On Saturday, January 11, 2014 9:35:52 PM UTC+1, Comer wrote:
>
>
> Now I am trying to create the Weyl tensor. Here is what I do and the
> response:
>
>
> W = tensorhead('W',[Lorentz]*4,[[2, 2]])
>
>
This definition is useless, it gets overridden later.
terma = tensor_mul(Rational(1,2)*g(-a,-c)*Ric(-d,-b))
> print terma.args
> terma = TensMul(*terma.args)
>
> termb = tensor_mul(Rational(1,2)*g(-a,-d)*Ric(-c,-b))
> print termb.args
> termb = TensMul(*termb.args)
>
> termc = tensor_mul(Rational(1,2)*g(-b,-c)*Ric(-d,-a))
> print termc.args
> termc = TensMul(*termc.args)
>
> termd = tensor_mul(Rational(1,2)*g(-b,-d)*Ric(-c,-a))
> print termd.args
> termd= TensMul(*termd.args)
>
> terme = tensor_mul(Rational(1,3)*R*g(-a,-c)*g(-d,-b))
> print terme.args
> terme = TensMul(*terme.args)
>
> termf = tensor_mul(Rational(1,3)*R*g(-a,-d)*g(-c,-b))
> print termf.args
> termf = TensMul(*termf.args)
>
W = Riem -terma + termb + termc - termd + terme -termf
>
>
You have to specify the indices in Riem. There are two objects here,
TensorHead and TensMul. TensorHead is a tensor without indices, TensMul is
a tensor with indices specified.
Riem is a TensorHead
Riem(-a, -b, -c, -d) is a TensMul
Of course you cannot add TensorHead and TensMul, furthermore if you add
TensMul they must have the same indices.ValueError: all tensors must have
the same indices.
So, I believe all terms have the same indices, just in different orders.
>
No, order does not count. It's just important that indices are the same.
Your *Riem* object has no indices at all.
> By construction the overall quantity should have the same symmetries in
> its 4 indices as the Riemann tensor. When I print the terms individually
> they all look as intended, but it chokes when I try to construct W using
> them. What am I doing wrong?
>
You're not putting the indices in Riem.
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