A G-module is defined by the action of a group G, generated by a set of matrices, on a d-dimensional vector space over a field, F = GF(q).
GModule returns a G-module record, where the component
.field is set to F,
.dimension to d,
.generators to the set of
generating matrices for G, and
.isGModule to true. These components
are set for every G-module record constructed using
Many of the functions described below return or update a G-module
record. Additional components which describe the nature of the action of
the underlying group G on the G-module are set by these functions.
Some of these carry information which may be of general use. These
components are described briefly in Components of a $G$-module record.
They need not appear in a G-module record, or may have the value
.component of a G-module record is accessed by
ComponentFlag and its value is set by
SetComponentFlag, where the
first letter of the component is capitalised in the function names. For
example, the component
.tensorBasis of module is set by
SetTensorBasisFlag( module, boolean ) and its value accessed by
TensorBasisFlag( module ). Such access functions and conventions
also apply to other records constructed by all of these functions.
If a function listed below takes as input a matrix group G, it also usually accepts a G-module.
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