section 3 · Library functions 📚

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M (continued)

Math::NumSeq::ReverseAddSteps(3pm)steps of the reverse-add algorithm to reach palindrome✨
Math::NumSeq::Runs(3pm)runs of consecutive integers✨
Math::NumSeq::SelfLengthCumulative(3pm)cumulative digit length of own values✨
Math::NumSeq::SophieGermainPrimes(3pm)Sophie Germain primes p and 2*p+1 prime✨
Math::NumSeq::SpiroFibonacci(3pm)recurrence around a square spiral✨
Math::NumSeq::SqrtContinued(3pm)continued fraction expansion of a square root✨
Math::NumSeq::SqrtContinuedPeriod(3pm)period of the continued fraction for sqrt(i)✨
Math::NumSeq::SqrtDigits(3pm)the digits of a square root✨
Math::NumSeq::SqrtEngel(3pm)Engel expansion of a square root✨
Math::NumSeq::Squares(3pm)perfect squares✨
Math::NumSeq::StarNumbers(3pm)star numbers 6*i*(i-1)+1✨
Math::NumSeq::SternDiatomic(3pm)Stern's diatomic sequence✨
Math::NumSeq::Tetrahedral(3pm)tetrahedral numbers i*(i+1)*(i+2)/6✨
Math::NumSeq::Totient(3pm)Euler's totient function, count of coprimes✨
Math::NumSeq::TotientCumulative(3pm)cumulative totients✨
Math::NumSeq::TotientPerfect(3pm)sum of repeated totients is N itself✨
Math::NumSeq::TotientSteps(3pm)count of repeated totients to reach 1✨
Math::NumSeq::TotientStepsSum(3pm)sum of repeated totients to reach 1✨
Math::NumSeq::Triangular(3pm)triangular numbers✨
Math::NumSeq::Tribonacci(3pm)Tribonacci numbers✨
Math::NumSeq::TwinPrimes(3pm)twin primes✨
Math::NumSeq::UlamSequence(3pm)integers uniquely the sum of two previous terms✨
Math::NumSeq::UndulatingNumbers(3pm)numbers with alternating digits ABABAB...✨
Math::NumSeq::WoodallNumbers(3pm)Woodall numbers i*2^i-1✨
Math::NumSeq::Xenodromes(3pm)integers with all digits unique✨
Math::Pari(3pm)Perl interface to PARI.✨
Math::PariInit(3pm)load "Math::Pari" with specified $primelimit and $initmem.✨
Math::PlanePath(3pm)points on a path through the 2-D plane✨
Math::PlanePath::AlternatePaper(3pm)alternate paper folding curve✨
Math::PlanePath::AlternatePaperMidpoint(3pm)alternate paper folding midpoints✨
Math::PlanePath::AlternateTerdragon(3pm)alternate terdragon curve✨
Math::PlanePath::AnvilSpiral(3pm)integer points around an "anvil" shape✨
Math::PlanePath::AR2W2Curve(3pm)2x2 self-similar curve of four patterns✨
Math::PlanePath::ArchimedeanChords(3pm)radial spiral chords✨
Math::PlanePath::AztecDiamondRings(3pm)rings around an Aztec diamond shape✨
Math::PlanePath::Base::Digits(3pm)helpers for digit based paths✨
Math::PlanePath::Base::Generic(3pm)various path helpers✨
Math::PlanePath::Base::NSEW(3pm)multi-inheritance mixin for North, South, East, West unit steps✨
Math::PlanePath::BetaOmega(3pm)2x2 half-plane traversal✨
Math::PlanePath::CCurve(3pm)Levy C curve✨
Math::PlanePath::CellularRule(3pm)cellular automaton points of binary rule✨
Math::PlanePath::CellularRule190(3pm)cellular automaton 190 and 246 points✨
Math::PlanePath::CellularRule54(3pm)cellular automaton points✨
Math::PlanePath::CellularRule57(3pm)cellular automaton 57 and 99 points✨
Math::PlanePath::CfracDigits(3pm)continued fraction terms encoded by digits✨
Math::PlanePath::ChanTree(3pm)tree of rationals✨
Math::PlanePath::CincoCurve(3pm)5x5 self-similar curve✨
Math::PlanePath::Columns(3pm)points in fixed-height columns✨
Math::PlanePath::ComplexMinus(3pm)i-1 and other complex number bases i-r✨
Math::PlanePath::ComplexPlus(3pm)points in complex base i+r✨
Math::PlanePath::ComplexRevolving(3pm)points in revolving complex base i+1✨
