Yes, it work, but only _after_ I defined my own absolute value function. See my previous message.
At 10:22 AM 6/6/2012, Stavros Macrakis wrote:
>What exactly do you consider "hopelessly broken" in this? In other words, which of these outputs would you want to be different, and what would you want them to be?
>
> -s
>
>On Wed, Jun 6, 2012 at 12:52 PM, Henry Baker <hbaker1 at pipeline.com> wrote:
>cabs() and abs() on complex numbers seem hopelessly broken.
>
>I defined my own cabs() function:
>myabs(a):=sqrt(a*conjugate(a));
>
>(%i7) myabs(a)^2=realpart(a)^2+imagpart(a)^2;
> 2 2
>(%o7) a conjugate(a) = realpart (a) + imagpart (a)
>(%i8) %,nouns;
> 2 2
>(%o8) a conjugate(a) = realpart (a) + imagpart (a)
>(%i9) %,a=ar+%i*ay;
> 2 2
>(%o9) (ar - %i ay) (%i ay + ar) = realpart (%i ay + ar) + imagpart (%i ay + ar)
>(%i10) %,expand;
> 2 2 2 2
>(%o10) ay + ar = realpart (%i ay + ar) + imagpart (%i ay + ar)
>(%i11) %,rectform;
> 2 2 2 2
>(%o11) ay + ar = realpart (%i ay + ar) + imagpart (%i ay + ar)
>(%i12) %,nouns;
> 2 2 2 2
>(%o12) ay + ar = ay + ar
>
>
>At 09:31 AM 6/6/2012, Henry Baker wrote:
>>Yes, but if I do the following, it doesn't work:
>>
>>(%i2) cabs(a)^2=realpart(a)^2+imagpart(a)^2;
>> 2 2 2
>>(%o2) abs(a) = realpart (a) + imagpart (a)
>>(%i3) %,a=r+%i*s;
>> 2 2 2
>>(%o3) (%i s + r) = realpart (%i s + r) + imagpart (%i s + r)
>>(%i4) %,expand;
>> 2 2 2 2
>>(%o4) - s + 2 %i r s + r = realpart (%i s + r) + imagpart (%i s + r)
>>(%i5) rectform(%);
>> 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:
>>>Henry:
>>>
>>>try this:
>>>
>>>a: r+%i*s;
>>>
>>>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.
>>>
>>>RJF
>>>
>>>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, ... ).
>>>>
>>>> -s
>>>>
>>>>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
>>>>
>>>>abs(a)^2=realpart(a)^2+imagpart(a)^2.
>>>>
>>>>I tell maxima:
>>>>
>>>>declare(a,complex);
>>>>abs(a)^2=realpart(a)^2+imagpart(a)^2;
>>>>
>>>>What do I tell maxima to get it to simplify this?