On Nov 14, 2014 8:57 AM, "Bill Page" <bill.p...@newsynthesis.org> wrote: > > On 14 November 2014 02:19, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > > On Fri, Nov 14, 2014 at 12:14 AM, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > >> ... > >> Ok, thanks for the confirmation. > >> > >> There is an issue though --- since |z| is not analytic, the > >> derivatives depend on the direction. So along "x" you get > > > > |z|' = \partial |z| / \partial x = d |z| / d z + d |z| / d conjugate(z) = > > conjugate(z) / (2*|z|) + z / (2*|z|) = Re(z) / |z| > > > > but along "y" you get: > > > > |z|' = \partial |z| / \partial i*y = d |z| / d z - d |z| / d conjugate(z) = > > conjugate(z) / (2*|z|) - z / (2*|z|) = i*Im(z) / |z| > > > > So I get something completely different. > > It seems to me that we should forget about x and y. All we really need is > > |z|' = d |z| / d z = conjugate(z) / (2*|z|) > > and the appropriate algebraic properties of conjugate.
Sure, we can make a CAS return this. But then you get the 1/2 there. > > > So which direction should be preferred in the CAS convention and why? > > > > Well, um, you did write: "Because I would like to get > > d|x| / d x = x / |x| > > for real x". > > The constant 1/2 is irrelevant. Well, but how do I recover the real derivative from the complex one if they differ by a factor of 1/2? In other words, what is the utility of such a definition then? I can see the utility of differentiating with respect to x, as at least you must recover the real derivative results. Ondrej > > Bill. > > -- > 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 post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- 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 post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
