InvariantRing : Index

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