Category

Higher Mathematical Computation

117 items

• 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

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

• 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

• 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

• ComplexTransformImage

Add a complex transformation to an image

• Composite

Get the nth composite number

• ConjugatePartition

Switch the rows and columns of a partition

• 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

Gives all possible ways to form proper brackets

• EgyptianFraction

Compute Egyptian fractions using different methods

• EulerianNumber

Get the number of permutations with a given number of ascents

• FactorGraph

Get a graph representation for the factorization of an integer

• 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

• 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

• FubiniNumber

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

• 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

• 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

• 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

• 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

• MultisetUnion

Perform the union operation on multisets

• 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

• 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

• 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

• 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

• 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