Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

It's known that there is no algorithm for deciding for any elementary function is it identically zero or not (http://en.wikipedia.org/wiki/Richardson%27s_theorem ).

But if I consider only constants - is there some algorithm for deciding for any constant expression composed from elementary functions (e. g. $\ln (\sin 1 - \tan (\pi^2))$), is it equal to zero or not?

share|improve this question
    
For constants? Just evaluate them. You can use some heuristics, like $e^x \neq 0 \forall x$. –  Newb Dec 24 '13 at 19:39
    
@Newb, computers use only finitely much memory. Real numbers don't. –  Karolis JuodelÄ— Dec 24 '13 at 19:47
    
Try deciding whether $\tan p - q = 0, p, q \in \mathbb{Z}$. I'm sure that this number can be made arbitrarily small. How will a computer decide if you can't? –  Karolis JuodelÄ— Dec 24 '13 at 19:50
    
Also there are expressions like $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} - 1$ (it's actually zero). –  ptashek Dec 24 '13 at 19:55
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.