Category

# Higher Mathematical Computation

136 items

• ### AggregationSystem

Evolve a 2D array of cells by randomly adding new cells at positions with certain neighborhood configurations

• ### AlgebraicSubstitutionTiling

Return a substitution tiling

• ### Antidiagonal

Give the antidiagonal of a matrix

• ### AntidiagonalMatrixQ

Tests whether a matrix is an antidiagonal matrix

• ### ArcsineLawRandomnessTest

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

• ### AreaBetweenCurves

Find the area between two plane curves

• ### AxisAngle

Generate the axis-angle representation of a three-dimensional rotation matrix

• ### BasisFromVector

Generate an orthonormal basis from a given 3D real vector

• ### BesselSimplify

Simplify Bessel functions in expression

• ### BinaryCodedTernary

Self-delimiting number representation

• ### BinaryRunRandomnessTest

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

• ### BitBooleanFunction

Apply a Boolean function to corresponding bits in integers

• ### 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, row- or column- simplifying conditions

• ### ChainD

Get the derivative with respect to a function

• ### ChaosGame

Plot iterations for the 2D chaos game

• ### ChebyshevPsi

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

• ### ChebyshevTheta

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

• ### 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

• ### ChristoffelSymbol

Return the Christoffel symbol for a given metric

• ### ChromaticNumber

Compute the vertex chromatic number of a graph

• ### ClausenCl

Compute the Clausen functions

• ### Cofactor

Get a cofactor of a matrix

• ### Collatz

Get the Collatz sequence starting with a given value

• ### ColumnSpace

Compute properties of the column space of a matrix

• ### Composite

Get the nth composite number

• ### ConjugatePartition

Switch the rows and columns of a partition

• ### Cos2PiOverFermatPrime

Closed form of cos(2π/p) where p is a Fermat prime (3, 5, 17, 257, 65537) a la Gauss

• ### CousinPrimes

Get the pairs of primes that differ by 4

• ### CumulativeAverages

Calculate the cumulative averages of a list

• ### CUSUMMaxRandomnessTest

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

• ### CyclicTagSystem

Compute the evolution of a cyclic tag system

• ### DerangementQ

Test whether the permutation list is completely scrambled

• ### Derangements

Give all the ways the numbers 1, 2, …, n can be scrambled completely

• ### DescendingSublists

Split a list at its left-to-right maxima

• ### DyckWords

Give all possible ways to form proper brackets

• ### EgyptianFraction

Compute Egyptian fractions using different methods

• ### EinsteinSummation

Given tensors and their indices, sum over repeated indices

• ### EulerianNumber

Get the number of permutations with a given number of ascents

• ### ExtendedGroebnerBasis

Compute a Groebner basis and a conversion matrix from the input polynomials to the basis

• ### FactorGraph

Get a graph representation for the factorization of an integer

• ### FactorialMod

Fast factorial modulo a given number

• ### FerrersDiagram

Display the Ferrers diagram of a partition with dots

• ### Fibbinary

Get the fibbinary sequence

• ### FindGroupIsomorphism

Find up to a specified number of isomorphisms between two permutation groups

• ### FindProperColorings

Find all proper k-colorings of a specified graph

• ### FormatFactorization

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

• ### FrobeniusSymbolFromPartition

Get a pair of lists representing the Ferrers diagram of a partition

• ### FromInversionVector

Construct the permutation list corresponding to the given inversion vector

• ### FromTensor

Convert TensorContract expressions into an equivalent form using Dot and Tr

• ### FubiniNumber

Count the number of ways to partition a set where the order of the subsets matters

• ### FunctionJectivity

Determine the injectivity and surjectivity of a function

• ### GeneralizedChaosGame

Create fractals by random partial jumps toward reference points

• ### Goldbach

Get all representations of an even integer as the sum of two primes

• ### HappyNumberQ

Test whether an integer is a happy number

Get steps of Hofstadter's MU riddle

• ### HookLengths

Get the list of lists whose entries are the hook lengths of the entries of a Young diagram

• ### IntegerPartitionFrequency

Counts the number of times an integer k appears within all possible ways to partition an integer n without calculating n’s integer partitions

• ### IntegerPartitionQ

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

• ### IntegralApproximationPlot3D

Compute and plot the approximation to the integral of a function of two variables on a rectangle using different methods and partition types

• ### InversionVectorQ

Check if a list is the inversion vector of a permutation written as a list

• ### IrregularPeriodogram

Compute a periodogram for data from unevenly spaced intervals

• ### IsingModelCA

Simulate the Ising model using a cellular automata

• ### KruskalAlgorithm

Find the minimal spanning tree for a given set of points in Euclidean space

• ### KSetPartitions

Give all possible ways to partition a set into a given number of subsets, ignoring order of blocks and within blocks

