def test_weyl_contraction_1st_3rd_indices_zero():
mw1 = anti_de_sitter_metric()
w1 = WeylTensor.from_metric(mw1)
t1 = simplify_sympy_array(
sympy.tensorcontraction(w1.change_config("ulll").tensor(), (0, 2)))
t0 = sympy.Array(np.zeros(shape=t1.shape, dtype=int))
assert t1 == t0
def test_TransformationMatrix_classmethod_new2old(cart2sph_matrix):
obj = cart2sph_matrix
cmp_array = Array([[1 / cos(q), 1 / sin(q)], [-1 / (p * sin(q)), 1 / (p * cos(q))]])
zero_array = Array(np.zeros(shape=cmp_array.shape, dtype=int))
assert simplify_sympy_array(cmp_array - obj) == zero_array
def test_SchoutenTensor_config_change():
metric = schwarzschild_metric()
t1 = SchoutenTensor.from_metric(metric)
t2 = t1.change_config("ul")
t3 = t2.change_config("ll")
assert t1.config == "ll" and t3.config == "ll"
compare = sympy.Array(np.zeros((4, 4), dtype=int))
testarr = simplify_sympy_array(t1.tensor() - t3.tensor())
assert testarr == compare
def test_weyl_conformal_rescaling():
# https://en.wikipedia.org/wiki/Weyl_tensor#Conformal_rescaling
a = sympy.symbols("a")
mw1 = anti_de_sitter_metric()
mw2 = MetricTensor(a * mw1.tensor(), mw1.symbols(), mw1.config)
w1 = WeylTensor.from_metric(mw1).change_config("ulll")
w2 = WeylTensor.from_metric(mw2).change_config("ulll")
cmp_arr = sympy.Array(np.zeros(shape=w1.tensor().shape, dtype=int))
assert simplify_sympy_array(w1.tensor() - w2.tensor()) == cmp_arr
assert w1.syms == w1.symbols()
assert w1.parent_metric == w1._parent_metric
def test_TransformationMatrix_inv_function(cart2sph_matrix):
assert cart2sph_matrix._inv is None
obj = cart2sph_matrix.inv()
assert cart2sph_matrix._inv is not None
obj = cart2sph_matrix.inv()
cmp_array = Array([[cos(q), sin(q)], [-1 * p * sin(q), p * cos(q)]])
zero_array = Array(np.zeros(shape=cmp_array.shape, dtype=int))
assert simplify_sympy_array(cmp_array - obj) == zero_array
def test_Minkowski_equality():
# Minkowski and MinkowskiCartesian are same
assert simplify_sympy_array(
MinkowskiCartesian().tensor()) == simplify_sympy_array(
Minkowski().tensor())
def test_check_two_metrics_are_equal(m1, m2):
zero_arr = Array(np.zeros(shape=m1.tensor().shape, dtype=int))
assert simplify_sympy_array(m1.tensor() - m2.tensor()) == zero_arr
def test_simplify_sympy_array_works_for_all(target):
try:
simplify_sympy_array(target)
assert True
except Exception:
assert False