FUNCTION:  Base - simple roots of a root system
CALLING SEQUENCE:  Base(R);
PARAMETERS:  R = a root system data structure
SYNOPSIS:
  Base(R) returns a list of simple roots for R, expressed as linear
  combinations of the standard orthonormal basis e1,e2,e3,...
  If R is not crystallographic, floating-point coordinates are used.
  If R is a root system name, the list of roots is ordered canonically in a
  way that does not vary with each Maple session. The base vectors for each
  irreducible component of R are listed consecutively, sorted first by
  series name (A,B,...,I), and then by rank within each series (so A2
  precedes A3, A10 precedes B2,...). The diagram function can be used to
  display the ordering of base vectors within a given irreducible component.
   
  If R is a Coxeter or Cartan matrix, the ordering of the rows and columns
  of the matrix dictates the ordering of the simple roots.
  If R is a list, it is assumed that R itself is a list of simple roots and
  Base(R) simply returns R.
  For a description of root system data structures, see Coxeter[Structure].
EXAMPLES:   
  Base(A2*B2);                yields         [e2-e1, e3-e2, e4, e5-e4]
  Base(");                    yields         [e2-e1, e3-e2, e4, e5-e4]
  Base(I2[5]);                yields    [e1, -.8090169945*e1+.5877852520*e2]
  CoxMat:=array([[1,3,2],[3,1,4],[2,4,1]]);
  Base(CoxMat);               yields             [e3-e2, e2-e1, e1]
SEE ALSO:  CartanMatrix, CoxMatrix, Diagram, NameOf, Structure.

