About NonCommutativeMultiply
- To: mathgroup at yoda.physics.unc.edu
- Subject: About NonCommutativeMultiply
- From: <flaminio at math.ufl.edu>
- Date: Fri, 31 Jan 92 14:23:54 EST
In an attempt to define a non commutative algebra over the complex by
using NonCommutativeMultiply I defined
Unprotect[NonCommutativeMultiply]
NonCommutativeMultiply[ a_ + b_ ,c_ ]:=
NonCommutativeMultiply[ a ,c] +
NonCommutativeMultiply[ b ,c]
NonCommutativeMultiply[ a_ , b_ + c_]:=
NonCommutativeMultiply[ a ,b] +
NonCommutativeMultiply[ a ,c]
NonCommutativeMultiply[ Times[a_ ,b_] , Times[d_ ,c_]]:=
Times[Times[a, d] ,NonCommutativeMultiply[ b , c]] /; NumberQ[a] &&
NumberQ[d]
But this does not produces the semplifications I wanted. For example
setting:
brac[a_, b_]:= a**b - b**a
mplus= (x - I y) /2
mminus= (x+ I y)/2
brac[mplus, mminus]
produces the following output
x ** x + x ** (I y) + (-I y) ** x + y ** y
------------------------------------------
4
where the semplifications x ** (I y) = I x ** y and (-I y) ** x = -I
y ** x have not been carried out. Any clue of why that is the case?
By the way the (mathematically) equivalent definition
mplus= x/2 - I y/2
mminus= x/2 + I y/2
do produce all the sempligfication I wanted.
livio flaminio