hey, i admit i was wrong at my statement . On Sun, Mar 4, 2012 at 8:30 PM, Joachim Durchholz <[email protected]> wrote:
> Am 04.03.2012 14:09, schrieb prateek papriwal: > > also the addition of two positive irrational number is also irrational . >> > > A trivial counterexample: > 2 +/- sqrt(2) are positive and irrational, yet their sum is 4, which is > rational. > > There are less trivial cases. > Such as the sum of 1/(sqrt2-1) and 2-sqrt(2), which is 3. > (Taken from Wikipedia and trivially modified, but unvalidated.) > > > In more generality, I'm a bit concerned that we're investing a lot of > effort into building a rationality test that works only for a small class > of numbers. It would probably be better to make this extensible, so that > people can add more algorithms as we pick up techniques. > > Background: Testing for rationality in general is an undecidable problem. > It is proven to be impossible to have an algorithm that will work for > arbitrary formulae. There are two possible failure modes: > - The algorithm is correct but may run into an endless loop. > - The algorithm is incorrect. > - The algorithm returns "rational", "irrational", or "don't know". > The third behaviour is not ideal, but I doubt the other two are acceptable. > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to sympy+unsubscribe@** > googlegroups.com <sympy%[email protected]>. > For more options, visit this group at http://groups.google.com/** > group/sympy?hl=en <http://groups.google.com/group/sympy?hl=en>. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
