def METHOD_NAME(self, m):
    r"""
    The degree of an element of the basis is defined as the dimension of the polyhedron.
    INPUT:
    - ``m`` -- an element of the basis (a polyhedron)
    EXAMPLES::
        sage: from sage.geometry.polyhedron.modules.formal_polyhedra_module import FormalPolyhedraModule
        sage: def closed_interval(a,b): return Polyhedron(vertices=[[a], [b]])
        sage: I01 = closed_interval(0, 1); I01.rename("conv([0], [1])")
        sage: I11 = closed_interval(1, 1); I11.rename("{[1]}")
        sage: I12 = closed_interval(1, 2); I12.rename("conv([1], [2])")
        sage: I02 = closed_interval(0, 2); I02.rename("conv([0], [2])")
        sage: M = FormalPolyhedraModule(QQ, 1, basis=[I01, I11, I12, I02])
    We can extract homogeneous components::
        sage: O = M(I01) + M(I11) + M(I12)
        sage: O.homogeneous_component(0)
        [{[1]}]
        sage: O.homogeneous_component(1)
        [conv([0], [1])] + [conv([1], [2])]
    We note that modulo the linear relations of polyhedra, this would only be a filtration,
    not a grading, as the following example shows::
        sage: X = M(I01) + M(I12) - M(I02)
        sage: X.degree()
        1
        sage: Y = M(I11)
        sage: Y.degree()
        0
    """
    return m.dimension()