(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.

        This method returns the ith simple root for E_n.

        Examples
        ========

        >>> from sympy.liealgebras.cartan_type import CartanType
        >>> c = CartanType("E6")
        >>> c.simple_root(2)
        [1, 1, 0, 0, 0, 0, 0, 0]
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.
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 .
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.

        This method returns the ith simple root for E_n.

        Examples
        ========

        >>> from sympy.liealgebras.cartan_type import CartanType
        >>> c = CartanType("E6")
        >>> c.simple_root(2)
        [1, 1, 0, 0, 0, 0, 0, 0]
        """
        n = self.n
        if i == 1:
            root = [-0.5]*8
            root[0] = 0.5
            root[7] = 0.5
            return root
        elif i == 2:
            root = [0]*8
            root[1] = 1
            root[0] = 1
            return root
        else:
            if i == 7 or i == 8 and n == 6:
                raise ValueError("E6 only has six simple roots!")
            if i == 8 and n == 7:
                raise ValueError("E7 has only 7 simple roots!")

            return self.basic_root(i-3, i-2)
def simple_root ( self , i ) : n = self . n if i == 1 : root = [ - 0.5 ] * 8 root [ 0 ] = 0.5 root [ 7 ] = 0.5 return root elif i == 2 : root = [ 0 ] * 8 root [ 1 ] = 1 root [ 0 ] = 1 return root else : if i == 7 or i == 8 and n == 6 : raise ValueError ( "E6 only has six simple roots!" ) if i == 8 and n == 7 : raise ValueError ( "E7 has only 7 simple roots!" ) return self . basic_root ( i - 3 , i - 2 )