Re: nested * and ** (rules for commutative quantities)

*To*: mathgroup at smc.vnet.net*Subject*: [mg7797] Re: [mg7658] nested * and ** (rules for commutative quantities)*From*: "C. Woll" <carlw at u.washington.edu>*Date*: Tue, 8 Jul 1997 22:41:10 -0400*Sender*: owner-wri-mathgroup at wolfram.com

On Tue, 8 Jul 1997, Marlies Brinksma wrote: > Dear Carl, > > ... > > > > Times[4, Op[1,t],NonCommutativeMultiply[Op[2,v],Op[2,x]],Op[3,a],Op[6,s]] > > > ^ > > > ... | > > I think you've missed one ] right behind Op[2,x]... ;) > > ... > Hi Marlies, You're absolutely right. So, instead, how about the following approach. Unprotect[NonCommutativeMultiply]; Clear[NonCommutativeMultiply]; Default[NonCommutativeMultiply]:=1; Op[n_,a_] ** Op[m_,b_] := Op[m,b] Op[n,a] /; (n=!=m) a_ ** b_?NumberQ := a b b_?NumberQ ** a_ := a b Op[n_,a_] ** (Op[n_,b_]**c_. d_) := Op[n,a]**Op[n,b]**c d (Op[n_,b_]**c_. d_) ** Op[n_,a_] := Op[n,b]**c**Op[n,a] d (Op[n_,a_]**c_. d_) ** (Op[n_,b_]**e_. f_) := (Op[n,a]**c**Op[n,b]**e d)**f a_Times ** b_ := a b b_ ** a_Times := a b Protect[NonCommutativeMultiply]; Some comments about the above definitions. a) The method works as follows: 1) First, absorb commuting quantities under a Times[ ] head. 2) Then, in adjacent expressions, collect Ops with the same index. 3) When there are no more Ops with the same index, then its okay to absorb adjacent expressions under a common Times[ ] head. b) You can choose as a default 1 (as above) or Sequence[]. The choice 1 is clearer, but the choice Sequence[] is marginally faster. c) You can avoid using defaults by adding some more definitions, e.g., Op[n_,a_] ** (Op[n_,b_] d_) := Op[n,a]**Op[n,b] d Op[n_,a_] ** (Op[n_,b_]**c_ d_) := Op[n,a]**Op[n,b]**c d d) If you have commuting quantities which are more complex than numbers, change the NumberQ test appropriately. e) The order of definitions is important. f) There is something I don't understand about the way mma is handling the first 3 definitions which causes it to exercise these definitions much more often then necessary. It may have something to do with using a default, which is why I suggested how you could avoid using a default. I believe this accomplishes what you asked for. Good luck! Carl Woll