Re: Using the RM for ADTs
Date: Wed, 8 Jul 2009 23:33:46 -0700 (PDT)
Message-ID: <48a4205b-e46f-4cb7-8c9e-d2a923135c80_at_x5g2000prf.googlegroups.com>
On Jul 9, 10:11 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> > As an example, consider a circuit consisting of 12 x 1 ohm resistors
Well, obviously some things won't be indistinguishable anymore after
you "just pick" one. Picking one means distinguishing it from all
others.
Note that distinguishing one of the nodes is insufficient to break all
symmetry. Call it "top". This immediately distinguishes a node on
the opposite corner (call it "bottom"). However there remains 3-way
symmetry in the nodes adjacent to "top", and a further 2-way symmetry
from any one of these nodes to the next three adjacent nodes as we
proceed towards the bottom of this lattice structure.
In your case picking a component lead can be regarded as picking an
ordered pair of adjacent nodes. That still leaves a 2-way symmetry as
described above.
> "David BL" <davi..._at_iinet.net.au> wrote in message
> > and 8 nodes wired up in the manner of a 3-dimensional cube. All the
> > resistors are indistinguishable and all the nodes are
> > indistinguishable, even in the context of the circuit that they appear
> > in.
>
> They are not indistinguishable. Just pick an arbitrary component lead, and
> the rest can be described in terms of it because each has different paths to
> it.