Dear Wolfgang,
Many thanks for both of your comments below. In fact, to be
sincere, I have never used the DECLARE command so far.
Therefore, your suggestion is very welcome. On the other
hand, I can reasonably assume that one could also denote
a symbol a or b in Mathematica to be real (instead of being
complex in general) and make Mathematica behave like
Maxima instead of making Maxima behave like Mathematica.
In any case, for me, as a simple user of computer algebra
systems, I prefer Maxima's assumption that a and b are
real numbers when using REALPART and IMAGPART
on a+i*b. (This is also my students' preference I believe.)
The conclusion for me is that Maxima offers various switches
and declarations one should be aware of, but this requires
study, experimentation and, if possible, consulting the source
files too. (This I have tried to do with the ODEAUX.MAC
file, but I failed! I must work further and have patience.)
I am grateful to you for both of your so interesting comments,
which will permit me a more careful use of Maxima.
Many thanks and best regards from Patras,
Nikos
----- Original Message -----
From: "Wolfgang Jenkner" <wjenkner at inode>
To: "Nikolaos I. Ioakimidis" <ioakimidis@otenet.gr>
Cc: "Maxima List" <maxima@www.ma.utexas.edu>
Sent: Friday, February 07, 2003 4:25 PM
Subject: Re: [Maxima] Simplification question
> "Nikolaos I. Ioakimidis" <ioakimidis@otenet.gr> writes:
>
> > I can also add that Maxima assumed in the commands realpart and
> > imagpart that the quantities a and b in a+%i*b are real (not
> > positive now). Example below: results a and b, respectively.
> >
> >
> > (C9) [realpart(a+%i*b), imagpart(a+%i*b)];
> > (D9) [a,b]
>
> Dear Prof. Ioakimidis,
>
> you are certainly aware of this, but lest the casual user be confused
> about Maxima's capability of doing elementary mathematics let me add
> that there are various switches and declarations for this kind of
> calculations. For example
>
> (C1) declare([a,b],complex);
> (D1) DONE
> (C2) [realpart(a+%i*b), imagpart(a+%i*b)];
> (D2) [REALPART(a) - IMAGPART(b), REALPART(b) + IMAGPART(a)]
> (C3)
>
>
> > Mathematica is more formal, Maxima more human (with more
> > assumptions, some of them made implicitly and not known to
> > the user).
>
> Unfortunately, it's not always straightforward to figure out the
> right incantation without experimenting or looking at the sources.
>
> Wolfgang