About data structure in Cadabra

Question

I wonder where I could find the complete description of Cadabra's data structure, this and this are a little simple, I need more details. More examples about how to program in Cadabra is also OK.

Comments

The latest fix by @cbehan is now in github master.

---

Ok, It works fine. Thanks.

---

Hi@cbehan@kasper, following code is still invalid

{\mu,\nu}::Indices(vector).
u^{\mu}::ImplicitIndex.
u^{\mu}::SelfNonCommuting.
tr{#}::Trace.
ex:=tr{u^{\mu} u^{\mu} u^{\nu} u^{\nu}}-tr{u^{\mu} u^{\nu} u^{\nu} u^{\mu}};
sort_product(_);

Version 2.2.9 (build 2310.4b47f18980 dated 2019-12-28), Linux

---

Ok. In this case, the letters are the same and the free indices are the same which means that a single sort order has not been determined yet. We will need to detect that this has happened and then put an ordering on the set of dummy index topologies.

In the above example, this means deciding whether we prefer {{1,2}, {3,4}} or {{1,4}, {2,3}}. More generally, we should expect to see all possible ways of breaking up {1, ..., 2n} into unordered pairs.

---

I knew this was coming... By far the easiest way to solve this is to piggyback on work Dom has been doing to make multi-term symmetries more manageable. @cbehan, I'll email you privately with details.

Answer 1

This is now handled cleanly by Dom's new meld algorithm, which is now on github. Instead of sort_product, just use meld(_). Documentation on this will be in a forthcoming paper.

Comments

Thanks. I have used this new algorithm for a while, but there are still some bugs in 'meld' algorithm, for example

{\mu,\nu}::Indices(vector).
V^{\mu\nu}::AntiSymmetric.
{{V^{\mu\nu},u^{\mu}}::NonCommuting.
u^{\mu}::SelfNonCommuting.
tr{#}::Trace.
ex:=tr{V^{\mu\nu}u^{\mu}u^{\nu}};
meld(_);

the result is zero, it's wrong.