FUNCTION: CgPositiveRoots - positive roots of a classical group

CALLING SEQUENCE:

CgPositiveRoots(typ, rank)

CG[CgPositiveRoots](typ, rank)

PARAMETERS:

typ = one of the classical group A, B, C or D

rank = the rank of the group

SYNOPSIS:

• The CgPositiveRoots function computes the positive roots of any classical group.

• The result is a list of lists.

• Whenever there is a conflict between the function name CgPositiveRoots and another name used in the same session, use the long form CG['CgPositiveRoots'].

EXAMPLES:

> with(CG):
> CgPositiveRoots(D, 4);
 
 [[1, -1, 0, 0], [1, 1, 0, 0], [1, 0, -1, 0], [1, 0, 1, 0], [1, 0, 0, -1],
 
  [1, 0, 0, 1],  [0, 1, -1, 0], [0, 1, 1, 0], [0, 1, 0, -1], [0, 1, 0, 1],
 
  [0, 0, 1, -1], [0, 0, 1, 1]]