@david the recent commits made by smith in the sympy gives True for >>>((2-sqrt(2))+sqrt(2)).is_rational
but for >>>(sqrt(3)+sqrt(5)).is_rational it gives none while for >>>(sqrt(2)+sqrt(3)).is_rational False On Sun, Mar 4, 2012 at 8:58 PM, prateek papriwal <[email protected]>wrote: > 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.
