Endomorphisms

Detailed Description

Functions
int	MakeEndomorphisms (const MatRep_t *rep, const Matrix_t *nsp, Matrix_t *endo[])
	Calculate the endomorphism ring. More...

Function Documentation

int MakeEndomorphisms	(	const MatRep_t *	rep,
		const Matrix_t *	nsp,
		Matrix_t *	endo[]
	)

Calculate the endomorphism ring.

This function calculates a basis for the endomorphism ring E of an irreducible module. The dimension of E is equal to the degree [F':F] of the splitting field extension for the module.

The function takes three input arguments: ngen is the number of generators of the algebra, and gen points to an array of ngen matrices containing the representations of the generators. nsp is the kernel of an identifying word for the module, i.e., an algebra element a with dim(ker(a_V))=[F':F].

On success, basis of E (a set of matrices) is stored into endo. If the function fails, no matrices are stored in endo.

Parameters

rep	Pointer to a matrix representation.
nsp	Idword kernel (see below).
endo	Pointer to result buffer.

Returns

0 on success, -1 on error.