On Feb 15, 8:38 am, Keshav Kini <keshav.k...@gmail.com> wrote: > On Wed, Feb 15, 2012 at 21:07, Stephen Montgomery-Smith > > <step...@missouri.edu> wrote: > > I have a concern over I^(0.5). It is plus or minus (1+I)/sqrt(2). The > > difficulty I have is with the "plus or minus". It is possible to define the > > positive square root of a real number so that sqrt(ab)=sqrt(a)*sqrt(b). But > > you cannot define the "positive" square root of a complex number and still > > retain that identity. > > Well, this is not really about defining principal roots of complex > numbers, it's about the symbolic expression "I" not conforming to > Sage's usual treatment of taking roots of complex numbers. CC((0, > 1))^(0.5) has been "0.707106781186548 + 0.707106781186547*I" for a > long time, I imagine.
Yeah, I don't think that we try to maintain this symbolically for that very reason. You can get it with various simplification functions, but of course then it is *simplified*, hence could run into trouble. sage: sqrt(-i)*sqrt(i) sqrt(-I)*sqrt(I) sage: sqrt(-i*i) 1 sage: (sqrt(-i)*sqrt(i)).simplify_full() (-1)^(1/4)*sqrt(-I) See some of the things linked to at http://trac.sagemath.org/sage_trac/ticket/3520, or Richard Fateman's interesting post about square roots at http://ask.sagemath.org/question/767/simplification-errors-in-simple-expressions?answer=1261#1261 -- 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
