[Maxima] complex expressions
hbaker1 at pipeline.com
Wed Jun 6 12:46:24 CDT 2012
Look at the left hand side of %o3 below: we took the _absolute value_ of a complex number, which should be _real_, and then squared it, which should be non-negative, and got a complex number.
That's pretty broken in my book.
At 10:20 AM 6/6/2012, Stavros Macrakis wrote:
>If I understand your issue correctly, it has nothing to do with realpart/imagpart "not working" -- it has to do with Maxima's noun/verb scheme.
>Expand doesn't convert nouns like 'realpart to their verb form. For that, try ev(%o3,nouns). Does that do what you want?
>On Wed, Jun 6, 2012 at 12:31 PM, Henry Baker <hbaker1 at pipeline.com> wrote:
>Yes, but if I do the following, it doesn't work:
> 2 2 2
>(%o2) abs(a) = realpart (a) + imagpart (a)
> 2 2 2
>(%o3) (%i s + r) = realpart (%i s + r) + imagpart (%i s + r)
> 2 2 2 2
>(%o4) - s + 2 %i r s + r = realpart (%i s + r) + imagpart (%i s + r)
> 2 2 2 2
>(%o5) - s + 2 %i r s + r = realpart (%i s + r) + imagpart (%i s + r)
>At 08:59 AM 6/6/2012, Richard Fateman wrote:
>>cabs(a)^2= realpart(a)^2 + imagpart(a)^2;
>>you can say declare(r,real); declare(s,real) if you wish, but
>>it seems to be unnecessary.
>>On 6/6/12 8:37 AM, Stavros Macrakis wrote:
>>>I believe that cabs(a) used to return sqrt('realpart(a)^2+'imagpart(a)^2), though it now returns 'abs(a) (prints as |a|). I think the former is more in the spirit of cabs (which is supposed to give you an explicit formula, not just punt to a nounform), so I would consider the current behavior to be a bug.
>>>If I remember correctly, a few years ago, someone tried to unify abs and cabs (I objected) -- this may be related to that?
>>>As a workaround, you can do cabs(rectform(a))^2 => 'realpart(a)^2+'imagpart(a)^2. Unfortunately, rectform(abs(a)) currently returns 'abs(a) -- again, I think this is a bug. If you're starting with the abs form, I suppose you could do subst(lambda([ex],cabs(rectform(ex))),'abs, ... ).
>>>On Wed, Jun 6, 2012 at 11:06 AM, Henry Baker <hbaker1 at pipeline.com> wrote:
>>>I'm trying to get maxima to prove that
>>>I tell maxima:
>>>What do I tell maxima to get it to simplify this?
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