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Macaulay2 / M2

The primary source code repository for Macaulay2, a system for computing in commutative algebra, algebraic geometry and related fields.
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Documentation with long headlines #1877

Open d-torrance opened 3 years ago

d-torrance commented 3 years ago

The following tags have headlines at least 100 characters in length. This results in a warning, and if debugLevel is positive, an error.

       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
o173 = |AlgebraicSplines :: cellularComplex                                 |create the cellular chain complex whose homologies are the singular homologies of the complex $\Delta$ relative to its boundary                                                                |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |AlgebraicSplines :: postulationNumber                               |computes the largest degree at which the hilbert function of the graded module M is not equal to the hilbertPolynomial                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |AlgebraicSplines :: ringStructure                                   |given a sub-module of a free module (viewed as a ring with direct sum structure) which is also a sub-ring, creates a ring map whose image is the module with its ring structure                |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |AlgebraicSplines :: stanleyReisner                                  |Creates a ring map whose image is the ring of piecewise continuous polynomials on $\Delta$.  If $\Delta$ is simplicial, the Stanley Reisner ring of $\Delta$ is returned.                      |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |AlgebraicSplines :: stanleyReisnerPresentation                      |creates a ring map whose image is the sub-ring of $C^0(\Delta)$ generated by $C^r(\Delta)$.  If $\Delta$ is simplicial, $C^0(\Delta)$ is the Stanley Reisner ring of $\Delta$.                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Bertini :: Bertini input file declarations: random numbers          |an option which designates symbols/strings/variables that will be set to be a random real number or random complex number                                                                      |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |BIBasis :: biBasis                                                  |constructs a reduced Boolean Gröbner basis for the given Ideal, if the second argument is true (default), and reduced Boolean Pommaret basis otherwise.                                       |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |BoijSoederberg :: isMassEliminate                                   |determines whether the Boij-Soederberg decomposition algorithm eliminates multiple Betti numbers at the same time                                                                              |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Bruns :: bruns                                                      |Returns an ideal generated by three elements whose 2nd syzygy module is isomorphic to a given module                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |CharacteristicClasses :: CharacteristicClasses                      |Chern classes and other characteristic classes of subschemes of certain smooth toric varieties, including products of projective spaces                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |CharacteristicClasses :: CheckToricVarietyValid                     |Checks if the input normal toric variety X is a valid choice for an ambient space when computing characteristic classes of subschemes V of X                                                   |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |CharacteristicClasses :: ChowRing                                   |Computes the Chow ring of a product of projective spaces m projective spaces given the coordinate ring                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |CharacteristicClasses :: isMultiHomogeneous                         |Checks if an ideal is homogeneous with respect to the grading on its ring (i.e. multi-homogeneous in the multi-graded case)                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |CohomCalg :: CohomCalg                                              |an interface to the CohomCalg software for computing cohomology of torus invariant divisors on a toric variety                                                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Cremona :: rationalMap(PolynomialRing,List)                         |rational map defined by the linear system of hypersurfaces passing through random points with multiplicity                                                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |DeterminantalRepresentations :: bivariateDiagEntries                |computes diagonal entries and eigenvalues for a determinantal representation of a bivariate polynomial                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |DGAlgebras :: killCycles                                            |Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.                                                                               |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |DiffAlg :: random(DiffAlgElement,Ring)                              |replaces the variables of the coefficient ring of a differential form or a vector field with random values                                                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Divisor :: IsGraded                                                 |an option used by numerous functions which tells it to treat the divisors as if we were working on the Proj of the ambient ring.                                                               |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Divisor :: MTries                                                   |an option used by embedAsIdeal how many times to try embedding the module as an ideal in a random way.                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Divisor :: ramificationDivisor                                      |compute the ramification divisor of a finite inclusion of normal domains or a blowup over a smooth base                                                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Dmodules :: cssExptsMult                                            |the exponents (and multiplicities) of the canonical series solutions of I in the direction of a weight vector                                                                                  |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Dmodules :: paramBpoly(RingElement,String)                          |compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients                                                                                      |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: ciResDeg                                     |compute a regularity index and partial degrees of the residual resultant over a complete intersection                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: degHomPolMap                                 |return the base of monomials in a subset of variables, and the matrix of coefficients of a morphism of free modules f:R(d1)+...+R(dn)->R_d with respect to these variables                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: detComplex                                   |This function calculates the determinant of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: listDetComplex                               |This function calculates the list with the determinants of some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.|
