OK, so Sage is doing this before calling Maxima.

It's probably more important that Sage simplify in general, so I will just 
have to watch out for this (and warn my students). 

Thank you,
Aaron

On Tuesday, March 21, 2017 at 1:29:25 PM UTC-10, William Stein wrote:
>
>
> On Tue, Mar 21, 2017 at 4:28 PM Aaron Tresham <[email protected] 
> <javascript:>> wrote:
>
>> If I run x^2/x in SMC, the output is x.
>>
>
> That is what is really going on here. Maxima isn't relevant at all. By the 
> time maxima sees your input, x^2/x has already beeb simplified to c. 
>
>
>
>
>> That is fine in some contexts (although the user should mentally add "x 
>> not equal to 0").
>>
>> I'm dealing with rational functions with holes, and Sage is eliminating 
>> the hole. Of course, it would be very nice if my students would notice the 
>> hole themselves.
>>
>> Aaron
>>
>>
>> On Tuesday, March 21, 2017 at 12:52:07 PM UTC-10, William Stein wrote:
>>
>>> What happens if you just type x^2/x ?
>>>
>> On Tue, Mar 21, 2017 at 3:35 PM Aaron Tresham <[email protected]> wrote:
>>>
>> Does anyone know if there is a similar group to discuss issues with 
>>>> Maxima? (I think that's where my problem lies).
>>>>
>>>> When I do something like:
>>>>
>>>> solve(x^2/x==0,x)
>>>>
>>>> I expect no solutions, but Sage gives me one solution, x==0. I'm 
>>>> assuming Sage uses Maxima here, and Maxima simplifies the fraction before 
>>>> solving (and fails to check afterwards). I can catch things like this 
>>>> myself, but I'm not sure my students would notice (especially if a hole is 
>>>> hidden inside a complicated rational function).
>>>>
>>>> Thanks,
>>>> Aaron
>>>>
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>>> -- 
>>>
>>> Best Regards,
>>> William Stein
>>>
>>> CEO, SageMath, Inc.
>>>
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> -- 
>
> Best Regards,
> William Stein
>
> CEO, SageMath, Inc.
>

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