       Re: representing the dihedral group {1,r,r^2...s,sr^2...}

• To: mathgroup at smc.vnet.net
• Subject: [mg98890] Re: [mg98796] representing the dihedral group {1,r,r^2...s,sr^2...}
• From: "David Park" <djmpark at comcast.net>
• Date: Mon, 20 Apr 2009 19:15:04 -0400 (EDT)
• References: <27278711.1240205625147.JavaMail.root@n11>

```Don't use Times to represent group multiplication, or modify Times and
Power.

Instead use something like SmallCircle.

SmallCircle[s, s^2]

You might leave that unevaluated, but then write an EvaluateGroupProducts
routine to evaluate the products from a group table or using an algorithm.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: obott0 at gmail.com [mailto:obott0 at gmail.com]

Hi, I'm trying to represent the dihedral group {1,r,r^2...s,sr^2...}
in mathematica so I can do for example:

s^3

and get s.

I tried this code:

Unprotect[Times, Power];
n = 4;
ClearAll[r, s, Times, Power];
SetAttributes[Times, {Flat}]
s^2 = 1;
r^n = 1;
Protect[Times, Power];

But this doesn't work for, for example, s^3. It is not able to
simplify it.

Thanks a lot!

Otto

```

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