docstr: Generate all the positive roots of A_n
  
  This is half of all of the roots of A_n; by multiplying all the
  positive roots by -1 we get the negative roots.
  
  Examples
  ========
  
  >>> from sympy.liealgebras.cartan_type import CartanType
  >>> c = CartanType("A3")
  >>> c.positive_roots()
  {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
          5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
code: def positive_roots(self):
      """Generate all the positive roots of A_n
  
      This is half of all of the roots of A_n; by multiplying all the
      positive roots by -1 we get the negative roots.
  
      Examples
      ========
  
      >>> from sympy.liealgebras.cartan_type import CartanType
      >>> c = CartanType("A3")
      >>> c.positive_roots()
      {1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
              5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}
  
      """
  
      roots = {
          1: [0, 1, -1],
          2: [1, -2, 1],
          3: [1, -1, 0],
          4: [1, 0, 1],
          5: [1, 1, -2],
          6: [2, -1, -1],
      }
      return roots
  
file_path: sympy/sympy/liealgebras/type_g.py
imports: from .cartan_type import Standard_Cartan
  from sympy.core.backend import Matrix
label_desc: Use image node_id 4 for calling the TypeG obj's underlying member method code with example usage: obj.positive_roots() and returns: roots