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_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_weyl_dim3():
list_metric = np.ones((3, 3), dtype=int).tolist()
symbolstr = "t r theta"
syms = sympy.symbols(symbolstr)
metric = MetricTensor(list_metric, syms)
obj = WeylTensor.from_metric(metric).arr
assert obj == sympy.Array(np.zeros((3, 3), dtype=int))
def test_weyl_ValueError_wrong_config_length():
testarr = np.ones((4, 4, 4, 4), dtype=int).tolist()
syms = sympy.symbols("x y z w")
try:
obj = WeylTensor(testarr, syms, config="uuu", parent_metric=None)
assert False
except ValueError:
assert True
def test_weyl_TypeError():
testarr = np.ones((4, 4, 4, 4), dtype=int).tolist()
syms = 0
try:
obj = WeylTensor(testarr, syms)
assert False
except TypeError:
assert True
def test_weyl_dim2():
list_metric = np.zeros((2, 2), dtype=int).tolist()
symbolstr = "t r"
syms = sympy.symbols(symbolstr)
metric = MetricTensor(list_metric, syms)
try:
obj = WeylTensor.from_metric(metric)
assert False
except ValueError:
assert True