InducedAction( module, basis )
SubGModule( module, basis )
QuotientGModule( module, basis )
These functions take a G-module module as input, together with a basis basis for a proper submodule, which is assumed to be normalised, in the weak sense that the first non-zero component of each vector in the basis is 1, and no two vectors in the basis have their first nonzero components in the same position. The basis is given as an r times n matrix, where r is the length of the basis.
Normally, one runs
IsIrreducible(module) first, and (assuming it
false) then runs these functions using
as the second argument.
InducedAction returns a 4-element list
containing the submodule, the quotient module, the original matrices
rewritten with respect to a basis in which a basis for the submodule
comes first, and the change-of-basis matrix;
SubGModule returns the
submodule having basis as basis;
QuotientGModule the corresponding
RandomIrreducibleSubGModule( module )
Find a basis for an irreducible submodule of module.
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