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: mapsComplex                                  |This function calculates the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: minorsComplex                                |calculate some minors of the maps of a graded ChainComplex in a subset of variables and fixed degree                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |EliminationMatrices :: regularityVar                                |computes the Castelnuovo-Mumford regularity of homogeneous ideals in terms of Betti numbers, with respect to some of the variables of the ring                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |FourTiTwo :: toBinomial                                             |creates a toric ideal from a given set of exponents of its generators; equivalent to "output --binomials" in 4ti2                                                                              |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |FourTiTwo :: toricGraverDegrees                                     |displays the degrees of all Graver basis elements for the toric ideal I_A; equivalent to "output --degrees foo.gra" in 4ti2                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |FrobeniusThresholds :: Search                                       |an option for the function nu to specify the search method for testing containments of powers of ideals                                                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |GraphicalModels :: gaussianVanishingIdeal(...,OldVersion=>...)      |optional argument in gaussianVanishingIdeal to use old method for gaussianRings coming from directed graphs                                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |GraphicalModels :: hiddenMap                                        |linear map between the ring of a model with one hidden variable and the ring of the corresponding fully observed model                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |GraphicalModels :: marginMap                                        |linear map on joint distributions for discrete random variables replacing marginals for indeterminates                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |GraphicalModels :: OldVersion                                       |optional argument in gaussianVanishingIdeal to use old method for gaussianRings coming from directed graphs                                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Graphs :: breadthFirstSearch                                        |runs a breadth first search on the digraph starting at a specified node and returns a list of the vertices in the order they were discovered                                                   |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Graphs :: depthFirstSearch                                          |runs a depth first search on the digraph or digraph and returns the discovery time and finishing time for each vertex in the digraph                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Graphs :: floydWarshall                                             |runs the Floyd-Warshall algorithm on a digraph to determine the minimum distance from one vertex to another in the digraph                                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Graphs :: reverseBreadthFirstSearch                                 |runs a reverse breadth first search on the digraph and returns a list of the vertexSet in the order they were discovered                                                                       |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Graphs :: topSort                                                   |outputs a hashtable containing original digraph, new digraph with vertices topologically sorted and a map from vertices of original digraph to new digraph.                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |InvariantRing :: RingOfInvariants                                   |the class of the rings of invariants under the action of a finite group, an Abelian group or a linearly reductive group                                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |InvariantRing :: secondaryInvariants(...,PrintDegreePolynomial=>...)|an optional argument for secondaryInvariants that determines the printing of an informative polynomial                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |InvolutiveBases :: pommaretMultVar                                  |return table of multiplicative variables for given module elements as determined by Pommaret division                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |K3Carpets :: carpetBettiTable                                       |compute the Betti tables of a carpet of given genus and Clifford index over a prime field of characteristic p                                                                                  |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |K3Carpets :: schreyerName                                           |get the names of generators in the (nonminimal) Schreyer resolution according to Schreyer's convention                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |KustinMiller :: Cyclic Polytopes                                    |Constructing minimal resolutions for Stanley-Reisner rings of boundary complexes of cyclic polytopes                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |LatticePolytopes :: isJetSpanned                                    |checks if the polarized toric variety associated to a set of lattice points is k-jet spanned at a given point.                                                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |LieTypes :: fusionCoefficient(...,MaxWordLength=>...)               |Optional argument to specify the allowable length of words in the affine Weyl group when computing fusion products.                                                                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |LieTypes :: fusionProduct(...,MaxWordLength=>...)                   |Optional argument to specify the allowable length of words in the affine Weyl group when computing fusion products.                                                                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |LieTypes :: MaxWordLength                                           |Optional argument to specify the allowable length of words in the affine Weyl group when computing fusion products.                                                                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Macaulay2Doc :: resolution(Matrix)                                  |given a module map represented by a matrix, produce a comparison map between resolutions of its source and target                                                                              |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |MixedMultiplicity :: homIdealPolytope                               |Compute the homogeneous ideal corresponding to the vertices of a lattice polytope in $\mathbb{R}^n$.                