'This method returns some general information about the Weyl group for
a given Lie algebra.  It returns the name of the group and the elements
it acts on, if relevant.'

def group_name(self):

    n = self.cartan_type.rank()
    if (self.cartan_type.series == 'A'):
        return (((('S' + str((n + 1))) + ':    the    symmetric    group    acting    on    ') + str((n + 1))) + '    elements.')
    if ((self.cartan_type.series == 'B') or (self.cartan_type.series == 'C')):
        return (('The    hyperoctahedral    group    acting    on    ' + str((2 * n))) + '    elements.')
    if (self.cartan_type.series == 'D'):
        return (('The    symmetry    group    of    the    ' + str(n)) + '-dimensional    demihypercube.')
    if (self.cartan_type.series == 'E'):
        if (n == 6):
            return 'The    symmetry    group    of    the    6-polytope.'
        if (n == 7):
            return 'The    symmetry    group    of    the    7-polytope.'
        if (n == 8):
            return 'The    symmetry    group    of    the    8-polytope.'
    if (self.cartan_type.series == 'F'):
        return 'The    symmetry    group    of    the    24-cell,    or    icositetrachoron.'
    if (self.cartan_type.series == 'G'):
        return 'D6,    the    dihedral    group    of    order    12,    and    symmetry    group    of    the    hexagon.'
