[re-posting a reply from a week ago that apparently did not go through because gmane was moving]
Nils Bruin wrote: > This model has the advantage that (sqrt(1+t)^2 -1)/t == 1 returns > true, as one would expect mathematically. Do you mean it has the advantage that cos(sin(tan(t^2)) - tan(sin(t^2))) == 1 returns True, as one would expect mathematically? ;-) Joking aside, if I hadn't be hit by that issue before, I would also expect to be able to trust equality more than that. And I would interpret the presence of an explicit O() term as a strong indication that inexact series won't be considered equal to anything. Perhaps more importantly, I find the fact that series and p-adics (but not intervals and balls) are doing that problematic for writing generic code. Suppose that a is a symbolic expression, or an element of any other parent where inequality is not decidable. Would you expect a.is_zero() to return True whenever Sage is unable to prove that a is nonzero? If not, what can code written for generic coefficient rings do to work with both expressions and series? Regarding power series in particular, the structure where cos(sin(tan(t^2)) - tan(sin(t^2))) == 1 exists and makes perfect sense, but it's the ring of polynomials mod t^20, not the ring of power series with precision 20. -- Marc -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/r09gso%2430f0%241%40ciao.gmane.io.
