original_docstring: Generates all the positive roots of A_n
  
          This is half of all of the roots of C_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]}
  
          
docstring: Generates all the positive roots of A_n
  This is half of all of the roots of C_n; by multiplying all the
  positive roots by -1 we get the negative roots.
  
  Examples
  
  
docstring_tokens: Generates all the positive roots of A_n This is half of all of the roots of C_n ; by multiplying all the positive roots by - 1 we get the negative roots . Examples
code: def positive_roots(self):
          """Generates all the positive roots of A_n
  
          This is half of all of the roots of C_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]}
  
          """
  
          n = self.n
          posroots = {}
          k = 0
          for i in range(0, n-1):
              for j in range(i+1, n):
                 k += 1
                 posroots[k] = self.basic_root(i, j)
                 k += 1
                 root = self.basic_root(i, j)
                 root[j] = 1
                 posroots[k] = root
  
          for i in range(0, n):
              k += 1
              root = [0]*n
              root[i] = 2
              posroots[k] = root
  
          return posroots
code_tokens: def positive_roots ( self ) : n = self . n posroots = { } k = 0 for i in range ( 0 , n - 1 ) : for j in range ( i + 1 , n ) : k += 1 posroots [ k ] = self . basic_root ( i , j ) k += 1 root = self . basic_root ( i , j ) root [ j ] = 1 posroots [ k ] = root for i in range ( 0 , n ) : k += 1 root = [ 0 ] * n root [ i ] = 2 posroots [ k ] = root return posroots
short_docstring: Generates all the positive roots of A_n
  This is half of all of the roots of C_n; by multiplying all the
  positive roots by -1 we get the negative roots.
short_docstring_tokens: Generates all the positive roots of A_n This is half of all of the roots of C_n ; by multiplying all the positive roots by - 1 we get the negative roots .
comment: """Generates all the positive roots of A_n
  
          This is half of all of the roots of C_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]}
  
          """