On Thursday, June 4, 2015 at 6:21:43 AM UTC-7, kcrisman wrote:
>
>
>
> 1. anyone who believes that sqrt(x^2) is |x| is mistaken. As Bill Page
>> says, there are two values.
>>
>
> Ah, the old 'function versus expression' debate. I really missed that.
>
>
>> 2. any system that automatically produces |x| can be tricked into
>> committing serious errors.
>> Currently, Maxima apparently does this.
>>
>
> But not in Sage's Maxima, because
>
> (%i1) sqrt(x^2);
> (%o1) abs(x)
> (%i2) domain:complex;
> (%o2) complex
> (%i3) sqrt(x^2);
> 2
> (%o3) sqrt(x )
>
>
>
>> Some people consider this a feature. Clearly we
>> have a difference of opinion about sqrt. Mathematica leaves the
>> expression unchanged.
>> 3. I tried Maxima 5.23.2 on the integral and got log(-1) which is
>> nonsense.
>>
>
> Try it again with domain:complex
>
Both x and -x are real if x is real. If setting domain:complex "fixes"
something, then it is certainly poorly named.
In Maxima, assume(y>0) results in sqrt(y^2) simplifying to y.
Some of us believe that sqrt(9) should be {-3,+3} even if 3^2=9.
>
>
>> 4. Mathematica 9 answers ln(2).
>>
>>
>>
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