class_docstr: Represent the root system of a simple Lie algebra
  
  Every simple Lie algebra has a unique root system.  To find the root
  system, we first consider the Cartan subalgebra of g, which is the maximal
  abelian subalgebra, and consider the adjoint action of g on this
  subalgebra.  There is a root system associated with this action. Now, a
  root system over a vector space V is a set of finite vectors Phi (called
  roots), which satisfy:
  
  1.  The roots span V
  2.  The only scalar multiples of x in Phi are x and -x
  3.  For every x in Phi, the set Phi is closed under reflection
      through the hyperplane perpendicular to x.
  4.  If x and y are roots in Phi, then the projection of y onto
      the line through x is a half-integral multiple of x.
  
  Now, there is a subset of Phi, which we will call Delta, such that:
  1.  Delta is a basis of V
  2.  Each root x in Phi can be written x = sum k_y y for y in Delta
  
  The elements of Delta are called the simple roots.
  Therefore, we see that the simple roots span the root space of a given
  simple Lie algebra.
  
  References
  ==========
  
  .. [1] https://en.wikipedia.org/wiki/Root_system
  .. [2] Lie Algebras and Representation Theory - Humphreys
docstr: Generate the simple roots of the Lie algebra
  
  The rank of the Lie algebra determines the number of simple roots that
  it has.  This method obtains the rank of the Lie algebra, and then uses
  the simple_root method from the Lie algebra classes to generate all the
  simple roots.
  
  Examples
  ========
  
  >>> from sympy.liealgebras.root_system import RootSystem
  >>> c = RootSystem("A3")
  >>> roots = c.simple_roots()
  >>> roots
  {1: [1, -1, 0, 0], 2: [0, 1, -1, 0], 3: [0, 0, 1, -1]}
code: def simple_roots(self):
      """Generate the simple roots of the Lie algebra
  
      The rank of the Lie algebra determines the number of simple roots that
      it has.  This method obtains the rank of the Lie algebra, and then uses
      the simple_root method from the Lie algebra classes to generate all the
      simple roots.
  
      Examples
      ========
  
      >>> from sympy.liealgebras.root_system import RootSystem
      >>> c = RootSystem("A3")
      >>> roots = c.simple_roots()
      >>> roots
      {1: [1, -1, 0, 0], 2: [0, 1, -1, 0], 3: [0, 0, 1, -1]}
  
      """
      n = self.cartan_type.rank()
      roots = {}
      for i in range(1, n + 1):
          root = self.cartan_type.simple_root(i)
          roots[i] = root
      return roots
  
file_path: sympy/sympy/liealgebras/root_system.py
imports: from .cartan_type import CartanType
  from sympy.core.basic import Atom
label_desc: Use image node_id 2 for calling the RootSystem obj's underlying member method code with example usage: obj.simple_roots() and returns: roots