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |NCAlgebra :: rightKernel                                            |Method for computing kernels of matrices over noncommutative rings in a given degree without using Bergman                                                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |NumericalSchubertCalculus :: randomSchubertProblemInstance          |Returns a random instance of a given Schubert problem by computing random matrices representing flags                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |OldPolyhedra :: sublatticeBasis                                     |computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |PhylogeneticTrees :: phyloToricFP                                   |Compute the invariants of a group-based phylogenetic tree model using the toric fiber product structure                                                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |PhylogeneticTrees :: phyloToricRandom                               |Compute a random invariant of a group-based phylogenetic tree model using the toric fiber product structure                                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Polyhedra :: sublatticeBasis                                        |computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |QuillenSuslin :: changeVar                                          |computes a change of variables which make the first entry of a unimodular row monic in a specified variable                                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |QuillenSuslin :: completeMatrix                                     |completes a unimodular matrix over a polynomial ring or Laurent polynomial ring to a square invertible matrix                                                                                  |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RandomComplexes :: randomChainComplex                               |random chain complex over the integers with prescribed ranks of the homology group and ranks of the matrices                                                                                   |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RandomCurvesOverVerySmallFiniteFields :: Details                    |keeps track of the precise step in the construction of canonical genus 14 and 15 curves. Default value is "false".                                                                             |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RandomMonomialIdeals :: CMStats                                     |fraction of monomial ideals (or other objects) in the given list whose quotient ring is Cohen-Macaulay                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RandomRationalPoints :: IntersectionAttempts                        |an option which controls how many linear intersections are attempted when looking for rational points                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RandomRationalPoints :: MaxCoordinatesToReplace                     |The maximum number of coordinates to turn into non-monomial functions when calling {\tt randomCoordinateChange}                                                                                |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RandomSpaceCurves :: knownUnirationalComponentOfSpaceCurves         |check whether there is a unirational construction for a component of the Hilbert scheme of space curves                                                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RationalMaps :: inverseOfMap                                        |Computes the inverse map of a given birational map between projective varieties. Returns an error if the map is not birational onto its image.                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RationalMaps :: jacobianDualMatrix                                  |Computes the Jacobian Dual Matrix, a matrix whose kernel describing the syzygies of the inverse map.                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RationalMaps :: mapOntoImage                                        |Given a map of rings, correspoing to X mapping to Y, this returns the map of rings corresponding to X mapping to f(X).                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RationalMaps :: MinorsCount                                         | An option controlling the behavior of isBirational and inverseOfMap (and other functions which call those).                                                                                   |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RationalMaps :: sourceInversionFactor                               |Computes the the common factor among the the components of the composition of the inverse map and the original map.                                                                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |ReactionNetworks :: negativeUndirectedLaplacian                     |Computes the negative of the Laplacian matrix of an undirected graph associated with a Reaction Network.                                                                                       |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |ReactionNetworks :: stoichiometricConeKer                           |Computes a matrix whose columns are the rays of the cone non-negative kernel of the stoichiometric matrix of a Reaction Network.                                                               |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RelativeCanonicalResolution :: getCoxDegrees                        |Computes the degree of a polynomial in the Cox ring corresponding to a section of a bundle on the scroll                                                                                       |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RelativeCanonicalResolution :: getScrollDegrees                     |Computes the degree of a section of a bundle on the scroll ring corresponding to a polynomial in the Cox ring                                                                                  |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |RelativeCanonicalResolution :: iteratedCone                         |Computes a (possibly non-minimal) resolution of C in P^{g-1} starting from the relative canonical resolution of C in P(E)                                                                      |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |ResLengthThree :: Labels                                            |an optional argument for multTableOneOne and MultTableOneTwo determining whether to label rows and columns                                                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |ResolutionsOfStanleyReisnerRings :: colorfulPresentation            |A presentation of the Stanley-Reisner ring of the barycentric subdivision of a simplicial complex over its colorful parameter ring                                                             |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SchurFunctors :: character                                          |Determines the character of a compostion of schur functors applied to the representation of GL(V) on V                                                                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SectionRing :: isMRegular                                           |isMRegular(F,G,m) tests where F is m-regular with respect to G (globally generated) in the sense of Castelnuovo-Mumford.  Omitting G assumes G=O_X(1).                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SectionRing :: mRegular                                             |mRegular(F,G) computes the regularity of F with respect to G (globally generated), in the sense of Castelnuovo-Mumford.  Omitting G assumes G=O_X(1).                