On Sun, Nov 2, 2008 at 11:58 AM, Kevin Buzzard <[EMAIL PROTECTED]> wrote: >> That would be inconsistent with the choice made by every other >> math software system ever written and with common mathematical >> usage as well. It would thus cause excessive confusion, and likely >> not be very useful. > > I can believe this. And yet if there's an "IsPositive" command in sage, what > does IsPositive(Sqrt(5)) give?
There is no IsPositive (or is_positive) command in Sage. If there were it would definitely give True because sage: float(sqrt(5)) 2.2360679774997898 > > I think that my main problem is that I am not used to maths packages that > think sqrt(5) is anything other than a positive real. Sage does think it is a positive real. You're used to math packages like Pari and Magma that both think sqrt(5) is a "positive rational", by which I somewhat sarcastically mean a finite-precision floating point number. Also, I bet you're also used to Magma, which thinks of sqrt(5) alternatively as a number field element which doesn't have a choice of sign. In Sage, sqrt(5) is the exact positive sqrt of 5. sage: a = sqrt(5) sage: a sqrt(5) sage: a^2 5 sage: expand((a+1)^2) 2*sqrt(5) + 6 sage: float(a) 2.2360679774997898 sage: numerical_approx(a, digits=40) 2.236067977499789696409173668731276235441 sage: QQ[a] Number Field in sqrt5 with defining polynomial x^2 - 5 Actually, at the point when I do QQ[a] and get a number field, a looses the choice of sign. That's changing in the next version of Sage though, due to work of Robert Bradshaw. > I'm just getting my > head around the consequences of the decision that it be an abstract object. > I can totally envisage someone writing some loop for m=1 to 100000, n=crazy > function of m, t=sqrt(n), blah blah computations with t, and the loop > bombing out because for some random big value of m, n turned out to be an > exact square. True. One big problem right now is the exact sqrt(5) in Sage is computed with behind the scenes using a pexpect interface to a slow lisp-based version of Maxima. This will change soon (we're moving to a C++ based backend for symbolic manipulation). There's a first version of the new backed in sage-3.2. > But I'll get used to it over time! > > Kevin If things are truly sufficiently annoying, they can be changed. (1) you can put a customization file $HOME/.sage/init.sage and it gets run when sage starts up, and (2) Sage is open source -- any compelling argument for changes is seriously considered (especially when the person making the argument is willing to do all the work). You can also do n.sqrt(prec=bits_of_precision) and n.isqrt() for the integer floor of the sqrt, quickly computed directly by gmp. sage: n = 9239082304 sage: n.sqrt(prec=30) 96120.145 sage: n.isqrt() 96120 William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
