> So you can assume that an empty list means only that sage's algorithms
> find no solution.
>
I just looked at the documentation of solve and could not find an explicit
statement about missed solutions.
Even if it is expectable that in some cases (which?) solve may not return
all solutions, it should be explicitly pointed out;
Especially it should be stated that an empty list does not necessarily
imply there are no solutions.
Other opinions? If everybody agrees, I will open a ticket.
Jakob
Am Mittwoch, 19. November 2014 09:07:55 UTC+1 schrieb Emmanuel Charpentier:
>
>
>
> Le mardi 18 novembre 2014 17:10:42 UTC+1, Chris Seberino a écrit :
>>
>> Emmanuel
>>
>> Any way to make Sage act like it can't find the solution (emit question
>> back to user) INSTEAD of emitting the empty set?
>>
>> "I can't find the solution" and "There is no solution" are NOT the same
>> thing?
>>
>
> Indeed. But proving that "There is no solution" might inded invorve some
> serious work. Consider (pseudocode) :
> var("a,b,c,n")
> assume(a,"integer",b,"integer",c,"integer",n,"integer",a>0,b>0,c>0,n>2)
> solve(a^n+b^n==c^n,[a,b,c,n])
> which has, indeed no solution. Proving this has been found a bit
> involved...
>
> So you can assume that an empty list means only that sage's algorithms
> find no solution.
>
> Your point is that, in your example, sage returns (incorrectly) an empty
> list.In other cases, it returns the original equation.
>
> Indeed. So what ?
>
> I have not (yet) found a specification for those two cases, but I think it
> depends on which algorithm has been used. (Maxima may return the empty list
> in cases solve'() does not succeds).
>
> Beware : in other cases, sage might return an implicit solution, given as
> an equation.
>
>> cs
>>>>
>>>
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