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MathGroup Archive 2001

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Re: Overriding Power

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26902] Re: [mg26808] Overriding Power
  • From: Jeff Hersh <frumple*NOSPAM* at home.com>
  • Date: Fri, 26 Jan 2001 23:29:46 -0500 (EST)
  • References: <200101240918.EAA03605@smc.vnet.net> <94r5j3$iba@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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
> Subject: [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>


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