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 -- 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 -- 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 rings
- 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 -- CSM classes, Segre classes and the Euler characteristic for some subschemes of smooth complete toric varieties
- Chordal -- routines that exploit chordal structure
- Classic -- a classic Macaulay parser
- CohomCalg -- interface to CohomCalg software for computing cohomology of torus invariant divisors on a toric variety
- CoincidentRootLoci -- 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 -- correspondence scrolls
Cremona -- rational maps between projective varieties
- Cyclotomic -- cyclotomic fields
- Depth -- aids in computations related to depth
- DeterminantalRepresentations -- determinantal representations
- DGAlgebras -- data type for DG algebras
DiffAlg -- specialized routines for differential forms
Divisor -- Weil divisors
- Dmodules -- D-modules
EdgeIdeals -- edge ideals
- Elimination -- elimination of variables
- EliminationMatrices -- 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 -- monomial ideals over exterior algebras
- FastLinAlg -- faster linear algebra operations
- FGLM -- Groebner bases via the FGLM algorithm
- FiniteFittingIdeals -- Fitting ideals of finite modules
- FirstPackage -- an example Macaulay2 package
- FormalGroupLaws -- commutative formal group laws
- FourierMotzkin -- convex hulls and polar cones
- FourTiTwo -- Interface to 4ti2
- FrobeniusThresholds -- F-thresholds
- GenericInitialIdeal -- find the generic initial ideal of a given ideal
- gfanInterface -- interface to Anders Jensen's Gfan software
- GradedLieAlgebras -- graded Lie algebras
GraphicalModels -- discrete and Gaussian graphical models
- Graphics -- create graphics
- Graphs -- graphs and directed graphs (digraphs)
- GroebnerWalk -- Groebner bases via the Groebner walk
- HigherCIOperators -- higher 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 -- 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 -- lattice polytopes
- LexIdeals -- lexicographic-type monomial ideals
- Licenses -- licensing of Macaulay2
LieTypes -- common types for Lie groups and Lie algebras
- LLLBases -- 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 -- matroids
- MCMApproximations -- MCM approximations and complete intersections
- MinimalPrimes -- minimal primes of an ideal
- Miura -- arithmetic of Miura curves
ModuleDeformations -- 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 -- multiplier ideals in 2-dimensional rings
- NAGtypes -- 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 -- non-minimal strands of a non-minimal resolution of a homogeneous module
Normaliz -- interface to Normaliz in Macaulay2
- NormalToricVarieties -- normal toric varieties
NumericalAlgebraicGeometry -- numerical algebraic geometry
- NumericalCertification -- numerical certification
- NumericalHilbert -- numerically compute local dual space and Hilbert functions
NumericalImplicitization -- numerical invariants of images of varieties
- NumericalSchubertCalculus -- numerical methods in Schubert Calculus
- NumericSolutions -- solving systems of polynomial equalities
OldPolyhedra -- convex polyhedra
OldToricVectorBundles -- 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 -- permanents of a matrix
PHCpack -- interface to PHCpack
- PhylogeneticTrees -- invariants for group-based phylogenetic models
PieriMaps -- maps between representations of the general linear group based on the Pieri formulas
- Points -- sets of points
Polyhedra -- convex polyhedra
- Polymake -- interfacing with polymake
Posets -- partially ordered sets (posets)
- PrimaryDecomposition -- functions for primary decomposition
- PruneComplex -- pruning chain complexes over polynomial and local rings
- Pullback -- pullback of rings
- PushForward -- push forwards of finite ring maps
- QthPower -- An implementation of the Qth-Power algorithm for computing integral closures
Quasidegrees -- quasidegrees and graded local cohomology
QuillenSuslin -- the Quillen-Suslin algorithm for bases of projective modules
- RandomCanonicalCurves -- Construction of random smooth canonical curves up to genus 14
- RandomComplexes -- random complexes over fields or the integers
- RandomCurves -- random curves
- RandomCurvesOverVerySmallFiniteFields -- general canonical curves of genus <= 15 over fields with small characteristic
- RandomGenus14Curves -- random smooth curves of genus 14
- RandomIdeals -- creating random ideals of various sorts
RandomMonomialIdeals -- Erdos-Renyi-type random monomial ideals
- RandomObjects -- a framework for making random objects in algebraic geometry
- RandomPlaneCurves -- random plane curves
- RandomSpaceCurves -- random smooth space curves
- RationalMaps -- 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 -- Castelnuovo-Mumford regularity of a homogeneous ideal
- RelativeCanonicalResolution -- the relative canonical resolution for g-nodal canonical curves with a fixed g^1_k
- ResidualIntersections -- conditions associated to residual intersection theory
Resultants -- resultants, discriminants, and Chow forms
- RunExternalM2 -- run Macaulay2 functions outside the current Macaulay2 process
- Schubert2 -- characteristic classes for varieties without equations
SchurComplexes -- Schur functors of complexes
- SchurFunctors -- Schur modules and maps between them
- SchurRings -- representation rings of general linear groups and of symmetric groups
- SCSCP -- SCSCP for Macaulay2
- SectionRing -- the section ring of a Weil Divisor
- SegreClasses -- test 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 -- 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 -- file ancillary to the paper "A construction of equivariant bundles on the space of symmetric forms"
- SLPexpressions -- straight line programs and algebraic circuits
SpaceCurves -- space curves
- SpechtModule -- invariants for permutation groups
- SpecialFanoFourfolds -- special cubic fourfolds and special prime Fano fourfolds of degree 10 and index 2
- SpectralSequences -- spectral sequences
- SRdeformations -- deformations of Stanley-Reisner rings and related computations
- StatePolytope -- the state polytope of an ideal
StronglyStableIdeals -- studying strongly stable ideals related to Hilbert polynomials
- Style -- style sheets and images for the documentation
- SumsOfSquares -- sums of squares
- SVDComplexes -- SVD (singular value decomposition) of a complex over the reals and related functions
SymbolicPowers -- symbolic powers
- SymmetricPolynomials -- symmetric polynomials
- TangentCone -- tangent cones
- TateOnProducts -- Tate resolutions on products of projective spaces
- TensorComplexes -- multilinear algebra with labeled bases
TestIdeals -- 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 -- 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 -- vector bundles on toric varieties
- TriangularSets -- triangular decompositions of ideals
- Triplets -- triplets of degree sequences and associated Betti diagrams and cohomology tables
- Tropical -- tropical geometry
- Truncations -- truncation of a module
- Units -- units conversion and physical constants
- VectorFields -- vector fields
VersalDeformations -- versal deformations and local Hilbert schemes
- VirtualResolutions -- 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