def test_TensorManager():
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
LorentzH = TensorIndexType('LorentzH', dummy_fmt='LH')
i, j = tensor_indices('i,j', Lorentz)
ih, jh = tensor_indices('ih,jh', LorentzH)
p, q = tensorhead('p q', [Lorentz], [[1]])
ph, qh = tensorhead('ph qh', [LorentzH], [[1]])
Gsymbol = Symbol('Gsymbol')
GHsymbol = Symbol('GHsymbol')
TensorManager.set_comm(Gsymbol, GHsymbol, 0)
G = tensorhead('G', [Lorentz], [[1]], Gsymbol)
assert TensorManager._comm_i2symbol[G.comm] == Gsymbol
GH = tensorhead('GH', [LorentzH], [[1]], GHsymbol)
ps = G(i) * p(-i)
psh = GH(ih) * ph(-ih)
t = ps + psh
t1 = t * t
assert t1 == ps * ps + 2 * ps * psh + psh * psh
qs = G(i) * q(-i)
qsh = GH(ih) * qh(-ih)
assert ps * qsh == qsh * ps
assert ps * qs != qs * ps
n = TensorManager.comm_symbols2i(Gsymbol)
assert TensorManager.comm_i2symbol(n) == Gsymbol
assert GHsymbol in TensorManager._comm_symbols2i
raises(ValueError, lambda: TensorManager.set_comm(GHsymbol, 1, 2))
TensorManager.set_comms((Gsymbol, GHsymbol, 0), (Gsymbol, 1, 1))
assert TensorManager.get_comm(n, 1) == TensorManager.get_comm(1, n) == 1
TensorManager.clear()
assert TensorManager.comm == [{
0: 0,
1: 0,
2: 0
}, {
0: 0,
1: 1,
2: None
}, {
0: 0,
1: None
}]
assert GHsymbol not in TensorManager._comm_symbols2i
nh = TensorManager.comm_symbols2i(GHsymbol)
assert GHsymbol in TensorManager._comm_symbols2i
def test_TensorManager():
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
LorentzH = TensorIndexType('LorentzH', dummy_fmt='LH')
i, j = tensor_indices('i,j', Lorentz)
ih, jh = tensor_indices('ih,jh', LorentzH)
p, q = tensorhead('p q', [Lorentz], [[1]])
ph, qh = tensorhead('ph qh', [LorentzH], [[1]])
Gsymbol = Symbol('Gsymbol')
GHsymbol = Symbol('GHsymbol')
TensorManager.set_comm(Gsymbol, GHsymbol, 0)
G = tensorhead('G', [Lorentz], [[1]], Gsymbol)
assert TensorManager._comm_i2symbol[G.comm] == Gsymbol
GH = tensorhead('GH', [LorentzH], [[1]], GHsymbol)
ps = G(i)*p(-i)
psh = GH(ih)*ph(-ih)
t = ps + psh
t1 = t*t
assert t1 == ps*ps + 2*ps*psh + psh*psh
qs = G(i)*q(-i)
qsh = GH(ih)*qh(-ih)
assert ps*qsh == qsh*ps
assert ps*qs != qs*ps
n = TensorManager.comm_symbols2i(Gsymbol)
assert TensorManager.comm_i2symbol(n) == Gsymbol
assert GHsymbol in TensorManager._comm_symbols2i
raises(ValueError, lambda: TensorManager.set_comm(GHsymbol, 1, 2))
TensorManager.set_comms((Gsymbol,GHsymbol,0),(Gsymbol,1,1))
assert TensorManager.get_comm(n, 1) == TensorManager.get_comm(1, n) == 1
TensorManager.clear()
assert TensorManager.comm == [{0:0, 1:0, 2:0}, {0:0, 1:1, 2:None}, {0:0, 1:None}]
assert GHsymbol not in TensorManager._comm_symbols2i
nh = TensorManager.comm_symbols2i(GHsymbol)
assert GHsymbol in TensorManager._comm_symbols2i
expr : TensExpr
Symbolic expression of tensors.
idxs : TensorIndex
Indices that encode the covariance and contravariance of the result.
"""
if idxs is None:
idxs = TensMul(expr).get_free_indices()
return expr.replace_with_arrays(ReplacementManager, idxs)
def indices(s, metric, is_up=True):
"""
Create indices using a method similar to ~sympy.symbols.
"""
if isinstance(s, string_types):
a = [x.name for x in symbols(s, seq=True)]
else:
raise ValueError(
"expected a string, received object of type {}".format(type(s)))
idxs = [Index(idx, metric, is_up) for idx in a]
if len(idxs) == 1:
return idxs[0]
return idxs
# metric tensors and general tensors commute with each other and themselves.
TensorManager.set_comm("general", "general", 0)
# partial derivatives only commute with themselves.
TensorManager.set_comm("partial", "partial", 0)