Simple example showing differences between position=free, fixed and independent

Question

Hi Troops,

I'm trying to find a simple example that shows the differences between the free, fixed and independent index property. The best that I could come up with is

{a,b,c,d,e,f,g,h#}::Indices(position=free).

\Gamma^{a}_{b c}::TableauSymmetry(shape={2}, indices={1,2});

foo := v_{a} \Gamma^{a}_{b c} - v^{a} \Gamma_{a c b};
canonicalise (foo);

{a,b,c,d,e,f,g,h#}::Indices(position=fixed).

foo := v_{a} \Gamma^{a}_{b c} - v^{a} \Gamma_{a c b};
canonicalise (foo);

{a,b,c,d,e,f,g,h#}::Indices(position=independent).

foo := v_{a} \Gamma^{a}_{b c} - v^{a} \Gamma_{a c b};
canonicalise (foo);

But that strikes me as too involved. Can anybody suggest a simpler example?

Thanks, Leo

Answer 1

See the updated chapter 1.4 of the reference guide, https://cadabra.science/notebooks/ref_indices.html .

Comments

Hi Kasper, Many thanks for the clear explanation. It all makes sense to me now :). Cheers, Leo