def test_mul():
from sympy.abc import x
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
a, b, c, d = tensor_indices('a,b,c,d', Lorentz)
sym = tensorsymmetry([1] * 2)
t = TensMul.from_data(S.One, [], [], [])
assert str(t) == '1'
A, B = tensorhead('A B', [Lorentz] * 2, [[1] * 2])
t = (1 + x) * A(a, b)
assert str(t) == '(x + 1)*A(a, b)'
assert t.types == [Lorentz]
assert t.rank == 2
assert t.dum == []
assert t.coeff == 1 + x
assert sorted(t.free) == [(a, 0, 0), (b, 1, 0)]
assert t.components == [A]
t = A(-b, a) * B(-a, c) * A(-c, d)
t1 = tensor_mul(*t.split())
assert t == t(-b, d)
assert t == t1
assert tensor_mul(*[]) == TensMul.from_data(S.One, [], [], [])
t = TensMul.from_data(1, [], [], [])
zsym = tensorsymmetry()
typ = TensorType([], zsym)
C = typ('C')
assert str(C()) == 'C'
assert str(t) == '1'
assert t.split()[0] == t
raises(ValueError, lambda: TIDS.free_dum_from_indices(a, a))
raises(ValueError, lambda: TIDS.free_dum_from_indices(-a, -a))
raises(ValueError, lambda: A(a, b) * A(a, c))
t = A(a, b) * A(-a, c)
raises(ValueError, lambda: t(a, b, c))
def test_mul():
from sympy.abc import x
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
a, b, c, d = tensor_indices('a,b,c,d', Lorentz)
sym = tensorsymmetry([1]*2)
t = TensMul.from_data(S.One, [], [], [])
assert str(t) == '1'
A, B = tensorhead('A B', [Lorentz]*2, [[1]*2])
t = (1 + x)*A(a, b)
assert str(t) == '(x + 1)*A(a, b)'
assert t.types == [Lorentz]
assert t.rank == 2
assert t.dum == []
assert t.coeff == 1 + x
assert sorted(t.free) == [(a, 0, 0), (b, 1, 0)]
assert t.components == [A]
t = A(-b, a)*B(-a, c)*A(-c, d)
t1 = tensor_mul(*t.split())
assert t == t(-b, d)
assert t == t1
assert tensor_mul(*[]) == TensMul.from_data(S.One, [], [], [])
t = TensMul.from_data(1, [], [], [])
zsym = tensorsymmetry()
typ = TensorType([], zsym)
C = typ('C')
assert str(C()) == 'C'
assert str(t) == '1'
assert t.split()[0] == t
raises(ValueError, lambda: TIDS.free_dum_from_indices(a, a))
raises(ValueError, lambda: TIDS.free_dum_from_indices(-a, -a))
raises(ValueError, lambda: A(a, b)*A(a, c))
t = A(a, b)*A(-a, c)
raises(ValueError, lambda: t(a, b, c))
def _trace_single_line1(t):
t = t.sorted_components()
components = t.components
ncomps = len(components)
g = LorentzIndex.metric
# gamma matirices are in a[i:j]
hit = 0
for i in range(ncomps):
if components[i] == GammaMatrix:
hit = 1
break
for j in range(i + hit, ncomps):
if components[j] != GammaMatrix:
break
else:
j = ncomps
numG = j - i
if numG == 0:
tcoeff = t.coeff
return t.nocoeff if tcoeff else t
if numG % 2 == 1:
return TensMul.from_data(S.Zero, [], [], [])
elif numG > 4:
