Subject: Simpliyfying the argument of a complex expression
From: Stavros Macrakis
Date: Wed, 19 Jan 2011 16:47:52 -0500
Well, the principal value of carg(exp(%i*x)) is actually not x, but
mod(x+%pi,2*%pi)-%pi.
I do wish sometimes we had a 'sloppy' mode (the opposite of pedantic
mode), which did things like atan(tan(x)) => x -- but of course you
have to be very careful with such things.
Ideally, assume(x>0,x<%pi/2) would allow atan2(sin(x),cos(x)) and
atan(sin(x)/cos(x)) to simplify to x, but unfortunately Maxima's
simplifier isn't smart enough to do that; it's not even smart enough
to know that with those assumptions, sin(x) > 0 and cos(x) > 0.
The best I can do is something like this:
expr: carg(expr(%i*x))$
assume(x>0,x<%pi/2)$
trigreduce( subst(lambda([a,b],atan(a/b)),atan2,expr) );
Maybe that helps?
-s
On Wed, Jan 19, 2011 at 04:21, Wilhelm Haager
<wilhelm.haager at htlstp.ac.at> wrote:
> Hi,
>
> Is there a possibility to cause Maxima simplyfying (or evaluating) an
> expression like
> "carg(exp(%i*x))" to "x" (and not just to "atan2(sin(x),cos(x))")?
>
> Thanks in advance,
> Wilhelm Haager
>
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