def test_mul_inverse(self):
ga = GeometricAlgebra(metric=dual_metric)
# a = 2
a = ga.from_tensor_with_kind(tf.fill([1], 2.0), kind="scalar")
# b = 3 + 3e0
b = ga.from_tensor_with_kind(tf.fill([2], 3.0), kind="mv")
# a * b = 2 * (3 + 3e0) = 6 + 6e0
c = ga.geom_prod(a, b)
self.assertTensorsEqual(c, ga.from_scalar(6.0) + 6.0 * ga.e("0"))
# a^-1 = 1 / 2
a_inv = ga.inverse(a)
self.assertTensorsEqual(ga.select_blades_with_name(a_inv, ""), 0.5)
# c = a * b
# => a_inv * c = b
self.assertTensorsEqual(ga.geom_prod(a_inv, c), b)
# Since a is scalar, should commute too.
# => c * a_inv = b
self.assertTensorsEqual(ga.geom_prod(c, a_inv), b)
# b is not simply invertible (because it does not square to a scalar)
# and will throw an exception
self.assertRaises(Exception, ga.simple_inverse, b)
# b is invertible with the shirokov inverse
b_inv = ga.inverse(b)
self.assertTensorsEqual(ga.geom_prod(b, b_inv), 1 * ga.e(""))
def test_inverse(self):
pga = GeometricAlgebra(pga_signature)
# a = 3e12 + 5e23
a = 3 * pga.e12 + 5 * pga.e23
# a_inv: -0.09*e_12 + -0.15*e_23
a_inv = pga.inverse(a)
# a a_inv should be 1
self.assertTensorsApproxEqual(pga.geom_prod(a, a_inv), 1 * pga.e(""))