An analogous technique for simplifying trigonometric expressions is to
convert them all to complex exponentials and then treat them as rational
functions in
y=exp(ix) where x is appropriately chosen to be the least common
multiple of all imaginary exponents.
Then rationally simplify the result, which is a ratio of polynomials in y.
This replaces all the "rules" you know about half angles etc with a
uniform procedure.
I do not know if there is some canonical transformation for the
expressions of interest here, but if there is one,
consider using it.
RJF
Leo Butler wrote:
> On Sun, 7 Mar 2010, Richard Fateman wrote:
>
> < I haven't been following this thread in any detail, but the programming of
> < bra/ket simplification has been,
> < I think, a fairly common topic. I think I even wrote some programs to do this
> < with Bruce Char over 30 years ago.
> <
> < In any case, my thought now is that local transformation rules is NOT the way
> < to do this, except
> < as a last resort. Instead, is there a canonical representation that all these
> < expressions can
> < be forced into? One which will necessarily be simplified (with respect to
> < that canonical form)?
>
> Richard, I'm intrigued. Could you elaborate on this?
> In particular, I am not familiar with techniques to
> force the expressions into a canonical form other than
> via simplification rules. Of course,
> with most Lie algebras, like the Heisenberg algebra,
> there is a prefered (if not canonical) representation.
>
> Leo
>
>