Sections GModule and IsGModule describe how to construct a G-module from a set of matrices or a group and how to test for a G-module.
Sections IsIrreducible for GModules, IsAbsolutelyIrreducible, IsSemiLinear, IsPrimitive for GModules, and IsTensor describe high-level functions which provide access to some of the algorithms mentioned in Contents of the matrix package; these are tests for reducibility, semi-linearity, primitivity, and tensor decomposition, respectively.
Section SmashGModule describes
SmashGModule which can be used to
explore whether a matrix group preserves certain decompositions with
respect to a normal subgroup.
Sections HomGModule, IsomorphismGModule, and CompositionFactors consider homomorphisms between and composition factors of G-modules.
Sections ClassicalForms, RecogniseClassical, and ConstructivelyRecogniseClassical describe functions for exploring classical groups.
Section RecogniseMatrixGroup describes the experimental function
Sections RecogniseClassicalCLG and RecogniseClassicalNP describe the low-level classical recognition functions.
Sections InducedAction, FieldGenCentMat, MinimalSubGModules, and SpinBasis describe the low-level Meataxe functions.
Sections SemiLinearDecomposition, TensorProductDecomposition,
MinBlocks, BlockSystemFlag, and Components of a $G$-module record
describe the low-level
Sections ApproximateKernel, RandomRelations, DisplayMatRecord, and
The record returned by RecogniseMatrixGroup describe the low-level
functions for the function
Sections DualGModule, InducedGModule, PermGModule, TensorProductGModule, ImprimitiveWreathProduct, and WreathPower describe functions to construct new G-modules from given ones.
Sections PermGroupRepresentation to Other utility functions describe functions which are somewhat independent of G-modules; these include functions to compute the order of a matrix, construct a permutation representation for a matrix group, and construct pseudo-random elements of a group.
Section References provides a bibliography.
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