On 15 March 2014 04:42, Jori Mantysalo <jori.mantys...@uta.fi> wrote:
> Solving equations:
>
> solve(e^x==e^3, x) --> [x == 3]
> solve(2^x==2^3, x) --> [x == log(8)/log(2)]
>
> So it does not simplify. But (log(8)/log(2)).full_simplify() returns
> log(8)/log(2), not 3. OK, I can do .simplify_radical(), but why
> full_simplify() doesn't try it?
>
> I also tried
>
> solve(2^x+3^x==13, x)
This is a rather special sort of S-unit equation: given any finite
set of primes S there are always only finitely many solutions to a+b=c
where a,b,c are coprime and with all their prime factors in S. Code
to solve this has been written in Sage as part of a larger project,
and I will encourage its author (my student Angelos Koutsianas) to
submit the special case to Sage.
However, it would be a rather different job to recognise your equation
as a special case with S={2,3,13} and pull out the subset of solutions
where a, b, c are powers of 2 with exponents x,x,1 and return x. We
do not plan to do that!
John
>
> Didn't work. However, are these kind of problems possible to solve at all,
> and if so, in some program that is already part of Sage?
>
> --
> Jori Mäntysalo
>
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