Suppose two elements of [the ring of periods](http://en.wikipedia.org/wiki/Ring_of_periods) are given by their systems of polynomial inequalities with rational coefficients. Is there a known algorithm deciding their equality? Is it known if their equality is algorithmically decidable at all?


It is quite obvious that if they are not equal, then it can be shown after finite number of steps just by evaluating them with big enough precision. The difficult part is when they are equal.



Algorithmic decidability of equality in the ring of periods
There is no known algorithm for that, and it is unknown if such an algorithm exists.


