On Tue, Feb 14, 2012 at 10:15 PM, Dr. David Kirkby <david.kir...@onetel.net> wrote: > On 02/15/12 05:58 AM, William Stein wrote: >> >> Hi, >> >> A student in my class (Andrey Sarantsev) just pointed out to me that >> in Sage-4.8 and Sage-5.0, we have >> >> sage: I^(0.5) >> None >> >> What? That's not good. >> >> I'm not just putting this on trac, because I don't even know how to >> search for whether this is there already. This seems like it should >> be a blocker bug. >> >> -- William >> > > Put me out of my misery. What is sqrt(i), and why? I've only ever raised i > (or j as us engineers use) to integer powers.
For starters, sqrt(i) is a number whose square is i, and engineers know what "squaring" is. If you write a complex number z in polar coordinates as z = rho*exp(I*theta) and alpha is real number, a common choice for the meaning of z^alpha is z^alpha = rho^(alpha) * exp(I*theta*alpha) We have I = exp(I*pi/2), so I^(1/2) = exp(I*pi/4). In terms of the standard picture, it's a point on the unit circle at a 45 degree angle from the x-axis. sage: CC(I^(1/2)) 0.707106781186548 + 0.707106781186547*I William > > Dave > -- > A: Because it messes up the order in which people normally read text. > Q: Why is top-posting such a bad thing? > A: Top-posting. > Q: What is the most annoying thing in e-mail? > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
