def test_expression_4(self):
function = Function('Tensor')(Symbol('T'))
tensor = Tensor(function, 4)
self.assertEqual(
Parser._generate_covdrv(tensor, function, [('beta', 'D')]),
r'\nabla_\beta T = \partial_\beta (T)')
function = Function('Tensor')(Symbol('TUU'), Symbol('mu'),
Symbol('nu'))
tensor = Tensor(function, 4)
self.assertEqual(
Parser._generate_covdrv(tensor, function, [('beta', 'D')]),
r'\nabla_\beta T^{\mu \nu} = \partial_\beta (T^{\mu \nu}) + \Gamma^\mu_{a \beta} (T^{a \nu}) + \Gamma^\nu_{a \beta} (T^{\mu a})'
)
function = Function('Tensor')(Symbol('TUD'), Symbol('mu'),
Symbol('nu'))
tensor = Tensor(function, 4)
self.assertEqual(
Parser._generate_covdrv(tensor, function, [('beta', 'D')]),
r'\nabla_\beta T^\mu_\nu = \partial_\beta (T^\mu_\nu) + \Gamma^\mu_{a \beta} (T^a_\nu) - \Gamma^a_{\nu \beta} (T^\mu_a)'
)
function = Function('Tensor')(Symbol('TDD'), Symbol('mu'),
Symbol('nu'))
tensor = Tensor(function, 4)
self.assertEqual(
Parser._generate_covdrv(tensor, function, [('beta', 'D')]),
r'\nabla_\beta T_{\mu \nu} = \partial_\beta (T_{\mu \nu}) - \Gamma^a_{\mu \beta} (T_{a \nu}) - \Gamma^a_{\nu \beta} (T_{\mu a})'
)
def test_expression_5(self):
tensor = Tensor(Function('Tensor')(Symbol('vU'), Symbol('mu')), 4)
self.assertEqual(
Parser._generate_covdrv(tensor, [('a', 'U'), ('b', 'D')],
'symbolic'),
r'\nabla_a \nabla_b v^\mu = \partial_a (\partial_b (v^\mu) + \Gamma^\mu_{c b} (v^c)) + \Gamma^\mu_{c a} (\partial_b (v^c) + \Gamma^c_{d b} (v^d))'
)
def test_expression_5(self):
function = Function('Tensor')(Symbol('vU'), Symbol('mu'))
tensor = Tensor(function, 4)
self.assertEqual(
Parser._generate_covdrv(tensor, function, [('a', 'D'),
('b', 'D')]),
r'\nabla_a \nabla_b v^\mu = \partial_a (\partial_b (v^\mu) + \Gamma^\mu_{c b} (v^c)) + \Gamma^\mu_{c a} (\partial_b (v^c) + \Gamma^c_{d b} (v^d)) - \Gamma^c_{b a} (\partial_c (v^\mu) + \Gamma^\mu_{b c} (v^b))'
)
def test_expression_5(self):
Parser.clear_namespace()
parse(r"""
% vardef -numeric -metric 'gDD' (4D)
% vardef -numeric 'vU' (4D)
T^\mu_b = \nabla_b v^\mu
""")
tensor = Parser._namespace['vU_cdD']
function = Parser._namespace['vU_cdD'].equation[0]
self.assertEqual(
Parser._generate_covdrv(tensor, function, 'a'),
r'\nabla_a \nabla_b v^\mu = \partial_a (\nabla_b v^\mu) + \text{Gamma}^\mu_{c a} (\nabla_b v^c) - \text{Gamma}^c_{b a} (\nabla_c v^\mu)'
)