(self)
return posroots
This method generates 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.

        Example
        ======
        >>> 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]}
This method generates 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.
This method generates 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 .
def positive_roots(self):
        """
        This method generates 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.

        Example
        ======
        >>> 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):
            for j in range(i+1, n+1):
               k += 1
               posroots[k] = self.basic_root(i, j)
        return posroots
def positive_roots ( self ) : n = self . n posroots = { } k = 0 for i in range ( 0 , n ) : for j in range ( i + 1 , n + 1 ) : k += 1 posroots [ k ] = self . basic_root ( i , j ) return posroots