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MathGroup Archive 2001

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Re: Re: Overriding Power


Jeff Hersh wrote:
> 
> I am implementing a package to do Geometric (Clifford) Algebra in an
> arbitrary dimensional space with an arbitrary signature. GA is composed
> of objects called blades, i.e. a scalar is a 0-blade, a vector is a
> 1-blade, etc. A sum of different blades is called a Multivector. The
> trick is that some objects commute with each other, others anti-commute
> and other do neither. My reasoning behind changing Times both aesthetic
> and for ease of input (since normal commutative multiplication only
> exists for scalars).
> 
> I have almost got the core of the package finished except for
> implementing a multivector to a power (including negative ones since GA
> makes division by blades and multivectors possible).
> 
> (As for other Mathematica functions, I am planning to implement my own
> versions of Expand, etc. via.
> 
> Expand[a_?MultivectorQ] := MyExpand[a]
> etc.)
> 
> Jeff
> 
> In article <94r5j3$iba at smc.vnet.net>, "Carl K. Woll"
> <carlw at u.washington.edu> wrote:
> 
> > Jeff,
> >
> > I don't think it's a good idea to remove the Orderless attribute from
> > Times.
> > Instead, use the operator NonCommutativeMultiply (**), or one of the many
> > other operators Mathematica supplies which have no builtin meaning. If
> > you
> > want to provide some more details on your package, perhaps somebody will
> > be
> > able to give you some more explicit advice.
> >
> > Carl Woll
> > Physics Dept
> > U of Washington
> >
> > ----- Original Message -----
> > From: "Jeff Hersh" <frumple*NOSPAM* at home.com>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> > Subject: [mg26980] [mg26902] [mg26808] Overriding Power
> >
> >
> > > Hello,
> > >
> > > I am working on a package that deals with non-communative
> > > multiplication
> > > and I have run into a problem with the Power function. As we know
> > > Power[a b,n] (where n is an integer) automatically gets converted to
> > > Power[a,n] Power[b,n]. However, with non-communative multiplication (I
> > > have removed the Orderless attribute from Times to make it
> > > non-communative) this isn't valid. Is there any way I can stop
> > > Mathematica from automatically doing this conversion?
> > >
> > > Jeff
> > > --
> > > Jeffrey Hersh,PhD
> > >
> > > Remove the *NOSPAM* to reply.
> > >
> > > <insert amusing quote here>
> > >
> >
> >
> --
> Jeffrey Hersh,PhD
> 
> Remove the *NOSPAM* to reply.
> 
> <insert amusing quote here>

Some ideas for handling noncommuting objects may be found in

http://library.wolfram.com/conferences/conference98/abstracts/symbolic_FAQ.html

in the noncommutative algebra section. Also there have been numerous
MathGroup threads related to this sort of issue. If you go to

http://library.wolfram.com/mathgroup/

and search the archives for NonCommutativeMultiply you will see numerous
messages, some of which may be of use for your particular needs.


Daniel Lichtblau
Wolfram Research


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