InvariantRing : Table of Contents

• InvariantRing -- invariants of group actions
• action -- the group action that produced a ring of invariants
• actionMatrix -- matrix of a linearly reductive action
• ambient(RingOfInvariants) -- the ambient polynomial ring where the group acted upon
• cyclicFactors -- of a diagonal action
• definingIdeal -- presentation of a ring of invariants as polynomial ring modulo the defining ideal
• degreesRing(DiagonalAction) -- of a diagonal action
• DiagonalAction -- the class of all diagonal actions
• diagonalAction -- diagonal group action via weights
• dim(GroupAction) -- dimension of the polynomial ring being acted upon
• equivariantHilbert -- stores equivariant Hilbert series expansions
• equivariantHilbertSeries -- equivariant Hilbert series for a diagonal action
• finiteAction -- the group action generated by a list of matrices
• FiniteGroupAction -- the class of all finite group actions
• generators(FiniteGroupAction) -- generators of a finite group
• generators(RingOfInvariants) -- the generators for a ring of invariants
• group -- list all elements of the group of a finite group action
• GroupAction -- the class of all group actions
• groupIdeal -- ideal defining a linearly reductive group
• hilbertIdeal -- compute generators for the Hilbert ideal
• hilbertSeries(RingOfInvariants) -- Hilbert series of the invariant ring
• hironakaDecomposition -- calculates a Hironaka decomposition for the invariant ring of a finite group
• hsop algorithms -- an overview of the algorithms used in primaryInvariants
• invariantRing -- the ring of invariants of a group action
• invariants -- computes the generating invariants of a group action
• invariants(...,DegreeBound=>...) -- degree bound for invariants of finite groups
• invariants(...,DegreeLimit=>...) -- GB option for invariants
• invariants(...,SubringLimit=>...) -- GB option for invariants
• invariants(...,UseCoefficientRing=>...) -- option to compute invariants over the given coefficient ring
• invariants(...,UseLinearAlgebra=>...) -- strategy for computing invariants of finite groups
• invariants(DiagonalAction) -- computes the generating invariants of a group action
• invariants(FiniteGroupAction) -- computes the generating invariants of a group action
• invariants(FiniteGroupAction,ZZ) -- basis for graded component of invariant ring
• invariants(LinearlyReductiveAction) -- invariant generators of Hilbert ideal
• invariants(LinearlyReductiveAction,ZZ) -- basis for graded component of invariant ring
• isAbelian -- check whether a finite matrix group is Abelian
• isInvariant -- check whether a polynomial is invariant under a group action
• LinearlyReductiveAction -- the class of all (non finite, non toric) linearly reductive group actions
• linearlyReductiveAction -- Linearly reductive group action
• molienSeries -- computes the Molien (Hilbert) series of the invariant ring of a finite group
• net(RingOfInvariants) -- format for printing, as a net
• numgens(DiagonalAction) -- number of generators of the finite part of a diagonal group
• numgens(FiniteGroupAction) -- number of generators of a finite group
• permutationMatrix -- convert a one-line notation or cyclic notation of a permutation to a matrix representation
• primaryInvariants -- computes a list of primary invariants for the invariant ring of a finite group
• primaryInvariants(...,Dade=>...) -- an optional argument for primaryInvariants determining whether to use the Dade algorithm
• primaryInvariants(...,DegreeVector=>...) -- an optional argument for primaryInvariants that finds invariants of certain degrees
• rank(DiagonalAction) -- of a diagonal action
• relations(FiniteGroupAction) -- relations of a finite group
• reynoldsOperator -- the image of a polynomial under the Reynolds operator
• ring(GroupAction) -- the polynomial ring being acted upon
• RingOfInvariants -- the class of the rings of invariants under the action of a finite group, an Abelian group or a linearly reductive group
• schreierGraph -- Schreier graph of a finite group
• secondaryInvariants -- computes secondary invariants for the invariant ring of a finite group
• secondaryInvariants(...,PrintDegreePolynomial=>...) -- an optional argument for secondaryInvariants that determines the printing of an informative polynomial
• UseNormaliz -- option for diagonal invariants
• weights -- of a diagonal action
• words -- associate a word in the generators of a group to each element