Cat::PermutationGroupInvariantRing – the category of invariant rings of permutation groups over a set

Dom::PermutationGroupInvariantRing(R) represents the category of invariant rings of permutation groups over a set, that is ....

Creating the Category

Cat::PermutationGroupInvariantRing(S)

Parameters:

Categories

Cat::FiniteGroupInvariantRing(R), Cat::GradedAlgebraWithBasis(R)

Details:

A Cat::PermutationGroupInvariantRing(R) is a

Entries

powersums – powersum invariant polynom

Cat::PermutationGroupInvariantRing::powersums()

Returns the ..

elementaries – elementaries invariant polynom

Cat::PermutationGroupInvariantRing::elementaries()

Returns ..

primaryInvariants – list of the primary invariants

Cat::PermutationGroupInvariantRing::primaryInvariants()

returns the list of the primary invariants

setPrimaryInvariants – sets the primary invariants

Cat::PermutationGroupInvariantRing::setPrimaryInvariants(list dom l)

Sets the primary invariants to the given list.

primaryInvariantsNames – primary invariants names

Cat::PermutationGroupInvariantRing::primaryInvariantsNames()

...

primaryInvariantsDegrees – list of the degrees of the primary invariants

Cat::PermutationGroupInvariantRing::primaryInvariantsDegrees()

returns the list of the degrees of the primary invariants

setPrimaryInvariantsDegrees – sets the degrees of the primary invariants

Cat::PermutationGroupInvariantRing::setPrimaryInvariantsDegrees(list dom l)

Sets the degree of the primary invariants to the given list.

HilbertSeries – ...

Cat::PermutationGroupInvariantRing::HilbertSeries(variable z)

Returns the ...

HilbertSeries_Polya – ...

Cat::PermutationGroupInvariantRing::HilbertSeries_Polya(variable z)

Returns the ...