Dear Colleagues,
Here (below) my computations with Maxima 5.9.0 rc4 on
Dan's question, already replied by Barton, are displayed.
Comparing (D7) and (D8), I cannot say I am satisfied with the
behaviour of Maxima with a distiction between the number 3/8
and the symbol b (instead of l2, letter l and 2, not 12) having been
used by Dan (abs(u) in the first case, with 3/8, u in the second
case, with b. Why?).
Because of the discussion on the assumption by Maxima in this case
that u is positive real (Professor Fateman's comments below), 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.
Mathematica makes no such assumptions and does not simplify
(u^b)^(1/b) neither (u^12)^(1/12) (l2 is twelve) (with Simplify
I mean, but Maxima'a ratsimp does nothing again, only radcan
works). Moreover, the real and imaginary part of a+I*b in
Mathematica are Re[a]-Im[b] and Im[a]+Re[b] as I have
verified (no assumption that a and b are real.) In this way of
thinking with complex numbers, I and my students are happy
with Maxima and not Mathematica.
Mathematica is more formal, Maxima more human (with more
assumptions, some of them made implicitly and not known to
the user).
Yet, in my opinion, the difference in (D7) and (D8) below seems
not to be natural for the user and I could call it a bug in my way
of thinking, since it causes confusion to the non-expert user of
Maxima in spite of Professor's Fateman comments below, which
I understand and respect.
Best regards from Patras,
Nikos
(C1) display2d : false;
(D1) FALSE
(C2) (u^12)^(1/12); (# 12 is twelve #)
(D2) ABS(u)
(C3) (u^(8/3))^(3/8);
(D3) ABS(u)
(C4) (u^b)^(1/b);
(D4) (u^b)^(1/b)
(C5) ratsimp((u^b)^(1/b));
(D5) (u^b)^(1/b)
(C6) radcan((u^12)^(1/12)); (# 12 is twelve #)
(D6) ABS(u) (# u has not been assumed positive real #)
(C7) radcan((u^(8/3))^(3/8));
(D7) ABS(u) (# u has not been assumed positive real #)
(C8) radcan((u^b)^(1/b));
(D8) u (# now u has been assumed positive real #)
(C9) [realpart(a+%i*b), imagpart(a+%i*b)];
(D9) [a,b]
(C10) build_info();
Maxima version: 5.9.0.rc4
Maxima build date: 12:4 1/30/2003
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL-2-5.0
----- Original Message -----
From: "Richard Fateman" <fateman at cs>
To: "Raymond Toy" <toy@rtp.ericsson.se>
Cc: <willisb@unk.edu>; <dan.stanger@ieee.org>; <maxima@mail.ma.utexas.edu>
Sent: Thursday, February 06, 2003 9:38 PM
Subject: Re: [Maxima] Simplification question
> In the absence of other instructions, radcan tries to impose
> a consistent "positive real" interpretation on radicals. The
> alternative of providing all 12 roots of the expression is
> painful; the choice of |u|, a non-algebraic quantity,
> is controversial. There is no answer that makes everyone
> happy, historically speaking.
>
> RJF
>
>
> Raymond Toy wrote:
> >>>>>>"willisb" == willisb <willisb@unk.edu> writes:
> >>>>>
> >
> > willisb> Yes.
> > willisb> (C1) (u^l2)^(1/l2);
> > willisb> (D1) (u^l2)^(1/l2)
> > willisb> (C2) radcan(%);
> > willisb> (D2) u
> >
> > Shoudn't this be abs(u), as mentioned in a different mail?
> >
> > Or at least the documentation for radcan should mention something
> > about it assuming positive numbers for this.
> >
> > Ray