[Maxima] matchdeclare and tellsimpafter

[Michel Talon]

Edwin Woollett wrote:

> I am looking at commutator algebra and want to
> pull out numbers and declared scalars from the
> commutator symbol comm(x,y).
> 
> Here I am only trying to pull out numerical factors.
> 
> (%i1) matchdeclare (aa, all,bb, all,cc, all,dd, all)$

Is this useful? Maybe it spoils your computation.


> 
> /* try just using the predicate numberp  */
> 
> (%i2) matchdeclare (mm, numberp)$
> 
> (%i3) tellsimpafter (comm (mm*aa, bb), mm*comm (aa, bb))$
> 
> (%i4) tellsimpafter (comm (aa, mm*bb), mm*comm (aa, bb))$
> 
> /* it works for first arg but not the second */
> 

Works for me this way:
niobe% maxima
(%i1) ? numberp
....
(%i2) matchdeclare (mm, numberp)$
(%i3) tellsimpafter (comm (mm*aa, bb), mm*comm (aa, bb))$

(%i4) tellsimpafter (comm (aa, mm*bb), mm*comm (aa, bb))$

(%i5) comm (2*a, b);
(%o5)                            comm(2 a, b)
(%i6) comm(2*aa,bb);
(%o6)                           2 comm(aa, bb)
(%i7) comm(aa,2*bb);
(%o7)                           2 comm(aa, bb)
(%i8) comm(aa/2,bb);
                                 comm(aa, bb)
(%o8)                            ------------
                                      2
(%i9) comm(aa,bb/2);
                                 comm(aa, bb)
(%o9)                            ------------
                                      2
(%i10) 

Of course you then need to use the Lie algebra commutators (like i did for 
the Poisson brackets and Jacobi identity) to transform any monomial in the 
enveloping algebra into ordered basis elements according to Poincaré 
Birkhoff Witt theorem. In principe this way you discover all identities 
stemming from the Lie algebra structure. Of course if you are in a concrete 
representation there are more identities to implement such as sigma^2=1
for the Pauli matrices.




-- 
Michel Talon