# find the open matrix indices and connect them:
a = t.split()
ind1 = a[i].get_indices()[0]
ind2 = a[i + 1].get_indices()[0]
aa = a[:i] + a[i + 2:]
t1 = tensor_mul(*aa) * g(ind1, ind2)
t1 = t1.contract_metric(g)
args = [t1]
sign = 1
for k in range(i + 2, j):
sign = -sign
ind2 = a[k].get_indices()[0]
aa = a[:i] + a[i + 1:k] + a[k + 1:]
t2 = sign * tensor_mul(*aa) * g(ind1, ind2)
t2 = t2.contract_metric(g)
t2 = simplify_gpgp(t2, False)
args.append(t2)
t3 = TensAdd(*args)
t3 = _trace_single_line(t3)
return t3
else:
a = t.split()
t1 = _gamma_trace1(*a[i:j])
a2 = a[:i] + a[j:]
t2 = tensor_mul(*a2)
t3 = t1 * t2
if not t3:
return t3
t3 = t3.contract_metric(g)
return t3
def _trace_single_line1(t):
t = t.sorted_components()
components = t.components
ncomps = len(components)
g = LorentzIndex.metric
# gamma matirices are in a[i:j]
hit = 0
for i in range(ncomps):
if components[i] == GammaMatrix:
hit = 1
break
for j in range(i + hit, ncomps):
if components[j] != GammaMatrix:
break
else:
j = ncomps
numG = j - i
if numG == 0:
tcoeff = t.coeff
return t.nocoeff if tcoeff else t
if numG % 2 == 1:
return TensMul.from_data(S.Zero, [], [], [])
elif numG > 4:
# find the open matrix indices and connect them:
a = t.split()
ind1 = a[i].get_indices()[0]
ind2 = a[i + 1].get_indices()[0]
aa = a[:i] + a[i + 2:]
t1 = tensor_mul(*aa)*g(ind1, ind2)
t1 = t1.contract_metric(g)
args = [t1]
sign = 1
for k in range(i + 2, j):
sign = -sign
ind2 = a[k].get_indices()[0]
aa = a[:i] + a[i + 1:k] + a[k + 1:]
t2 = sign*tensor_mul(*aa)*g(ind1, ind2)
t2 = t2.contract_metric(g)
t2 = simplify_gpgp(t2, False)
args.append(t2)
t3 = TensAdd(*args)
t3 = _trace_single_line(t3)
return t3
else:
a = t.split()
t1 = _gamma_trace1(*a[i:j])
a2 = a[:i] + a[j:]
t2 = tensor_mul(*a2)
t3 = t1*t2
if not t3:
return t3
t3 = t3.contract_metric(g)
return t3
def test_add1():
assert TensAdd() == 0
# simple example of algebraic expression
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
a,b,d0,d1,i,j,k = tensor_indices('a,b,d0,d1,i,j,k', Lorentz)
# A, B symmetric
A, B = tensorhead('A,B', [Lorentz]*2, [[1]*2])
t1 = A(b,-d0)*B(d0,a)
assert TensAdd(t1).equals(t1)
t2a = B(d0,a) + A(d0, a)
t2 = A(b,-d0)*t2a
assert str(t2) == 'A(a, L_0)*A(b, -L_0) + A(b, L_0)*B(a, -L_0)'
t2b = t2 + t1
assert str(t2b) == '2*A(b, L_0)*B(a, -L_0) + A(a, L_0)*A(b, -L_0)'
p, q, r = tensorhead('p,q,r', [Lorentz], [[1]])
t = q(d0)*2
assert str(t) == '2*q(d0)'
t = 2*q(d0)
assert str(t) == '2*q(d0)'
t1 = p(d0) + 2*q(d0)
assert str(t1) == '2*q(d0) + p(d0)'
t2 = p(-d0) + 2*q(-d0)
assert str(t2) == '2*q(-d0) + p(-d0)'
t1 = p(d0)
t3 = t1*t2
assert str(t3) == '2*p(L_0)*q(-L_0) + p(L_0)*p(-L_0)'
