It is a bug because %e^(1.0*%i*%pi) and %e^(2.0*%i*%pi) are unsimplified,
and all output from all Maxima commands should be simplified (that is,
should have the *default* simplifications performed). See below. Not that
I'm particularly happy with %o8 and %o10, either....
-s
Compare:
(%i7) %e^(1.0*%i*%pi);
(%o7) - 1.0
(%i8) %e^(1.0*%i*%pi),numer;
(%o8) 1.2246063538223773E-16 %i - 1.0
(%i9) %e^(2.0*%i*%pi);
(%o9) 1.0
(%i10) %e^(2.0*%i*%pi),numer;
(%o10) 1.0 - 2.4492127076447545E-16 %i
On Mon, May 9, 2011 at 12:00, <mxue at vroomlab.com> wrote:
>
> Perhaps this should not be considered as a bug since:
>
> %e^(%i*%pi) = -1
>
> Michael
>
> -------------------------------------------------------------------------------------
>
> Quote:
>
> Message: 4
> Date: Mon, 2 May 2011 12:15:35 -0400
> From: Stavros Macrakis <macrakis at alum.mit.edu>
> To: Renzo Del Fabbro <renzodelfabbro at alice.it>
> Cc: maxima <maxima at math.utexas.edu>
> Subject: Re: [Maxima] Simplify exponential expression
> Message-ID: <BANLkTik+12Zn+F+_vigaAtbPcn3XZ2b_7A at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Probably. ev is a funny command (not a function, really, because it
> controls the evaluation of its arguments), and can have surprising effects.
>
> In general, xxx:abc$ ev(xxx,def); is NOT equivalent to ev(abc,def).
>
> For example, ev(factor(6)) => 2*3, but factor(6)$ev(%) => 6
>
> Even worse:
>
> solve(x^2=2,x)$ %,numer;
> [x = -1.414213562373095,x = 1.414213562373095]
>
> ev(solve(x^2=2,x),numer);
> [x = 1.414213551646055*%e^(1.0*%i*%pi),x =
> 1.414213551646055*%e^(2.0*%i*%pi)]
>
> This is a bug, but it does show that ev(...) is not equivalent to
> ...$ev(%);
>
> -s
>
>
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>