Re: simplifying operator experessions with Dot, Times and Plus

*To*: mathgroup at smc.vnet.net*Subject*: [mg35519] Re: [mg35481] simplifying operator experessions with Dot, Times and Plus*From*: Andrzej Kozlowski <andrzej at yhc.att.ne.jp>*Date*: Wed, 17 Jul 2002 02:09:14 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

The reason why Dot won't work is that it is meant operate on explicit vectors, which in Mathematica means lists, like In[7]:= {a,b,c}.{x,y,z} Out[7]= a x+b y+c z and not on symbols that stand for vectors, as in your case. It would not be a good idea to try to modify Dot to behave differently in case you then tried using it on list and started getting strange results. A better approach is to define your own dot product: In[1]:= SetAttributes[dot, {Flat, OneIdentity}] In[2]:= dot[x_ + y_, w_] := dot[x, w] + dot[y, w]; dot[w_, x_ + y_] := dot[w, x] + dot[w, y]; dot[x_, 0] = 0; dot[0, x_] = 0; dot[(a_)?NumericQ*x_, y_] := a*dot[x, y]; dot[x_, (b_)?NumericQ*y_] = b*dot[x, y]; Next you can temporarily replace Dot by dot, for example: In[8]:= Block[{Dot = dot}, -ex[0, 1] . (ex[0, 1] . ex[1, 2] - ex[1, 2] . ex[0, 1])] /. dot -> Dot Out[8]= -ex[0, 1] . ex[0, 1] . ex[1, 2] + ex[0, 1] . ex[1, 2] . ex[0, 1] Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ On Tuesday, July 16, 2002, at 04:49 AM, JL wrote: > I am trying to expand a large expression that has terms that look as > follows: > > -ex[0,1].(ex[0,1].ex[1,2]-ex[1,2].ex[0,1]) > > where ex[i,j] are unevaluated expressions. I would like Mathematica to > simplify this and analogous expressions so that they read: > > ex[0,1].ex[1,2].ex[0,1]-ex[0,1].ex[0,1].ex[1,2] > > However, I cannot seem to find anything that will work. The problem is > that > I need to keep track of the order of the expressions ex[i,j]. If Dot > were > replaced by Times, there would be no problem whatsoever. > > If anyone knows how to help me with this problem, I would greatly > appreciate > it. > > Thanks, > > Jeremy Levy > jlevy at pitt.edu > > > > > > >