• ### KullbackLeiblerDivergence

Calculate the Kullback-Leibler divergence between two distributions

• ### LargestPrimeFactor

Find the largest prime factor of a given integer

• ### LargestPrimeGap

Give the greatest gap between the primes up to the argument

• ### LehmerCodeFromPermutation

Create the Lehmer code corresponding to a given permutation

• ### Logit

The logit function from probability

• ### LSystemPlot

Display an L-system

• ### LuckyNumbers

Get a list of lucky numbers

• ### MobileAutomaton

Compute the evolution of a mobile automaton

• ### MobileAutomatonPlot

Visualization of the evolution of a mobile automaton

• ### MobileAutomatonRulePlot

Generate the rule icon for a mobile automaton

• ### MultisetCardinality

Determine the cardinality for a multiset

• ### MultisetComplement

Perform the complement operation on multisets

• ### MultisetDiceDissimilarity

Compute the Dice dissimilarity of two multisets

• ### MultisetInclusionQ

Test whether or not one multiset is included in another multiset

• ### MultisetIntersection

Perform the intersection operation on multisets

• ### MultisetJaccardDissimilarity

Compute the Jaccard dissimilarity of two multisets

• ### MultisetProduct

Perform the product operation on multisets

• ### MultisetSokalSneathDissimilarity

Compute the Sokal–Sneath dissimilarity of two multisets

• ### MultisetSum

Perform the sum operation on multisets

• ### MultisetSupport

Determine the support for a multiset

• ### MultisetSymmetricDifference

Get the symmetric difference of the given lists

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

• ### NFAPlot

Plot a nondeterministic finite automaton

• ### NFASimulation

Simulate the behavior of a nondeterministic finite automaton

• ### NInverseLaplaceTransform

Find the numerical approximation for the inverse Laplace transform

• ### Nullity

Compute the nullity of a matrix

• ### PartitionCrank

Get Dyson's crank of an integer partition

• ### PartitionFromFrobeniusSymbol

Construct the corresponding partition, given a Frobenius symbol

• ### PartitionRank

The largest part minus the number of parts of a partition

• ### PascalsTriangle

Display a given number of rows in Pascal's triangle

• ### PenroseTile

Make plots of Penrose tiles

• ### PermutationInvolutionQ

Test whether a permutation equals its inverse

• ### PhiNumberSystem

Get a list of powers of the golden ratio which sum to a given integer

• ### PowerSubdivide

Subdivide an interval such that the ratio of subsequent elements is constant

• ### PowerTowerMod

Give the remainder on division of a power tower expression

• ### PrimeQCertificateCheck

Test if a certificate can be used for ascertaining the primality or compositeness of a number

• ### PrimitiveRootOfUnityList

Get the set of primitive nth roots of unity

• ### ProvablePrimeQ

Certify a number as provably prime

Compute the quadratic residues of an integer

• ### 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

• ### Quaternion

Represent a quaternion object

• ### RaggedDigitsPlot

Plot an array of digits, allowing them to be ragged on the left

• ### RationalInterpolation

Find a rational interpolation of a function

• ### ReasonableRuler

Find a near minimal set of marks for an integer length ruler so that all smaller integer distances are measurable

• ### RiemannSurfacePlot3D

Plot Riemann surfaces of compositions of elementary functions

• ### RowSpace

Compute properties of the row space of a matrix

• ### RunCountRandomnessTest

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

• ### RunLengthRandomnessTest

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

• ### SequentialSubstitutionSystemPlot

Visualization of the evolution of a sequential substitution system

• ### SequentialSubstitutionSystemRulePlot

Generate the rule icon for a sequential substitution system

• ### SerialRandomnessTest

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

• ### SexyPrimes

Get the pairs of primes that differ by 6

• ### SimplexMeasure

Get the measure of a simplex or simplicial complex

• ### SmallestPartsFunction

Total number of smallest parts in the partitions of a positive integer

• ### SpectralRandomnessTest

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

• ### StandardSimplex

Get the standard simplex for a specified dimension

• ### StemLeafPlot

Construct a stem-and-leaf diagram

• ### SymbolicSystem

Get the evolution of a symbolic system

• ### TagSystem

Compute the evolution of a tag system

• ### TagSystemRulePlot

Generate the rule icon for a tag system

• ### 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

• ### ToInversionVector

Get the inversion vector of a permutation written as a list

• ### Totatives

Get the integers from 1 to n that have no common proper factor with n

• ### ToTensor

Convert an expression involving Dot and Tr into an equivalent expression using TensorContract

• ### TwinPrimes

Get the pairs of primes that differ by 2

• ### UlamSequence

Starting with the third term, give the least integer expressible uniquely as the sum of two distinct earlier terms

• ### ValidGraphColoring

Check if the given graph coloring is valid

• ### VarianceAround

Calculate the variance of a list along with its uncertainty

• ### WastefulNumberQ

Test whether an integer is a wasteful number

• ### ZeckendorfRepresentation

Give the 0–1 list that indicates the unique nonconsecutive Fibonacci numbers that sum to the non-negative integer input