On Fri, Nov 12, 2010 at 3:44 PM, Derrick <we.sana...@gmail.com> wrote: > Any clue why bool(arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2)))) returns > false where the expressions are mathematically equivalent.
Because an expression being equal to zero is, in general, and undecideable question. If it can't tell, it'd rather error on the side of caution (not being equal) than claim they're equal. > I found that arcsin(x) - 2*arctan(x/(1+sqrt(1-x^2))) is not exactly 0 > for all x in [-1,1]. True. You can't even represent arcsin(x) exactly as a floating point number for most values of x. There's rounding error and all when you combine operations as well. > In sage, is there any way to compare expressions > with some numerical precision? sage: expr.subs(x=1/3).n() 0.000000000000000 sage: expr.subs(x=1/3).n(100) 3.9443045261050590270586428264e-31 sage: expr.subs(x=1/3).n(1000) 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