Math::PlanePath::CoprimeColumns(3pm)coprime X,Y by columns✨
Math::PlanePath::Corner(3pm)points shaped around in a corner✨
Math::PlanePath::CornerAlternating(3pm)points shaped around a corner alternately✨
Math::PlanePath::CornerReplicate(3pm)replicating U parts✨
Math::PlanePath::CretanLabyrinth(3pm)infinite Cretan labyrinth✨
Math::PlanePath::CubicBase(3pm)replications in three directions✨
Math::PlanePath::DekkingCentres(3pm)5x5 self-similar✨
Math::PlanePath::DekkingCurve(3pm)5x5 self-similar edge curve✨
Math::PlanePath::DiagonalRationals(3pm)rationals X/Y by diagonals✨
Math::PlanePath::Diagonals(3pm)points in diagonal stripes✨
Math::PlanePath::DiagonalsAlternating(3pm)points in diagonal stripes of alternating directions✨
Math::PlanePath::DiagonalsOctant(3pm)points in diagonal stripes for an eighth of the plane✨
Math::PlanePath::DiamondArms(3pm)four spiral arms✨
Math::PlanePath::DiamondSpiral(3pm)integer points around a diamond shaped spiral✨
Math::PlanePath::DigitGroups(3pm)X,Y digits grouped by zeros✨
Math::PlanePath::DivisibleColumns(3pm)X divisible by Y in columns✨
Math::PlanePath::DragonCurve(3pm)dragon curve✨
Math::PlanePath::DragonMidpoint(3pm)dragon curve midpoints✨
Math::PlanePath::DragonRounded(3pm)dragon curve, with rounded corners✨
Math::PlanePath::FactorRationals(3pm)rationals by prime powers✨
Math::PlanePath::FibonacciWordFractal(3pm)turns by Fibonacci word bits✨
Math::PlanePath::File(3pm)points from a file✨
Math::PlanePath::FilledRings(3pm)concentric filled lattice rings✨
Math::PlanePath::Flowsnake(3pm)self-similar path through hexagons✨
Math::PlanePath::FlowsnakeCentres(3pm)self-similar path of hexagon centres✨
Math::PlanePath::FractionsTree(3pm)fractions by tree✨
Math::PlanePath::GcdRationals(3pm)rationals by triangular GCD✨
Math::PlanePath::GosperIslands(3pm)concentric Gosper islands✨
Math::PlanePath::GosperReplicate(3pm)self-similar hexagon replications✨
Math::PlanePath::GosperSide(3pm)one side of the Gosper island✨
Math::PlanePath::GrayCode(3pm)Gray code coordinates✨
Math::PlanePath::GreekKeySpiral(3pm)square spiral with Greek key motif✨
Math::PlanePath::HeptSpiralSkewed(3pm)integer points around a skewed seven sided spiral✨
Math::PlanePath::HexArms(3pm)six spiral arms✨
Math::PlanePath::HexSpiral(3pm)integer points around a hexagonal spiral✨
Math::PlanePath::HexSpiralSkewed(3pm)integer points around a skewed hexagonal spiral✨
Math::PlanePath::HilbertCurve(3pm)2x2 self-similar quadrant traversal✨
Math::PlanePath::HilbertSides(3pm)sides of Hilbert curve squares✨
Math::PlanePath::HilbertSpiral(3pm)2x2 self-similar spiral✨
Math::PlanePath::HIndexing(3pm)self-similar right-triangle traversal✨
Math::PlanePath::Hypot(3pm)points in order of hypotenuse distance✨
Math::PlanePath::HypotOctant(3pm)octant of points in order of hypotenuse distance✨
Math::PlanePath::ImaginaryBase(3pm)replications in four directions✨
Math::PlanePath::ImaginaryHalf(3pm)half-plane replications in three directions✨
Math::PlanePath::KnightSpiral(3pm)integer points around a square, by chess knight moves✨
Math::PlanePath::KochCurve(3pm)horizontal Koch curve✨
Math::PlanePath::KochelCurve(3pm)3x3 self-similar R and F✨
Math::PlanePath::KochPeaks(3pm)Koch curve peaks✨
Math::PlanePath::KochSnowflakes(3pm)Koch snowflakes as concentric rings✨
Math::PlanePath::KochSquareflakes(3pm)four-sided Koch snowflakes✨
Math::PlanePath::LTiling(3pm)2x2 self-similar of four pattern parts✨
Math::PlanePath::MPeaks(3pm)points in expanding M shape✨
Math::PlanePath::MultipleRings(3pm)rings of multiples✨