t3 = t2*t1
assert str(t3) == '2*p(L_0)*q(-L_0) + p(L_0)*p(-L_0)'
t1 = p(d0) + 2*q(d0)
t3 = t1*t2
assert str(t3) == '4*p(L_0)*q(-L_0) + 4*q(L_0)*q(-L_0) + p(L_0)*p(-L_0)'
t1 = p(d0) - 2*q(d0)
assert str(t1) == '-2*q(d0) + p(d0)'
t2 = p(-d0) + 2*q(-d0)
t3 = t1*t2
assert t3 == p(d0)*p(-d0) - 4*q(d0)*q(-d0)
t = p(i)*p(j)*(p(k) + q(k)) + p(i)*(p(j) + q(j))*(p(k) - 3*q(k))
assert t == 2*p(i)*p(j)*p(k) - 2*p(i)*p(j)*q(k) + p(i)*p(k)*q(j) - 3*p(i)*q(j)*q(k)
t1 = (p(i) + q(i) + 2*r(i))*(p(j) - q(j))
t2 = (p(j) + q(j) + 2*r(j))*(p(i) - q(i))
t = t1 + t2
assert t == 2*p(i)*p(j) + 2*p(i)*r(j) + 2*p(j)*r(i) - 2*q(i)*q(j) - 2*q(i)*r(j) - 2*q(j)*r(i)
t = p(i)*q(j)/2
assert 2*t == p(i)*q(j)
t = (p(i) + q(i))/2
assert 2*t == p(i) + q(i)
t = S.One - p(i)*p(-i)
assert (t + p(-j)*p(j)).equals(1)
t = S.One + p(i)*p(-i)
assert (t - p(-j)*p(j)).equals(1)
t = A(a, b) + B(a, b)
assert t.rank == 2
t1 = t - A(a, b) - B(a, b)
assert t1 == 0
t = 1 - (A(a, -a) + B(a, -a))
t1 = 1 + (A(a, -a) + B(a, -a))
assert (t + t1).equals(2)
t2 = 1 + A(a, -a)
assert t1 != t2
assert t2 != TensMul.from_data(0, [], [], [])
t = p(i) + q(i)
raises(ValueError, lambda: t(i, j))
def _trace_single_line1(t):
t = t.sorted_components()
components = t.components
ncomps = len(components)
g = self.LorentzIndex.metric
sg = DiracSpinorIndex.delta
# gamma matirices are in a[i:j]
hit = 0
for i in range(ncomps):
if isinstance(components[i], GammaMatrixHead):
hit = 1
break
for j in range(i + hit, ncomps):
if not isinstance(components[j], GammaMatrixHead):
break
else:
j = ncomps
numG = j - i
if numG == 0:
spinor_free = [_[0] for _ in t._tids.free if _[0].tensortype is DiracSpinorIndex]
tcoeff = t.coeff
if spinor_free == [DiracSpinorIndex.auto_left, -DiracSpinorIndex.auto_right]:
t = t*DiracSpinorIndex.delta(-DiracSpinorIndex.auto_left, DiracSpinorIndex.auto_right)
t = t.contract_metric(sg)
return t/tcoeff if tcoeff else t
else:
return t/tcoeff if tcoeff else t
if numG % 2 == 1:
return TensMul.from_data(S.Zero, [], [], [])
elif numG > 4:
t = t.substitute_indices((-DiracSpinorIndex.auto_right, -DiracSpinorIndex.auto_index), (DiracSpinorIndex.auto_left, DiracSpinorIndex.auto_index))
a = t.split()
ind1, lind1, rind1 = a[i].args[-1]
ind2, lind2, rind2 = a[i + 1].args[-1]
aa = a[:i] + a[i + 2:]
t1 = tensor_mul(*aa)*g(ind1, ind2)*sg(lind1, rind1)*sg(lind2, rind2)
t1 = t1.contract_metric(g)
t1 = t1.contract_metric(sg)
args = [t1]
sign = 1
for k in range(i + 2, j):
sign = -sign
ind2, lind2, rind2 = a[k].args[-1]
aa = a[:i] + a[i + 1:k] + a[k + 1:]
t2 = sign*tensor_mul(*aa)*g(ind1, ind2)*sg(lind1, rind1)*sg(lind2, rind2)
