Category

# Symbolic & Numeric Computation

195 items

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

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

Represent the distribution of a quadratic form with a multivariate normal

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

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