complex conjugation

[chrisd at sci.kun.nl]

Hello,

On Sat, 22 Nov 2003, Richard B. Kreckel wrote:

> It would be helpful (for us and yourself, probably) to quickly whip up a
> list of what exactly you want to do with the conjugation.  On numeric
> types it's clear.  On polynomials, there wouldn't be much you can do,
> probably, because you cannot just stick assumptions on free symbols.

I would just assume that all symbols are real. If a user then wants
complex ones, he can have additionally a list looking like

{a==astar,astar==a,b==bstar,bstar==b}

and do something like

conjugate(x).subs(symbolconjs)

if he wants conjugation.

> On
> other functions without any free symbols involved, what would you expect?
> Would you expect a transformation like this one being performed by the
> evaluator?
>     conjugate(sin(2))  ->  sin(2)
> Oops!  Knowledge about sin() would be needed...

I would say that the default behaviour of functions should be
conjugate(f(arg)) --> f(conjugate(arg)). Then there should be a new
function option to specify a different behaviour for your particular
function. I was wondering a bit about what to do with the log. For that
function the default behaviour is okay, except for the real negative axis.
I would say that just bluntly using the default behaviour, ignoring
possible problems, would be best.

>
> >            but I do not know yet how to implement it.
>

Bye,
Chris Dams