t2 = t2.contract_metric(g)
t2 = t2.contract_metric(sg)
t2 = GammaMatrixHead.simplify_gpgp(t2, False)
args.append(t2)
t3 = TensAdd(*args)
#aa = _tensorlist_contract_metric(aa, g(ind1, ind2))
#t3 = t3.canon_bp()
t3 = self._trace_single_line(t3)
return t3
else:
a = t.split()
if len(t.components) == 1:
if t.components[0] is DiracSpinorIndex.delta:
return 4 # FIXME only for D=4
t1 = self._gamma_trace1(*a[i:j])
a2 = a[:i] + a[j:]
t2 = tensor_mul(*a2)
t3 = t1*t2
if not t3:
return t3
t3 = t3.contract_metric(g)
return t3
def test_add1():
assert TensAdd() == 0
# simple example of algebraic expression
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
a, b, d0, d1, i, j, k = tensor_indices('a,b,d0,d1,i,j,k', Lorentz)
# A, B symmetric
A, B = tensorhead('A,B', [Lorentz] * 2, [[1] * 2])
t1 = A(b, -d0) * B(d0, a)
assert TensAdd(t1).equals(t1)
t2a = B(d0, a) + A(d0, a)
t2 = A(b, -d0) * t2a
assert str(t2) == 'A(a, L_0)*A(b, -L_0) + A(b, L_0)*B(a, -L_0)'
t2b = t2 + t1
assert str(t2b) == '2*A(b, L_0)*B(a, -L_0) + A(a, L_0)*A(b, -L_0)'
p, q, r = tensorhead('p,q,r', [Lorentz], [[1]])
t = q(d0) * 2
assert str(t) == '2*q(d0)'
t = 2 * q(d0)
assert str(t) == '2*q(d0)'
t1 = p(d0) + 2 * q(d0)
assert str(t1) == '2*q(d0) + p(d0)'
t2 = p(-d0) + 2 * q(-d0)
assert str(t2) == '2*q(-d0) + p(-d0)'
t1 = p(d0)
t3 = t1 * t2
assert str(t3) == '2*p(L_0)*q(-L_0) + p(L_0)*p(-L_0)'
t3 = t2 * t1
assert str(t3) == '2*p(L_0)*q(-L_0) + p(L_0)*p(-L_0)'
t1 = p(d0) + 2 * q(d0)
t3 = t1 * t2
assert str(t3) == '4*p(L_0)*q(-L_0) + 4*q(L_0)*q(-L_0) + p(L_0)*p(-L_0)'
t1 = p(d0) - 2 * q(d0)
assert str(t1) == '-2*q(d0) + p(d0)'
t2 = p(-d0) + 2 * q(-d0)
t3 = t1 * t2
assert t3 == p(d0) * p(-d0) - 4 * q(d0) * q(-d0)
t = p(i) * p(j) * (p(k) + q(k)) + p(i) * (p(j) + q(j)) * (p(k) - 3 * q(k))
assert t == 2 * p(i) * p(j) * p(k) - 2 * p(i) * p(j) * q(k) + p(i) * p(
k) * q(j) - 3 * p(i) * q(j) * q(k)
t1 = (p(i) + q(i) + 2 * r(i)) * (p(j) - q(j))
t2 = (p(j) + q(j) + 2 * r(j)) * (p(i) - q(i))
t = t1 + t2
assert t == 2 * p(i) * p(j) + 2 * p(i) * r(j) + 2 * p(j) * r(i) - 2 * q(
i) * q(j) - 2 * q(i) * r(j) - 2 * q(j) * r(i)
t = p(i) * q(j) / 2
assert 2 * t == p(i) * q(j)
t = (p(i) + q(i)) / 2
assert 2 * t == p(i) + q(i)
t = S.One - p(i) * p(-i)
assert (t + p(-j) * p(j)).equals(1)
t = S.One + p(i) * p(-i)
assert (t - p(-j) * p(j)).equals(1)
t = A(a, b) + B(a, b)
assert t.rank == 2
t1 = t - A(a, b) - B(a, b)
assert t1 == 0
t = 1 - (A(a, -a) + B(a, -a))
t1 = 1 + (A(a, -a) + B(a, -a))
assert (t + t1).equals(2)
t2 = 1 + A(a, -a)
assert t1 != t2
assert t2 != TensMul.from_data(0, [], [], [])
t = p(i) + q(i)
raises(ValueError, lambda: t(i, j))