Math::PlanePath::OctagramSpiral(3pm)integer points drawn around an octagram✨
Math::PlanePath::PeanoCurve(3pm)3x3 self-similar quadrant traversal✨
Math::PlanePath::PeanoDiagonals(3pm)3x3 self-similar quadrant traversal across squares✨
Math::PlanePath::PentSpiral(3pm)integer points in a pentagonal shape✨
Math::PlanePath::PentSpiralSkewed(3pm)integer points in a pentagonal shape✨
Math::PlanePath::PixelRings(3pm)pixellated concentric circles✨
Math::PlanePath::PowerArray(3pm)array by powers✨
Math::PlanePath::PyramidRows(3pm)points stacked up in a pyramid✨
Math::PlanePath::PyramidSides(3pm)points along the sides of pyramid✨
Math::PlanePath::PyramidSpiral(3pm)integer points drawn around a pyramid✨
Math::PlanePath::PythagoreanTree(3pm)primitive Pythagorean triples by tree✨
Math::PlanePath::QuadricCurve(3pm)eight segment zig-zag✨
Math::PlanePath::QuadricIslands(3pm)quadric curve rings✨
Math::PlanePath::QuintetCentres(3pm)self-similar "plus" shape centres✨
Math::PlanePath::QuintetCurve(3pm)self-similar "plus" shaped curve✨
Math::PlanePath::QuintetReplicate(3pm)self-similar "+" tiling✨
Math::PlanePath::R5DragonCurve(3pm)radix 5 dragon curve✨
Math::PlanePath::R5DragonMidpoint(3pm)R5 dragon curve midpoints✨
Math::PlanePath::RationalsTree(3pm)rationals by tree✨
Math::PlanePath::Rows(3pm)points in fixed-width rows✨
Math::PlanePath::SacksSpiral(3pm)circular spiral squaring each revolution✨
Math::PlanePath::SierpinskiArrowhead(3pm)self-similar triangular path traversal✨
Math::PlanePath::SierpinskiArrowheadCentres(3pm)self-similar triangular path traversal✨
Math::PlanePath::SierpinskiCurve(3pm)Sierpinski curve✨
Math::PlanePath::SierpinskiCurveStair(3pm)Sierpinski curve with stair-step diagonals✨
Math::PlanePath::SierpinskiTriangle(3pm)self-similar triangular path traversal✨
Math::PlanePath::SquareArms(3pm)four spiral arms✨
Math::PlanePath::SquareReplicate(3pm)replicating squares✨
Math::PlanePath::SquareSpiral(3pm)integer points drawn around a square (or rectangle)✨
Math::PlanePath::Staircase(3pm)integer points in stair-step diagonal stripes✨
Math::PlanePath::StaircaseAlternating(3pm)stair-step diagonals up and down✨
Math::PlanePath::TerdragonCurve(3pm)triangular dragon curve✨
Math::PlanePath::TerdragonMidpoint(3pm)dragon curve midpoints✨
Math::PlanePath::TerdragonRounded(3pm)triangular dragon curve, with rounded corners✨
Math::PlanePath::TheodorusSpiral(3pm)right-angle unit step spiral✨
Math::PlanePath::TriangleSpiral(3pm)integer points drawn around an equilateral triangle✨
Math::PlanePath::TriangleSpiralSkewed(3pm)integer points drawn around a skewed equilateral triangle✨
Math::PlanePath::TriangularHypot(3pm)points of triangular lattice in order of hypotenuse distance✨
Math::PlanePath::UlamWarburton(3pm)growth of a 2-D cellular automaton✨
Math::PlanePath::UlamWarburtonQuarter(3pm)growth of a 2-D cellular automaton✨
Math::PlanePath::VogelFloret(3pm)circular pattern like a sunflower✨
Math::PlanePath::WunderlichMeander(3pm)3x3 self-similar "R" shape✨
Math::PlanePath::WunderlichSerpentine(3pm)transpose parts of Peano curve, including coil order✨
Math::PlanePath::WythoffArray(3pm)table of Fibonacci recurrences✨
Math::PlanePath::WythoffPreliminaryTriangle(3pm)Wythoff row containing X,Y recurrence✨
Math::PlanePath::ZOrderCurve(3pm)alternate digits to X and Y✨
Math::Polygon(3pm)Class for maintaining polygon data✨
Math::Polygon::Calc(3pm)Simple polygon calculations✨
Math::Polygon::Clip(3pm)frame a polygon in a square✨
Math::Polygon::Convex(3pm)Collection of convex algorithms✨
