Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose two elements of the 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.

share|improve this question
2  
There is a deep conjecture here which is explained nicely in the paper of Kontsevich-Zagier. –  Moosbrugger Dec 8 '11 at 22:05
3  
This is Problem 1 of Kontsevich-Zagier. They say: "Problem 1 therefore looks completely intratable now and may remain so for many years" (page 7). ihes.fr/~maxim/TEXTS/Periods.pdf –  François G. Dorais Dec 9 '11 at 4:02
add comment

1 Answer

up vote 7 down vote accepted

There is no known algorithm for that, and it is unknown if such an algorithm exists.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.