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SectionRing :: sectionRing                                          |sectionRing(I) produces the section ring of an ample divisor.  If I is an ideal, one can input I to get the section ring of the corresponding divisor.                                         |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: containedInSingularLocus                            |This method tests is an irreducible variety is contained in the singular locus of the reduced scheme of an irreducible scheme                                                                  |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: intersectionProduct                                 |A class in the Chow ring of the ambient space representing the Fulton-MacPherson intersection product of two schemes inside a variety                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: projectiveDegree                                    |This method computes a single projective degree of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: projectiveDegrees                                   |This method computes the projective degrees of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: segre                                               |This method computes the Segre class of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces                                                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: SegreClasses                                        |Tests containment of varieties and computes algebraic multiplicity of subvarieties and Fulton-MacPherson intersection products - via a very general Segre class computation                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SegreClasses :: segreDimX                                           |This method computes the dimension X part of the Segre class of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |Seminormalization :: findElementMappingToTarget                     |given a ring map and an element of the target, this find an element from the source whose image is the given one                                                                               |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SlackIdeals :: graphFromSlackMatrix                                 |creates the vertex-edge incidence matrix for the bipartite non-incidence graph with adjacency matrix the given slack matrix                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SlackIdeals :: Saturate                                             |choose whether to saturate with respect to the product of all variables at the same time or variable by variable.                                                                              |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SlackIdeals :: slackFromGaleCircuits(...,Tolerance=>...)            |specifies the tolerance to compute the slack matrix of a polytope from a Gale transform of a polytope                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SpectralSequences :: filteredComplex(List)                          |obtain a filtered complex from a list of chain complex maps or a nested list of simplicial complexes                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |StatGraphs :: collateVertices                                       |convert a mixed graph into a new mixed graph where each component subgraph has the same set of vertices                                                                                        |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |StatGraphs :: partitionLMG                                          |partition the vertices of a loopless mixed graph into adjacent to undirected edges and adjacent to bidirected edges                                                                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |StronglyStableIdeals :: stronglyStableIdeals                        |Compute the saturated strongly stable ideals in the given ambient space with given Hilbert polynomial                                                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |SymbolicPowers :: CIPrimes                                          |an option to compute the symbolic power by taking the intersection of the powers of the primary components                                                                                     |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |TateOnProducts :: BundleType                                        |Option in beilinson with values PrunedQuotient, QuotientBundle, DummyQuotientBundle, SubBundle, FreeBundle, or MapsBetweenFreeBundles                                                          |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |TateOnProducts :: tateExtension                                     |extend the terms in the Beilinson window to a part of a corner complex of the corresponding Tate resolution                                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |TestIdeals :: ascendIdeal                                           |find the smallest ideal containing a given ideal which is compatible with a given Cartier linear map                                                                                           |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |TestIdeals :: ascendModule                                          |find the smallest submodule of free module containing a given submodule which is compatible with a given Cartier linear map                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |TestIdeals :: frobeniusTraceOnCanonicalModule                       |find an element of a polynomial ring that determines the Frobenius trace on the canonical module of a quotient of that ring                                                                    |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |ToricInvariants :: ToricInvariants                                  |Given a projective toric variety, the package computes the degree and codimension of the dual, the Euclidean distance degree, polar degrees, and Chern-Mather class                            |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |VersalDeformations :: checkTangentSpace                             |checks if dimension of space of sections of the normal bundle agrees with that calculated using normalMatrix                                                                                   |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
       |WeylGroups :: isReduced(BasicList,WeylGroupElement)                 |whether an Weyl group element can be multiplied by some simple reflections with length increasing at each step                                                                                 |
       +--------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

The FourTiTwo tags in particular can cause build errors if MakeDocumentation => false is passed to installPackage and then later running the Saturation tests:

 error: test(s) #28 of package Saturation failed.

            needsPackage "SymbolicPowers"
      -- warning: document: documentation headlines must be less than 100 characters long:
      --   "creates a toric ideal from a given set of exponents of its generators; equivalent to \"output --binomials\" in 4ti2"
     /build/macaulay2-1.17.1.1+git87.8019041+ds/M2/Macaulay2/packages/FourTiTwo.m2:312:1:(2):[34]: error: warning issued, debugLevel > 0
mahrud commented 3 years ago

Relevant: https://github.com/Macaulay2/M2/issues/1181#issuecomment-670469539 and https://github.com/Macaulay2/M2/issues/1501.

DanGrayson commented 3 years ago

It would be good to get the authors to shorten those.