[Maxima] complex number arithmetic
macrakis at alum.mit.edu
Thu Apr 16 17:51:13 CDT 2009
On Thu, Apr 16, 2009 at 5:56 PM, Richard Fateman
<fateman at cs.berkeley.edu> wrote:
> You need to choose a principal value for multiple-valued roots.
Agreed, but this is orthogonal: Maxima already has conventions
(whether they are currently correct or not...) in rectform.
> Also try rectform((1+%i)^(1+%i)) for a fun time.
That is why I specified "whenever the result is correctly expressed in
numbers only", the simplest case of which is integral powers.
>> With large integer powers, maybe it's not clear what is best.
Well, we already expand large integer powers of rationals. Why is the
expanded form of (2/3+%i)^100 any worse than (2/3)^100? It's not even
rectform((%i+2/3)^100000) takes only 0.02 secs.
>> Computations such as
>>> a : (2/3 + %i)^(10^9 + 1);
>>> b : (2/3 + %i)^(10^9);
>>> a/b --> (long number) / (long number) --> 2/3 + %i
>>> are somewhat embarrassing.
Embarrassing in what way? That Maxima can't take advantage of the
shortcut? Does it matter? It is actually surprisingly fast for
By the way, I noticed that Maxima, trying to be helpful, writes
rectform((2+%i)^1001) using sin(1001*atan(...)), which messes up
subsequent arithmetic quite badly....
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