Here is a list of the packages that are distributed with Macaulay2. The ones that have been refereed are marked with a star.
- AbstractToricVarieties -- links abstract simplicial (normal) toric varieties to Schubert2
- AdjointIdeal -- Adjoint ideals of plane curves and related computations
- AlgebraicSplines -- Package for splines on simplicial complexes, polytopal complexes, and graphs
- AnalyzeSheafOnP1 -- Decompose a Sheaf on P1
- BeginningMacaulay2 -- Mathematicians' Introduction to Macaulay2
- Benchmark -- standard Macaulay2 benchmarks
- Bertini -- Interface to Bertini
- BGG -- Bernstein-Gelfand-Gelfand correspondence
- BIBasis -- Involutive Pommaret basis in a Boolean ring
- BinomialEdgeIdeals -- Package for computations with binomial edge ideals
Binomials -- Specialized routines for binomial ideals
- BoijSoederberg -- betti diagram operations useful for investigating the Boij-Soederberg conjectures
- Book3264Examples -- Examples to accompany the eponymous book by Eisenbud and Harris
- BooleanGB -- Groebner Bases for Ideals in Boolean Polynomial Quotient Ring
- Browse -- a method for browsing and examining Macaulay2 data structures
- Bruns -- make a 3-generator ideal with an "any" resolution
- ChainComplexExtras -- Some additional ChainComplex Functions.
- ChainComplexOperations -- sym2, wedge2, chi2 of a ChainComplex
CharacteristicClasses -- Computes CSM classes, Segre classes and the Euler Char. for some Subschemes of Smooth Complete Toric Varieties
- Chordal -- A package that exploits chordal structure
- Classic -- a classic Macaulay parser
- CohomCalg -- interface to CohomCalg software for computing cohomology of torus invariant divisors on a toric variety
- CoincidentRootLoci -- A package for computations with coincident root loci
- CompleteIntersectionResolutions -- Analyzing Resolutions over a Complete Intersection
- Complexes -- Chain complexes
ConformalBlocks -- for conformal block divisors
- ConvexInterface -- Interface to Convex
- ConwayPolynomials -- a database of Conway polynomials
- CorrespondenceScrolls -- CorrespondenceScrolls
Cremona -- Some computations for rational maps between projective varieties
- Cyclotomic -- Routines for cyclotomic fields
- Depth -- aids in computations related to depth
- DeterminantalRepresentations -- a package for computing determinantal representations
- DGAlgebras -- Data type for DG algebras
DiffAlg -- Specialized routines for differential forms
Divisor -- a package for working with Weil divisors
- Dmodules -- functions for computations with D-modules
EdgeIdeals -- a package for edge ideals.
- Elimination -- a package for elimination of variables
- EliminationMatrices -- Package for computing resultants
- EllipticCurves -- Group law on elliptic curves (and counting points with brute force methods)
- EllipticIntegrals -- uniformization of elliptic curves
- EngineTests -- a test suite for the Macaulay2 engine
- EnumerationCurves -- Enumeration of rational curves via torus actions
- EquivariantGB -- Equivariant Groebner bases and related algorithms
- ExampleSystems -- examples of polynomial systems
ExteriorIdeals -- A Macaulay2 package for manipulating monomial ideals over exterior algebra
- FGLM -- Compute Groebner bases via the FGLM algorithm
- FiniteFittingIdeals -- A package for computing Fitting ideals of finite modules
- FirstPackage -- an example Macaulay2 package
- FormalGroupLaws -- Package to deal with commutative formal group laws
- FourierMotzkin -- convex hulls and polar cones
- FourTiTwo -- Interface to 4ti2
- FThresholds -- A package for calculations of F-thresholds
- GenericInitialIdeal -- find the generic initial ideal of a given ideal
- gfanInterface -- Interface to Anders Jensen's Gfan software
- GradedLieAlgebras -- computations in graded Lie algebras
GraphicalModels -- A package for discrete and Gaussian graphical models
- Graphics -- Create graphics
- Graphs -- Package for processing graphs and directed graphs (digraphs)
- GroebnerWalk -- Compute Groebner bases via the Groebner walk
- HigherCIOperators -- Higer CI operators
HighestWeights -- decompose free resolutions and graded modules with a semisimple Lie group action
HodgeIntegrals -- Hodge integrals on the moduli space of curves
- HyperplaneArrangements -- hyperplane arrangements
- IntegralClosure -- Integral Closure
InvariantRing -- a package to construct the invariant ring of a finite group
- InverseSystems -- equivariant Macaulay inverse systems
- InvolutiveBases -- Methods for Janet bases and Pommaret bases in Macaulay 2
