def test_EinsteinTensor_trace_negetive_of_Ricci_Scalar_in_4D(metric):
# https://en.wikipedia.org/wiki/Einstein_tensor#Trace
G1 = EinsteinTensor.from_metric(metric)
G2 = G1.change_config("ul")
val1 = simplify(tensorcontraction(G2.tensor(), (0, 1)))
val2 = RicciScalar.from_metric(metric).expr
assert simplify(val1 + val2) == 0
def test_RicciScalar_raise_TypeError():
x, y = sympy.symbols("x y")
try:
R = RicciScalar(x ** 2 * y * 3, 0)
assert False
except TypeError:
assert True
### "DeSitter"
mink = DeSitter()
t = mink.tensor()
pprint(t)
### @end
assert isinstance(sch, einsteinpy.symbolic.metric.MetricTensor)
snippets['DeSitter'] = latex(t)
### "AntiDeSitter"
mink = AntiDeSitter()
t = mink.tensor()
pprint(t)
### @end
assert isinstance(sch, einsteinpy.symbolic.metric.MetricTensor)
snippets['AntiDeSitter'] = latex(t)
### "Ricci-curvatures"
scalar_curvature_de_sitter = RicciScalar.from_metric(DeSitter())
scalar_curvature_anti_de_sitter = RicciScalar.from_metric(AntiDeSitter())
### @end
snippets['DeSitter-curvature'] = latex(scalar_curvature_de_sitter.expr)
snippets['AntiDeSitter-curvature'] = latex(
scalar_curvature_anti_de_sitter.expr)
snippets['AntiDeSitter-simplified'] = latex(
simplify(scalar_curvature_anti_de_sitter.expr))
### "save-latex"
with open("snippets.json", 'w') as f:
json.dump(snippets, f)
def test_RicciScalar_inbuilt_simplify_works():
x, y = sympy.symbols("x y")
R = RicciScalar((-y) + 2 * sin(x) * cos(x) + y - sin(2 * x), (x, y))
val = R.simplify(set_self=True)
assert R.expr == 0
assert sum(val) == 0
def test_RicciScalar_is_constant_for_ADS_spacetime():
# R is -12 for anti-de-Sitter spacetime
mt = anti_de_sitter_metric()
R = RicciScalar.from_metric(mt)
assert sympy.simplify(R.expr).is_constant()
def test_RicciScalar_expr_property():
x, y = sympy.symbols("x y")
R = RicciScalar(x**2 * y * 3, (x, y))
assert sympy.simplify(R._expr - R.expr) == 0