tensor product does not transform correctly with the metric

[danielmaitre]

a tensor product of two vectors does not behave in the same way as a tensor defined with the same indices. I would expect the two lines printed by this snippet to be the same, but there is a sign difference.

from sympy.tensor.tensor import TensorIndexType, tensorhead, tensor_indices

undotted = TensorIndexType('undotted', dummy_fmt='a',metric=True)
undotted.data=[[0,1],[-1,0]]
dotted = TensorIndexType('dotted', dummy_fmt='ad',metric=True)
dotted.data=[[0,1],[-1,0]]

a0 = tensor_indices('a0', undotted)
ad0 = tensor_indices('ad0', dotted)

S = tensorhead('S', [dotted, undotted], [[1],[1]])
l= tensorhead('l', [ undotted],[[1]],comm=2)
lt= tensorhead('lt', [ dotted],[[1]],comm=2)

l(a0).data=[1,10]
lt(ad0).data=[2,3]

ltl=lt(ad0)*l(a0)

S(ad0,a0).data = ltl(ad0,a0).data

S(ad0,a0).data

print S(-ad0,-a0).data

print ltl(-ad0,-a0).data