From dik@cwi.nl Mon Dec 27 18:43:04 1993
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Date: Tue, 28 Dec 93 00:43:02 +0100
From: Dik.Winter@cwi.nl
Message-Id: <9312272343.AA25571.dik@boring.cwi.nl>
To: Cube-Lovers@life.ai.mit.edu
Subject: Re: Group theory basics (Re: Symmetry)
One additional remark:
> > Well, if P is a rotation operator, you could perform a rotation
> > two ways. I guess one is pre-multiplication and one is
> > post-multiplication.
> > 1) For i = 1 to 24 B(i) = A(P(i))
> I would write this as B = P A, and say that A is premultiplied by P,
> or equivalently that P is postmultiplied by A.
There is quite a bit of confusion about this. When permutation
groups are considered; even text-books do not agree. When A and P
are permutations you can find both that P A means: apply P first, A next,
but also: apply A first, P next. (The first meaning comes from the pure
group theorists, the second meaning more from the algebra inclined.)
Sorry to confuse the issue, but when I read such texts I have always to
think hard to get at the intended meaning. I think the functional
notation is much clearer and leads to less confusion.
Of course, doing notations for cube rotations the group theorists
notation is applied, but when doing abstract operations...