editing in last mail last line >>>(sqrt(2)+sqrt(2)).is_rational False
On Sun, Mar 4, 2012 at 9:12 PM, prateek papriwal <[email protected]>wrote: > @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.