- K3Carpets -- K3 double structure on scrolls
- Kronecker -- Kronecker and rational normal forms
KustinMiller -- Unprojection and the Kustin-Miller complex construction
- LatticePolytopes -- A package for computations with lattice polytopes
- LexIdeals -- A Macaulay 2 package for manipulating lexicographic-type monomial ideals
- Licenses -- licensing of Macaulay2
LieTypes -- Common types for Lie groups and Lie algebras
- LLLBases -- a package for computing Lenstra-Lenstra-Lovasz bases
- LocalRings -- Operations over a local ring (R, P)
- M0nbar -- calculations for divisors and F-curves on the moduli space of stable n-pointed genus zero curves
- MapleInterface -- Interface to Maple
- Markov -- Markov ideals, arising from Bayesian networks in statistics
Matroids -- a package for computations with matroids
- MCMApproximations -- MCM Approximations and Complete Intersections
- MinimalPrimes -- minimal primes of an ideal
- Miura -- The Arithmetic of Miura Curves
ModuleDeformations -- Computing versal deformations of maximal Cohen-Macaulay modules
- MonodromySolver -- solving polynomial systems via monodromy
MonomialAlgebras -- Monomial algebras
- MultiGradedRationalMap -- degree and birationality of multi-graded rational maps
MultiplierIdeals -- multiplier ideals, log canonical thresholds, and jumping numbers
- MultiplierIdealsDim2 -- Package for computing MI in 2-dimensional rings
- NAGtypes -- Common types used in Numerical Algebraic Geometry
Nauty -- Interface to nauty
- NautyGraphs -- Interface to nauty (Graphs fork)
- NCAlgebra -- Data types for Noncommutative algebras
- NoetherNormalization -- place an ideal in Noether normal position
- NonminimalComplexes -- Obtaining the non-minimal strands of a non-minimal resolution of a homogeneous module
Normaliz -- a package to use Normaliz in Macaulay 2
- NormalToricVarieties -- a package for working with normal toric varieties
NumericalAlgebraicGeometry -- Numerical Algebraic Geometry
- NumericalCertification -- numerical certification
- NumericalHilbert -- numerically compute local dual space and Hilbert functions
- NumericalImplicitization -- a package for computing numerical invariants of images of varieties
- NumericalSchubertCalculus -- a Macaulay2 package for using numerical methods in Schubert Calculus
- NumericSolutions -- solving systems of polynomial equalities
OldPolyhedra -- A package for computations with convex polyhedra
OldToricVectorBundles -- A package for computations with vector bundles on toric varieties
- OpenMath -- OpenMath for Macaulay2
- PackageCitations -- citation of Macaulay2 packages
- PackageTemplate -- an example Macaulay2 package
- Parametrization -- Rational parametrization of rational plane curves and related computations
- Parsing -- a framework for creating recursive descent parsers
- Permanents -- Compute the permanents of a matrix
PHCpack -- Interface to PHCpack
- PhylogeneticTrees -- invariants for group-based phylogenetic models
PieriMaps -- computations of matrices between representations of the general linear group based on the Pieri formulas
- Points -- computing with sets of points
Polyhedra -- A package for computations with convex polyhedra
- Polymake -- a package for interfacing with polymake
Posets -- Package for processing partially ordered sets (posets)
- PrimaryDecomposition -- functions for primary decomposition
- PruneComplex -- Prunes a given complex over R, R_m, and R_p
- Pullback -- pullback of rings
- PushForward -- push forwards of finite ring maps
- QthPower -- An implementation of the Qth-Power algorithm for computing integral closures
Quasidegrees -- a package to compute quasidegrees and graded local cohomology
QuillenSuslin -- QuillenSuslin
- RandomCanonicalCurves -- Construction of random smooth canonical curves up to genus 14
- RandomComplexes -- random complexes over fields or the integers
- RandomCurves -- Construction of random curves
- RandomCurvesOverVerySmallFiniteFields -- computation of general canonical curves of genus <= 15 over fields with small characteristic
- RandomGenus14Curves -- Construction of random smooth curves of genus 14
- RandomIdeals -- a package for creating random ideals of various sorts
- RandomMonomialIdeals -- A package for generating Erdos-Renyi-type random monomial ideals
- RandomObjects -- a framework for making random objects in algebraic geometry
- RandomPlaneCurves -- Construction of random plane curves
- RandomSpaceCurves -- Construction of random smooth space curves
- RationalMaps -- A package for working with rational maps.
