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BettiCharacters : Table of Contents
BettiCharacters
-- finite group characters on free resolutions and graded modules
action
-- define finite group action
Action
-- the class of all finite group actions
ActionOnComplex
-- the class of all finite group actions on complexes
ActionOnGradedModule
-- the class of all finite group actions on graded modules
net(Action)
-- format for printing, as a net
ring(Action)
-- get ring of object acted upon
ringActors
-- get action on ring generators
target(Action)
-- get object acted upon
action(ChainComplex,List,List,ZZ)
-- define finite group action on a resolution
action(Module,List,List)
-- define finite group action on a graded module
Sub
-- format ring actors as one-row substitution matrices
actors
-- group elements of an action
actors(ActionOnComplex,ZZ)
-- group elements of action on resolution
actors(ActionOnGradedModule,List)
-- group elements acting on components of a module
inverseRingActors
-- get inverse of action on ring generators
numActors
-- number of acting elements
character
-- compute characters of finite group action
Character
-- the class of all characters of finite group representations
Character Array
-- homological shift
directSum(Character)
-- direct sum of characters
dual
-- dual character
net(Character)
-- format for printing, as a net
tensor(Character,Character)
-- tensor product of characters
character(ActionOnComplex)
-- compute all Betti characters of minimal free resolution
character(ActionOnComplex,ZZ)
-- compute Betti characters of minimal free resolution
character(ActionOnGradedModule,List)
-- compute characters of graded components of a module
character(PolynomialRing,ZZ,HashTable)
-- construct a character
character(CharacterDecomposition,CharacterTable)
-- recover character from decomposition
Character operations
-- shift, direct sum, dual, and tensor product
characterTable
-- construct a character table
CharacterTable
-- the class of all character tables of finite groups
net(CharacterTable)
-- format for printing, as a net
Labels
-- custom labels for irreducible characters
decomposeCharacter
-- decompose a character into irreducible characters
CharacterDecomposition
-- the class of all finite group character decompositions
net(CharacterDecomposition)
-- format for printing, as a net
Equality checks
-- compare actions and characters
symmetricGroupActors
-- permutation action of the symmetric group
symmetricGroupTable
-- character table of the symmetric group
BettiCharacters Example 1
-- Specht ideals / subspace arrangements
BettiCharacters Example 2
-- Symbolic powers of star configurations
BettiCharacters Example 3
-- Klein configuration of points
BettiCharacters Example 4
-- a multigraded example