Kronecker delta behavior

[rjrosati]

At the moment, the upstream contract_metric will transform KD(-i,-j) metric(j,k) into KD(-i,k).
This isn't what the Kronecker delta means to me (i.e. always the identity matrix). Is this actually standard somewhere?

Okay, even avoiding this issue, any expression with Kronecker deltas, after enough manipulation, will be a mess of several deltas contracted with each other. canon_bp and contract_metric don't seem to simplify this at all. Should we have a new function, contract_delta or equivalent that reduces these expressions?

For example, here is the Ricci scalar I calculated from the metric 6*α*delta(-i,-j) / (1-F(i)*F(j)*delta(-i,-j))^2:

(-24)*α*(-1)*(ts1 - 1)**(-3)*KD(f_0, -f_0)*KD(f_1, -f_1) + 24*α*(-1)*(ts1 - 1)**(-3)*KD(f_0, f_1)*KD(-f_0, -f_1) + (-864)*α**2*(ts1 - 1)**(-6)*F(f_0)*F(f_1)*KD(-f_0, f_2)*KD(-f_1, f_3)*KD(-f_2, f_4)*KD(-f_3, -f_4) + (-144)*α*(ts1 - 1)**2*1/(ts1**6 - 6*ts1**5 + 15*ts1**4 - 20*ts1**3 + 15*ts1**2 - 6*ts1 + 1)*F(f_0)*F(f_1)*KD(-f_0, f_2)*KD(-f_1, -f_2)*KD(f_3, -f_3) + (-144)*α**2*(ts1 - 1)**(-6)*F(f_0)*F(f_1)*KD(-f_0, f_2)*KD(-f_1, -f_2)*KD(f_3, -f_3)*KD(f_4, -f_4) + 144*α*(ts1 - 1)**2*1/(ts1**6 - 6*ts1**5 + 15*ts1**4 - 20*ts1**3 + 15*ts1**2 - 6*ts1 + 1)*F(f_0)*F(f_1)*KD(-f_0, f_2)*KD(-f_1, f_3)*KD(-f_2, -f_3) + 432*α**2*(ts1 - 1)**(-6)*F(f_0)*F(f_1)*KD(-f_0, f_2)*KD(-f_1, -f_2)*KD(f_3, f_4)*KD(-f_3, -f_4) + 576*α**2*(ts1 - 1)**(-6)*F(f_0)*F(f_1)*KD(-f_0, f_2)*KD(-f_1, f_3)*KD(-f_2, -f_3)*KD(f_4, -f_4))

The correct answer should only depend on α and the TensorIndexType dimension.