itensor - contracting antisymmetric and symmetric indices

In theory, Itensor should be able to do this:

(%i1) load(itensor)$
(%i2) decsym(A,2,0,[anti(all)],[]);
(%o2)                                done
(%i3) decsym(S,0,2,[],[sym(all)]);
(%o3)                                done
(%i4) ishow(A([i,j],[])*S([],[i,j]))$
                                    i j
(%t4)                              S    A
                                         i j
(%i5) canform(%);
(%o5)                                  0

Well, it doesn't, not yet anyway. It's on my rather longish to-do list. In
the meantime, here's an alternative that may be sometimes useful:

(%i1) load(itensor)$
(%i2) decsym(S,0,2,[],[sym(all)]);
(%o2)                                done
(%i3) components(A([i,j],[]),1/2*(aa([i,j],[])-aa([j,i],[])));
(%o3)                                done
(%i4) ishow('A([i,j],[])*S([],[i,j]))$
                                    i j
(%t4)                              S    A
                                         i j
(%i5) canform(ev(%,A));
(%o5)                                  0


Viktor


 

-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Michal Kowalski
Sent: Sunday, December 30, 2007 2:15 PM
To: maxima at math.utexas.edu
Subject: itensor - contracting antisymmetric and symmetric indices

It is well known that contracting two antisymmetric indices with two
symmetric
ones yields zero. Could itensor package recognize this property? I was
unable to
get any positive results... (Despite forcing some defcon rules for
particular
tensors, but I need to learn Maxima about this contraction law in general).

Thanks for help,
M.D.
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