Yes, there are bugs lurking here with the wedge product. This _really_
shouldn't happen:
(%i7) ishow((o([i],[])*s([j],[]))~o([k],[]))$
(%t7) 0
(%i8) ishow((o([j],[])*s([i],[]))~o([k],[]))$
o (o s - s o )
j i k i k
(%t8) - ------------------
2
I added this to the bug tracker.
But there is another, more general issue also, namely that itensor is not
designed to work with numeric indices. For itensor, indices are abstract and
are used for algebraic bookkeeping. So your %i2 expression really does not
make much sense to itensor.
The point is that itensor treats a thing that looks like symbol(list,list)
as an indexed object (i.e., a tensor) and tries to apply the wedge product
rules, even if list,list happens to be [1],[]. In other words, itensor does
not know that s([1],[]) is a number, not a tensorial object. The function
definition workaround really works only because the function is evaluated
(and the tensor-looking object is replaced with a number) before itensor
kicks in.
On a related note, I've long been contemplating replacing '~' with '/\' as
the wedge product operator in itensor.
Viktor
-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Jaan Vajakas
Sent: Saturday, July 16, 2011 4:37 PM
To: maxima at math.utexas.edu
Subject: Wedge product
Hi,
I am new to Maxima so I apologize if the following question is trivial.
Why does the wedge product command in package itensor behave like this:
(%i2) ishow((o([j],[])*s([1],[]))~o([k],[]))$
(%t2) s o o
1 j k
I would expect the answer to be zero, not
s([1],[]))*o([j],[])*o([k],[]).
Anyway, at least if I assign components to s then the wedge product
works as I expect:
(%i3) s(l1,l2,[l3]):=kdelta(l1,[1])$
(%i4) ishow((o([j],[])*s([1],[]))~o([k],[]))$
(%t4) 0
Is the former behavior a bug or am I getting something wrong?
I am using Maxima 5.17.0.
Best regards,
Jaan Vajakas
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