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[x]
and solution[y]
themselves. But I am hoping that sage can do this for me.
I tried to do Rational((log(...)/log(...)).n())
or (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?