Sorry about the double post. I should have written.
if a>b then a-b = +sqrt(a^2-2*a*b+b^2) elseif a<b then b-a = +sqrt(a^2-2*a*b+b^2) elseif equal(a,b) then 0 =
+sqrt(a^2-2*a*b+b^2)
--------------------------------------------------
From: "Richard Hennessy" <rich.hennessy at verizon.net>
Sent: Sunday, August 29, 2010 3:53 PM
To: "Barton Willis" <willisb at unk.edu>; "Richard Fateman" <fateman at cs.berkeley.edu>
Cc: <maxima at math.utexas.edu>; <drgst at web.de>
Subject: Re: [Maxima] I need advice on how to use radcan
> --------------------------------------------------
> From: "Barton Willis" <willisb at unk.edu>
> Sent: Sunday, August 29, 2010 10:14 AM
> To: "Richard Fateman" <fateman at cs.berkeley.edu>
> Cc: <maxima at math.utexas.edu>; <drgst at web.de>
> Subject: Re: [Maxima] I need advice on how to use radcan
>
>> -----maxima-bounces at math.utexas.edu wrote: -----
>>
>>>The introduction of abs() in the answers to radcan makes a hash of its attempt to make algebraic sense.
>>
>> Example:
>>
>> (%i1) radcan(sqrt(a^2)), domain : real, radexpand : true;
>> (%o1) abs(a)
>>
>> (%i2) radcan(sqrt(a^2-2*a*b+b^2)), domain : real, radexpand : true;
>> (%o2) b-a
>>
>> The outputs %o1 and %o2 are inconsistent, I think. My Macsyma 2.2 gives abs(b-a) for %o2
>> and abs(a) for %o1, by the way.
>
> Yes, they are inconsistent. A correct but not very concise equivalent is
>
> if a>b then a-b = +sqrt(a^2-2*a*b+b^2) elseif a<b then b-a = +sqrt(a^2-2*a*b+b^2) elseif equal(a,b) then a (or b) =
> +sqrt(a^2-2*a*b+b^2)
>
> A far more concise answer is
>
> abs(a-b) = +sqrt(a^2-2*a*b+b^2)
>
> which can be considered a "simplification", the "if" is a "complification" but I admit it is still informative.
> Another simplification would be %if(a-b>0,a-b,b-a)
>
> Rich
>
>>
>> The user documentation for radcan should be improved. Something like:
>>
>> For any n-variable Maxima expression e, the equation radcan(e) = e is an identity on some
>> nonempty open subset D of C^n. The set D might differ from what you would like it to be.
>>
>> --Barton
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>
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