- RationalPoints -- find the common zeroes of a set of polynomials with coefficients in a finite field
- ReactionNetworks -- reaction networks
ReesAlgebra -- Rees algebras
- ReflexivePolytopesDB -- simple access to Kreuzer-Skarke database of reflexive polytopes of dimensions 3 and 4
- Regularity -- computes the Castelnuovo-Mumford regularity of a given homogeneous ideal
- RelativeCanonicalResolution -- computation of the relative canonical resolution for g-nodal canonical curves with a fixed g^1_k
- ResidualIntersections -- Package for studying conditions associated to Residual Intersection theory
Resultants -- Resultants, discriminants, and Chow forms
- RunExternalM2 -- run Macaulay2 functions outside the current Macaulay2 process
- Schubert2 -- computations of characteristic classes for varieties without equations
- SchurFunctors -- computations of Schur modules and maps between them
- SchurRings -- representation rings of general linear groups and of symmetric groups
- SCSCP -- SCSCP for Macaulay2
- SectionRing -- computing the section ring of a Weil Divisor
- SegreClasses -- tests containment of varieties and computes algebraic multiplicity of subvarieties and Fulton-MacPherson intersection products - via a very general Segre class computation
- SemidefiniteProgramming -- semidefinite programming
- Seminormalization -- a package for computing seminormalization of rings
- Serialization -- reversible conversion of all Macaulay2 objects to strings
- SimpleDoc -- a simple documentation function
- SimplicialComplexes -- simplicial complexes
SimplicialDecomposability -- various decomposability routines for simplicial complexes
- SLnEquivariantMatrices -- Ancillary file to the paper "A construction of equivariant bundles on the space of symmetric forms"
- SLPexpressions -- Straight Line Programs and Algebraic Circuits
- SOS -- sums of squares
SpaceCurves -- Generation of space curves
- SpectralSequences -- spectral sequences
- SRdeformations -- Deformations of Stanley-Reisner rings and related computations
- StatePolytope -- for computing the state polytope of an ideal
StronglyStableIdeals -- studying strongly stable ideals related to Hilbert polynomials
- Style -- style sheets and images for the documentation
- SVDComplexes -- SVD (singular value decomposition) of a complex over the reals and related functions
- SymbolicPowers -- Calculations involving symbolic powers
- SymmetricPolynomials -- symmetric polynomials
- TangentCone -- tangent cones
- TateOnProducts -- Tate resolutions on products of projective spaces
- TensorComplexes -- multilinear algebra with labeled bases
- TestIdeals -- A package for calculations of singularities in positive characteristic
- Text -- documentation and hypertext
- Topcom -- interface to a small part of topcom
TorAlgebra -- Classification of local rings based on multiplication in homology
- ToricInvariants -- computes Euclidean distance degrees, polar degrees, degree and codimension of the dual, and Chern-Mather classes of toric varieties X_A from the polytope conv(A) or from its Gale dual
- ToricTopology -- Toric topology
ToricVectorBundles -- A package for computations with vector bundles on toric varieties
- TriangularSets -- A package for triangular decompositions of ideals
- Triplets -- Triplets of degree sequences, and associated Betti diagrams and cohomology tables
- Tropical -- A package for doing computations in tropical geometry
- Truncations -- truncation of a module
- Units -- units conversion and physical constants
- VectorFields -- a package for computations with vector fields
VersalDeformations -- A package for calculating versal deformations and local Hilbert schemes
- VirtualResolutions -- Methods for virtual resolutions on products of projective spaces
- Visualize -- Interactive visualization and manipulation of combinatorial objects in a browser
- WeylGroups -- Root systems and Weyl groups
- XML -- an XML parser