecimal form of a real number

  • RotatedEllipseMatrix

    Create a binary matrix with a rotated, ellipse-shaped region of 1s

  • RoundedPercentageShare

    Calculate rounded percentages that always sum to 100%

  • RowSpace

    Compute properties of the row space of a matrix

  • RowSpaceBasis

    Return a basis for the subspace spanned by the rows of the matrix

  • RunCountRandomnessTest

    Conduct a runs up–based randomness test on a sequence of random reals between 0 and 1

  • RungeKuttaMethod

    Solve differential equations using the Runge-Kutta method

  • RunLengthRandomnessTest

    Conduct a randomness test on a sequence of random reals between 0 and 1 using run lengths of increasing subsequences

  • SameSpanQ

    Determine whether two lists of vectors span the same subspace

  • SecDegree

    Computes the secant of an angle given in degrees

  • SerialRandomnessTest

    Conduct an empirically derived test that assesses randomness using the frequencies of serial combinations of 0s and 1s

  • SimplexBoundary

    Find the topological boundary of a simplex or simplicial complex

  • SimplexMedian

    Get the simplex median of the elements of a matrix

  • SimplifyRepeatedSubexpressions

    Replace repeated subexpressions in an expression with new symbols

  • SinDegree

    Compute the sine of an angle given in degrees

  • SmootherStep

    An improved sigmoidal interpolation function

  • SmoothStep

    A sigmoidal interpolation function

  • SpectralRandomnessTest

    Use a discrete cosine transform–based method to test the randomness of a sequence of random reals

  • SqrtSpace

    Move back and forth from the squared space or square root space of an algebraic number field

  • StationaryPoints

    Compute the stationary points of a function of one or more variables

  • StudentTCI

    Estimate the confidence interval based on Student t distribution

  • SuggestPlotRange

    Get a variable range against which to plot a given function

  • SumBasis

    Find a basis for the sum of a list of subspaces of ℝ^n

  • TanDegree

    Compute the tangent of an angle given in degrees

  • TangentLine

    Compute properties of the tangent line to a curve at a given point

  • TensorCoordinateTransform

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

  • ToNegabinary

    Get the negabinary representation of an integer

  • TotalVariation

    Get the total variation of a matrix

  • Trapezoid

    Create quadrilateral polygon with two parallel sides

  • TriangleEdgesQ

    Test if three given lengths make a triangle

  • TwoSidedPValue

    Find the probability of the absolute value of the test statistic being at least as extreme as the given value

  • UnitMatrix

    Get a matrix with a 1 in a selected position and 0s elsewhere

  • VarianceAround

    Calculate the variance of a list along with its uncertainty

  • VarianceRatioCI

    Estimate the confidence interval of the ratio of the population variances

  • VariationalBound

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

  • VariationalD

    Get the variational derivative of a functional

  • WishartDistribution

    Represent the Wishart distribution

  • ZeroDiagonal

    Replace the diagonal of an arbitrary matrix with zeros

  • ZetaSimplify

    Simplify zeta functions in expressions