Element conversion functions

Because of the variety of optional parameters available for conversion between the three kinds of representation, it is recommended that the user use actions and isomorphisms, rather than these conversion functions.

The parameter basis determines which basis is used for the matrices; the options are "standard", "root", and "weight". The parameter Local determines whether the permutations and words are written with respect to the roots of W itself or its overgroup. The parameter Group determines whether the word returned is in the Coxeter presentation or is just a sequence of integers.

WordToPerm( W, w ) : GrpCox, [] -> GrpPermElt

    Local: BoolElt                      Default: false

Convert the word w for the Coxeter group W to a permutation.

WordToMatrix( W, w ) : GrpCox, [] -> AlgMatElt

WordToDualMatrix( W, w ) : GrpCox, [] -> AlgMatElt

    basis: MonStgElt                    Default: "standard"

    Local: BoolElt                      Default: false

Convert the word w for the Coxeter group W to a matrix acting on the (co)root space.

PermToWord( W, p ) : GrpCox, GrpPermElt -> SeqEnum

    Local: BoolElt                      Default: false

    Group: BoolElt                      Default: false

Convert the permutation p in the Coxeter group W to a word.

MatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum

DualMatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum

    basis: MonStgElt                    Default: "standard"

    Local: BoolElt                      Default: false

    Group: BoolElt                      Default: false

Convert the matrix M acting on the (co)root space of the Coxeter group W to a word.

MatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt

DualMatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt

    basis: MonStgElt                    Default: "standard"

    Local: BoolElt                      Default: false

Convert the matrix M acting on the (co)root space of the Coxeter group W to a permutation.

PermToMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt

PermToDualMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt

    basis: MonStgElt                    Default: "standard"

    Local: BoolElt                      Default: false

Convert the permutation p in the Coxeter group W to a matrix acting on the (co)root space.

WordOnRoot( W, r, w ) : GrpCox, RngIntElt, . -> RngIntElt

    Local: BoolElt                      Default: false

The image of the rth root of the Coxeter group W under the word w.

WordOnRootSpace( W, v, w ) : GrpCox, ., . -> .

WordOnCorootSpace( W, v, w ) : GrpCox, ., . -> .

    basis: MonStgElt                    Default: "standard"

    Local: BoolElt                      Default: false

The image of v in the (co)root space of the Coxeter group W under the word w.