'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 B_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 n-th
simple root is the root with a 1 in the nth position
and zeroes elsewhere.
This method returns the ith simple root for the B series.
Examples
>>> from sympy.liealgebras.cartan_type import CartanType
>>> c = CartanType("B3")
>>> c.simple_root(2)
[0, 1, -1]'

def simple_root(self, i):

    n = self.n
    if (i < n):
        return self.basic_root((i - 1), i)
    else:
        root = ([0] * self.n)
        root[(n - 1)] = 1
        return root