Math::Polygon::Surface(3pm)Polygon with exclusions✨
Math::Polygon::Transform(3pm)Polygon transformation✨
Math::Prime::Util(3pm)Utilities related to prime numbers, including fast sieves and factoring✨
Math::Prime::Util::ChaCha(3pm)Pure Perl ChaCha20 CSPRNG✨
Math::Prime::Util::ECAffinePoint(3pm)Elliptic curve operations for affine points✨
Math::Prime::Util::ECProjectivePoint(3pm)Elliptic curve operations for projective points✨
Math::Prime::Util::Entropy(3pm)Get a good random seed✨
Math::Prime::Util::GMP(3pm)Utilities related to prime numbers and factoring, using GMP✨
Math::Prime::Util::MemFree(3pm)An auto-free object for Math::Prime::Util✨
Math::Prime::Util::PP(3pm)Pure Perl version of Math::Prime::Util✨
Math::Prime::Util::PPFE(3pm)PP front end for Math::Prime::Util✨
Math::Prime::Util::PrimalityProving(3pm)Primality proofs and certificates✨
Math::Prime::Util::PrimeArray(3pm)A tied array for primes✨
Math::Prime::Util::PrimeIterator(3pm)An object iterator for primes✨
Math::Prime::Util::RandomPrimes(3pm)Generate random primes✨
Math::Prime::Util::ZetaBigFloat(3pm)Perl Big Float versions of Riemann Zeta and R functions✨
Math::Prime::XS(3pm)Detect and calculate prime numbers with deterministic tests✨
Math::Quaternion(3pm)Perl class to represent quaternions✨
Math::Random(3pm)Random Number Generators✨
Math::Random::Free(3pm)free drop-in replacement for Math::Random✨
Math::Random::ISAAC(3pm)Perl interface to the ISAAC PRNG algorithm✨
Math::Random::ISAAC::PP(3pm)Pure Perl port of the ISAAC PRNG algorithm✨
Math::Random::ISAAC::XS(3pm)C implementation of the ISAAC PRNG algorithm✨
Math::Random::MT(3pm)The Mersenne Twister PRNG✨
Math::Random::MT::Auto(3pm)Auto-seeded Mersenne Twister PRNGs✨
Math::Random::MT::Auto::Range(3pm)Range-valued PRNGs✨
Math::Random::OO(3pm)Consistent object-oriented interface for generating random numbers✨
Math::Random::OO::Bootstrap(3pm)Generate random numbers with bootstrap resampling from a non-parametric distribution✨
Math::Random::OO::Normal(3pm)Generates random numbers from the normal (Gaussian) distribution✨
Math::Random::OO::Uniform(3pm)Generates random numbers from the uniform distribution✨
Math::Random::OO::UniformInt(3pm)Generates random integers with uniform probability✨
Math::Random::Secure(3pm)Cryptographically-secure, cross-platform replacement for rand()✨
Math::Random::Secure::RNG(3pm)The underlying PRNG, as an object.✨
Math::Random::TT800(3pm)Matsumoto's TT800 Pseudorandom number generator✨
Math::RandomOrg(3pm)Retrieve random numbers and data from random.org.✨
Math::Round(3pm)Perl extension for rounding numbers✨
Math::SparseMatrix(3pm)Provides basic sparse matrix operations such as creation, reading from file, reading transpose from file and writing to file.✨
Math::SparseVector(3pm)Supports sparse vector operations such as setting a value in a vector, reading a value at a given index, obtaining all indices, addition and dot product of two sparse vectors, and vector…✨
Math::Spline(3pm)Cubic Spline Interpolation of data✨
Math::Symbolic(3pm)Symbolic calculations✨
Math::Symbolic::AuxFunctions(3pm)Auxiliary functions for Math::Symbolic hierarchy✨
Math::Symbolic::Base(3pm)Base class for symbols in symbolic calculations✨
Math::Symbolic::Compiler(3pm)Compile Math::Symbolic trees to Perl code✨
Math::Symbolic::Constant(3pm)Constants in symbolic calculations✨
Math::Symbolic::Custom(3pm)Aggregate class for tree tests and transformations✨
Math::Symbolic::Custom::Base(3pm)Base class for tree tests and transformations✨