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Packages » InvariantRing :: invariants

Synopsis

• Usage:

  invariants G

• Inputs:
  • G, an instance of the type GroupAction, a specific type of group action on a polynomial ring
• Optional inputs:
  • Strategy (missing documentation) => ..., default value UseNormaliz, the strategy used to compute diagonal invariants, options are UsePolyhedra or UseNormaliz.
  • DegreeBound => ..., default value infinity, degree bound for invariants of finite groups
  • DegreeLimit => ..., default value {}, GB option for invariants
  • SubringLimit => ..., default value infinity, GB option for invariants
  • UseCoefficientRing => ..., default value false, option to compute invariants over the given coefficient ring
  • UseLinearAlgebra => ..., default value false, strategy for computing invariants of finite groups
• Outputs:
  • L, a list, a minimal set of generating invariants for the group action

Description

This function is provided by the package InvariantRing. This function can be used to compute the generating invariants of a diagonal group action, finite group action or linearly reductive group action. It can also be used to compute a basis of a graded component of the invariant ring. Below is a list of the many ways to use this function:

• invariants(FiniteGroupAction): computes the generating invariants of a finite group action
• invariants(DiagonalAction): computes the generating invariants of a diagonal group action
• invariants(LinearlyReductiveAction): computes the generating invariants of a linearly reductive action
• invariants(FiniteGroupAction,ZZ) or invariants(FiniteGroupAction,List): computes a basis for graded component of the invariant ring of a finite group action
• invariants(LinearlyReductiveAction,ZZ) or invariants(LinearlyReductiveAction,List): computes a basis for graded component of the invariant ring of a linearly reductive group action

Caveat

Some optional inputs are only relevant to certain use cases of this method. Please consult the documentation pages for the different cases to learn which optional inputs are used.

See also

• invariantRing -- the ring of invariants of a group action
• isInvariant -- check whether a polynomial is invariant under a group action