Hi Ralf, On 2018-03-27, Ralf Stephan <gtrw...@gmail.com> wrote: > sage: (2^23+1)/3 > 2796203 > sage: _.is_prime() > False > sage: factor(2796203) > 2796203 > > It turns out that Rational.is_prime does not exist and the fallback gives > false answers.
My first association: We should change the printed form of a rational number. The integer 2796203 should print as 2796203, but the corresponding rational number should be printed as 2796203/1. In that way, if a user copy-and-pastes printed output back into Sage, there won't be a confusion between integers and rationals. I know that it is hardly possible to achieve that pasting of printed output will ALWAYS create a copy of the printed object. However, in cases where it is easily possible (the real number 1 should print as 1.0, the rational number 1 should print as 1/1, the complex number 1 should print as 1.0+0.0*I etc), we should do it. My second association: The fallback of is_prime should print a clear warning in the case that the input's parent is a field. Such as: WARNING: The given number is defined as element of <self.parent()>, which is a field. There are no prime numbers in a field, so, probably you want to convert the number into <self.parent().ring_of_integers()>. It might be good to add an optional argument to the method that allows to switch the warning off. > Then, I tried to print a list of primes of the above form, using the global > is_prime: > > sage: for n in range(1,100): > ....: if is_prime((2^n - (-1)^n)/3): > ....: print((2^n - (-1)^n)/3) > ....: > sage: > > No output. Turns out `is_prime(ZZ((2^n - (-1)^n)/3))` works. Really? How > long does Sage exist without a fix to that? I suppose you are aware that from a maths point of view it isn't a bug, since your code is (implicitly!) asking for prime numbers in QQ. However, I agree that it is (for most users) unintended behaviour, and as a corollary to "explicit is better than implicit", we have "implicit is not as good as explicit". I believe, when mathematically sound behaviour of SageMath is very likely not what a user wants, then printing a fat warning that can optionally be switched off (as above) is the correct fix. Just don't raise an error, and please do not change the function to give a mathematically wrong answer ((3/1).is_prime() returning "True" would be wrong). Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
