I view the jacobi identity as a way to re-express
a particular simplification. If different
simplification schemes reduce the starting
expression down to series to the
general form:
expr1 = a1*comm(a,b)+a2*comm(b,c) +....
expr2 = b1*comm(a,b) + b2*comm(b,c) + ....
then, if one asks whether the
results are equivalent, one should make use somehow
of the jacobi identity to try to work expr1 into
expr2, and if one cannot, then the results of the
simplification are not consisten.
ted
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----- Original Message -----
From: Barton Willis
To: Edwin Woollett
Cc: maxima mailing list
Sent: Sunday, November 21, 2010 7:54 AM
Subject: Re: [Maxima] matchdeclare and tellsimpafter
Ted,
Consider the expression comm(a,b).c - c.comm(a,b) + b . comm(a,c) -
comm(a,c).b + comm(b,c).a - a . comm(b,c).
The Jacobi identity tells us that this expression vanishes, but I don't
think your simplification rules crunch
it to zero:
(%i32) comm(a,b).c - c.comm(a,b) + b . comm(a,c) - comm(a,c).b +
comm(b,c).a - a . comm(b,c)$
(%i33) expand(subst('comm = lambda([a,b],a.b - b.a),%));
(%o33) 0
--Barton
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