Re: Re: Overriding Power

*To*: mathgroup at smc.vnet.net*Subject*: [mg26980] Re: [mg26902] Re: [mg26808] Overriding Power*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Tue, 30 Jan 2001 03:38:29 -0500 (EST)*References*: <200101240918.EAA03605@smc.vnet.net> <94r5j3$iba@smc.vnet.net> <200101270429.XAA21545@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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

**References**:**Overriding Power***From:*Jeff Hersh <frumple*NOSPAM*@home.com>

**Re: Overriding Power***From:*Jeff Hersh <frumple*NOSPAM*@home.com>