Thanks for the link to that interesting site. I have looked around a bit, having already read some of the pdf-documents at http://digitalcommons.usu.edu/dg_pres/. I will certainly bookmark the site.

It was in fact so(6) + so(6).

By the way, do you know whether there exists, as a proper document (manual, booklet,...), some overall introduction to the DifferentialGeometry package? The Maple help pages on the subject (as, by the way, the help pages on other big Maple packages, such as the Physics one) seem to me impenetrable, the information being far too scattered. Without your help above, I would have had a hard time figuring out how to proceed. To me, the ever increasing complexity of Maple should be accompanied by some manual or some book to help the user properly navigate.

@Torre: Fabulous! It works like a charm. Using your recipe in combination with combinat[permute](...) to run through permutations of the simple roots, the Cartan matrix corresponding to the expected Lie algebra is found.

@Markiyan Hirnyk: Good suggestion. Unfortunately, although at least somewhat informative, using it seems to show only that Decompose 'gets stuck' with its very first task: using Query to try to determine whether the Lie algebra is at all decomposable (which we know it is; it may quite possibly just be the Lie algebra of SO(6) x SO(6)).

@sun_oriented: I am happy to hear that.

@Markiyan Hirnyk: I see what you mean. Then it is certainly not easy, I think.

@ecterrab: Thanks for your quick response/action. There is a problem, though: I am using Maple 17, not 18, and I have no intention of updating (at least not yet).

@ecterrab: Thanks for that fix.

@ecterrab: Ok, that makes perfect sense. I did not attempt any download of the update to Maple 18, as I was thinking something along the lines you describe. I much appreciate your offer to have a look at a possible personal fix for me, thanks.

Hi Edgardo,

Perhaps I misunderstand you, but to me it seems that the Physics update version for Maple 17 (the second link available at Maple Physics: Research & Development) is the same as previously (version stamp still being 2014, March 19, 4:0 hours), the problem thus, of course, persisting.

PS: By the way, my sirname is Fredsted; but please use my first name, John.

@Preben Alsholm: I experience the problem also for older versions of the Physics package: I have just tested it for two update versions dating back from the beginning of January this year. But if I remove any update, i.e., if I revert to the Physics package as it was shipped with Maple 17.02 (version stamp: 2013, September 6, 0:45 hours), then, consistent with your findings, the problem disappears. Tada!

But that, however, is not really an option for me, because then, for instance, the problem posted in Grassmannians in the Physics package, and there corrected by Edgardo Cheb-Terrab with an update, will re-emerge. Further worse it becomes when one realizes that according to http://www.maplesoft.com/products/maple/features/physicsresearch.aspx the latest Physics update for Maple 17 is also the final one.

But not for you to worry, of course; I hope that Edgardo Cheb-Terrab will notice this thread and take appropiate action.

@ecterrab: Thanks for that feedback. I had not previously read the ?Conventions,Physics help page; that I have done now, although not in depth. It just strengthens my impression that the Physics environment is indeed a very powerful one; my respect for a job well done.

This conventions page is, I think, more valuable to me than are the example pages, although the latter are, of course, quite useful. For it provides me with some overall road map to the Physics package, thus having not to search more or less aimlessly among examples each time I have some problem I want to solve.

Having just glanced through the attached pdf-document, it is quite obvious to me that the tensor capabilities of the Physics package, among these the ones relevant for General Relativity, are very powerful. For instance, having to specify only the metric in order to obtain all relevant quantities, like the Christoffel symbols and the Riemann, Ricci, Einstein, and Weyl tensors, is very nice.

What I am missing, though, and that not only for the tensor part of the Physics package, but for the Physics package as a whole, is some manual where a road map to the ideas behind, the structure, etc., are laid out. For I find it difficult to penetrate the complexity of the Physics package, and perhaps others do as well. Does there exist such a manual, or are there any plans of producing any such?

@Joe Riel: Thanks for both the depends and unapply solutions. The latter is readily applicable in my setup, so I will use that.

...

Second thoughts, there being a problem with the unapply solution: The code (just an example)

A := Matrix([[2,3],[3,4]]):
ip := unapply(Transpose(psi1) . A . psi2,(psi1,psi2));
ip(Vector(2),Vector(2));

(for simplicity suppressing here the type-checking of psi1 and psi2, i.e., the original problem) raises "Error, (in LinearAlgebra:-Multiply) cannot multiply a column Vector and a Matrix". Why? Does the unapply somehow neutralize the action of Transpose, or what?

PS: As you perhaps can guess from the example, I want the function of mine to construct a certain inner product on grounds of properties of the module passed to it.

@Joe Riel: Thanks for the fix using subs.

It surprises me quite a bit to learn that to this somewhat innocently looking problem there is no both simple and pretty solution: the subs-trick is somewhat nasty looking, I agree; and the solution using objects (thanks for your efforts) is not simple, at least not to me (my skills are insufficient, I guess).

PS: My example was indeed intentionally simplified.