problem with canonicalise?

Question

Hi,

I have the following code:

{M,N,P}::Indices(position=free);
{M,N,P}::Integer(1..D);
\partial{#}::Derivative;
d::Depends(\partial{#});
\eta^{M N}::Metric;
\eta_{M N}::InverseMetric;
exp:= A^{F} (\eta^{M N})*(1/(D-1))*\partial_{F}{d} + A^{F} (\eta^{N M})*(1/(D-1))*\partial_{F}{d};
canonicalise(_);
collect_terms(_);

By using "canonicalise" I was expecting Cadabra to recognize that the second term is equal to the first one, but it just returns the same expression. I think the problem is the (D-1) factor in the denominator, somehow spoils the canonicalise command and the symmetric property of the metric. Any suggestion how could this be solved?

thank you,

Victor

Answer 1

Ah, interesting one ;-) The reason why this fails is that canonicalise is made to not do anything with products which contain sums as factors; it only canonicalises pure monomials. Normally that doesn't cause any trouble.

Unfortunately, I messed up this check, making it search the expression tree arbitrarily deep. As a result, the check mentioned above flags the 1/(D-1) as containing a sum D-1, and canonicalise refuses to touch your expression. You can see this because the \eta^{N M} does not get its indices sorted.

I'll need to fix this properly, but as a workaround, use e.g. 1/Dm1 for 1/(D-1) and then replace Dm1 later.

Comments

ok! thank you for the answer!!! bye!