BettiCharacters : Index

• Action -- the class of all finite group actions
• action -- define finite group action
• action(...,Sub=>...) -- format ring actors as one-row substitution matrices
• action(ChainComplex,List) -- define finite group action on a resolution
• action(ChainComplex,List,List,ZZ) -- define finite group action on a resolution
• action(Ideal,List) -- define finite group action on a graded module
• action(Ideal,List,List) -- define finite group action on a graded module
• action(Module,List) -- define finite group action on a graded module
• action(Module,List,List) -- define finite group action on a graded module
• action(PolynomialRing,List) -- define finite group action on a graded module
• action(PolynomialRing,List,List) -- define finite group action on a graded module
• action(QuotientRing,List) -- define finite group action on a graded module
• action(QuotientRing,List,List) -- define finite group action on a graded module
• ActionOnComplex -- the class of all finite group actions on complexes
• ActionOnComplex == ActionOnComplex -- compare actions and characters
• ActionOnGradedModule -- the class of all finite group actions on graded modules
• ActionOnGradedModule == ActionOnGradedModule -- compare actions and characters
• 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
• actors(ActionOnGradedModule,ZZ) -- group elements acting on components of a module
• BettiCharacters -- finite group characters on free resolutions and graded modules
• 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
• Character -- the class of all characters of finite group representations
• character -- compute characters of finite group action
• Character ** Character -- tensor product of characters
• Character ++ Character -- direct sum of characters
• Character / CharacterTable -- decompose a character into irreducible characters
• Character == Character -- compare actions and characters
• Character Array -- homological shift
• Character operations -- shift, direct sum, dual, and tensor product
• 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(ActionOnGradedModule,ZZ) -- compute characters of graded components of a module
• character(ActionOnGradedModule,ZZ,ZZ) -- compute characters of graded components of a module
• character(CharacterDecomposition,CharacterTable) -- recover character from decomposition
• character(PolynomialRing,ZZ,HashTable) -- construct a character
• CharacterDecomposition -- the class of all finite group character decompositions
• CharacterDecomposition * CharacterTable -- recover character from decomposition
• CharacterTable -- the class of all character tables of finite groups
• characterTable -- construct a character table
• characterTable(...,Labels=>...) -- custom labels for irreducible characters
• characterTable(List,Matrix,PolynomialRing,List) -- construct a character table
• characterTable(List,Matrix,PolynomialRing,RingMap) -- construct a character table
• decomposeCharacter -- decompose a character into irreducible characters
• decomposeCharacter(Character,CharacterTable) -- decompose a character into irreducible characters
• directSum(Character) -- direct sum of characters
• dual -- dual character
• dual(Character,List) -- dual character
• dual(Character,RingMap) -- dual character
• Equality checks -- compare actions and characters
• inverseRingActors -- get inverse of action on ring generators
• inverseRingActors(...,Sub=>...) -- format ring actors as one-row substitution matrices
• inverseRingActors(Action) -- get inverse of action on ring generators
• Labels -- custom labels for irreducible characters
• net(Action) -- format for printing, as a net
• net(Character) -- format for printing, as a net
• net(CharacterDecomposition) -- format for printing, as a net
• net(CharacterTable) -- format for printing, as a net
• numActors -- number of acting elements
• numActors(Action) -- number of acting elements
• ring(Action) -- get ring of object acted upon
• ringActors -- get action on ring generators
• ringActors(...,Sub=>...) -- format ring actors as one-row substitution matrices
• ringActors(Action) -- get action on ring generators
• Sub -- format ring actors as one-row substitution matrices
• symmetricGroupActors -- permutation action of the symmetric group
• symmetricGroupActors(PolynomialRing) -- permutation action of the symmetric group
• symmetricGroupTable -- character table of the symmetric group
• symmetricGroupTable(PolynomialRing) -- character table of the symmetric group
• target(Action) -- get object acted upon
• tensor(Character,Character) -- tensor product of characters