docstr: The ith simple root for the C series
  
  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 C_n, the first n-1 simple roots are the same as
  the roots in A_(n-1) (a 1 in the ith position, a -1
  in the (i+1)th position, and zeroes elsewhere).  The
  nth simple root is the root in which there is a 2 in
  the nth position and zeroes elsewhere.
  
  Examples
  ========
  
  >>> from sympy.liealgebras.cartan_type import CartanType
  >>> c = CartanType("C3")
  >>> c.simple_root(2)
  [0, 1, -1]
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code: def simple_root(self, i):
      """The ith simple root for the C series
  
      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 C_n, the first n-1 simple roots are the same as
      the roots in A_(n-1) (a 1 in the ith position, a -1
      in the (i+1)th position, and zeroes elsewhere).  The
      nth simple root is the root in which there is a 2 in
      the nth position and zeroes elsewhere.
  
      Examples
      ========
  
      >>> from sympy.liealgebras.cartan_type import CartanType
      >>> c = CartanType("C3")
      >>> c.simple_root(2)
      [0, 1, -1]
  
      """
  
      n = self.n
      if i < n:
          return self.basic_root(i - 1, i)
      else:
          root = [0] * self.n
          root[n - 1] = 2
          return root
  
file_path: sympy/sympy/liealgebras/type_c.py
imports: from .cartan_type import Standard_Cartan
  from sympy.core.backend import eye
label_desc: Use image node_id 4 for calling the TypeC obj's underlying member method code with example usage: obj.simple_root(i) and returns: self, root