- Introduction
- Invariant Rings of Finite Groups
- Group Actions on Polynomials
- Permutation Group Actions on Polynomials
- Matrix Group Actions on Polynomials
- Algebraic Group Actions on Polynomials
- Verbosity
- Construction of Invariants of Specified Degree
- ReynoldsOperator(f, G) : RngMPolElt, GrpMat -> RngMPolElt
- InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]
- InvariantsOfDegree(R, d, k) : RngInvar, RngIntElt, RngIntElt -> [ RngMPolElt ]
- Example RngInvar_InvariantsOfDegree (H117E2)
- SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->
- Example RngInvar_InvariantsOfDegree (H117E3)
- Construction of G-modules
- GModule(G, P, d) : Grp, RngMPol, RngIntElt -> ModGrp, Map, @ RngMPolElt @
- GModule(G, I, J) : Grp, RngMPol, RngMPol -> ModGrp, Map, @ RngMPolElt @
- GModule(G, Q) : Grp, RngMPolRes -> ModGrp, Map, @ RngMPolElt @
- Example RngInvar_GModule (H117E4)
- Molien Series
- Primary Invariants
- Secondary Invariants
- Fundamental Invariants
- The Module of an Invariant Ring
- The Algebra of an Invariant Ring and Algebraic Relations
- Properties of Invariant Rings
- Steenrod Operations
- Minimalization and Homogeneous Module Testing
- MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
- HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
- HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
- Example RngInvar_MinimalAlgebraGenerators (H117E15)
- Example RngInvar_HomogeneousModuleTest2 (H117E16)
- Attributes of Invariant Rings and Fields
- Invariant Rings of Linear Algebraic Groups
- Invariant Fields
- Invariants of the Symmetric Group
- Bibliography
V2.28, 13 July 2023