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. > 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. 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.
