# coding=utf-8
from sympy.liealgebras.cartan_type import CartanType
from sympy.matrices import Matrix

def test_type_G():
    c = CartanType("G2")
    m = Matrix(2, 2, [2, -1, -3, 2])
    assert c.cartan_matrix() == m
    assert c.simple_root(2) == [1, -2, 1]
    assert c.basis() == 14
    assert c.roots() == 12
    assert c.dimension() == 3
    diag = "0≡<≡0\n1   2"
    assert diag == c.dynkin_diagram()
    assert c.positive_roots() == {1: [0, 1, -1], 2: [1, -2, 1], 3: [1, -1, 0],
            4: [1, 0, 1], 5: [1, 1, -2], 6: [2, -1, -1]}