if you are looking to proof equivalence to zero,  you could use the 
zeroequiv command in maxima, which is
going to be, in general, pretty fast.   But as i recall, if it says "false" 
that merely means it could not prove the
expression is zero.  Look for discussion of bugs / features in maxima 
mailing list some years ago


On Friday, November 7, 2014 2:04:54 PM UTC-8, Nils Bruin wrote:
>
> On Friday, November 7, 2014 1:43:13 PM UTC-8, Thierry 
> (sage-googlesucks@xxx) wrote:
>>
>> > Incidentally I observe that Sympy has the same behavior, so we can't 
>> > just nick their factoring algorithm -- maybe some other package we can 
>> > try the same example to see if any of them handle it quickly? 
>>
>> How did you observe the same behaviour for sympy ?
>>
>
> I'm pretty sure Robert is alluding to the fact that the factoring in sympy 
> is also slow:
>
> sage: %time (exp(256*(x+1)) - 1)._sympy_().factor()
> CPU times: user 20.3 s, sys: 11 ms, total: 20.3 s
> Wall time: 20.3 s
> (E*exp(x) - 1)*(E*exp(x) + 1)*(exp(2)*exp(2*x) + 1)*(exp(4)*exp(4*x) + 
> 1)*(exp(8)*exp(8*x) + 1)*(exp(16)*exp(16*x) + 1)*(exp(32)*exp(32*x) + 
> 1)*(exp(64)*exp(64*x) + 1)*(exp(128)*exp(128*x) + 1)
>
> Apparently, sympy doesn't try factoring as part of its zero test (or at 
> least arrives at a definitive answer for this example). However, note that 
> the answers of sympy and maxima are different: sympy says "false" because 
> the expression is not identically 0 and maxima says "unknown" because the 
> expression is not identically 0, but is 0 for some values of x (or at least 
> I hope that is what maxima is doing). So maxima is determining more 
> information.
>

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