class_docstr: This class contains the information about
  the A series of simple Lie algebras.
  ====
docstr: Every lie algebra has a unique root system.
  Given a root system Q, there is a subset of the
  roots such that an element of Q is called a
  simple root if it cannot be written as the sum
  of two elements in Q.  If we let D denote the
  set of simple roots, then it is clear that every
  element of Q can be written as a linear combination
  of elements of D with all coefficients non-negative.
  
  In A_n the ith simple root is the root which has a 1
  in the ith position, a -1 in the (i+1)th position,
  and zeroes elsewhere.
  
  This method returns the ith simple root for the A series.
  
  Examples
  ========
  
  >>> from sympy.liealgebras.cartan_type import CartanType
  >>> c = CartanType("A4")
  >>> c.simple_root(1)
  [1, -1, 0, 0, 0]
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code: def simple_root(self, i):
      """
      Every lie algebra has a unique root system.
      Given a root system Q, there is a subset of the
      roots such that an element of Q is called a
      simple root if it cannot be written as the sum
      of two elements in Q.  If we let D denote the
      set of simple roots, then it is clear that every
      element of Q can be written as a linear combination
      of elements of D with all coefficients non-negative.
  
      In A_n the ith simple root is the root which has a 1
      in the ith position, a -1 in the (i+1)th position,
      and zeroes elsewhere.
  
      This method returns the ith simple root for the A series.
  
      Examples
      ========
  
      >>> from sympy.liealgebras.cartan_type import CartanType
      >>> c = CartanType("A4")
      >>> c.simple_root(1)
      [1, -1, 0, 0, 0]
  
      """
  
      return self.basic_root(i - 1, i)
  
file_path: sympy/sympy/liealgebras/type_a.py
imports: from sympy.liealgebras.cartan_type import Standard_Cartan
  from sympy.core.backend import eye
label_desc: Use image node_id 4 for calling the TypeA obj's underlying member method code with example usage: obj.simple_root(i) and returns: self