Determine rationality of an expression?
I am trying to determine whether an expression is rational or not - and if it rational, to get the numerator and denominator.
To give you some context, I first use "solve" to get a
[ x == ..., y == ... ] solution, and then I compute
log(solution[x])/log(solution[y]). In some cases, this expression is a rational. I would like to be able to determine when it is a rational.
Of course it is rational in some very predictable cases - i.e., when the two logarithms are commensurate, and there are ways of checking this on the value of
solution[y] themselves. But I am hoping that sage can do this for me.
I tried to do
(log(...)/log(...)).n() in QQ, but of course that does not work, as
.n() converts the expression to some arbitrary precision float. Doing
(log(...)/log(...)) in QQ always returns False even, for instance, for the case
(log(100)/log(10)) = 2.
How can I do this?