On Nov 14, 2014 11:30 AM, "Bill Page" <bill.p...@newsynthesis.org> wrote: > > On 14 November 2014 13:18, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > > > > On Nov 14, 2014 8:57 AM, "Bill Page" <bill.p...@newsynthesis.org> wrote: > >> > >> 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. > > > > Yes. > > >> ... > >> 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? > > > > What do you mean by "the real derivative"?
The absolute value doesn't have a complex derivative, but it has a real derivative, over the real axis. > Perhaps we can just define that as > > d f / d z + d f / d conjugate(z) > > > 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. > > > > You are not differentiating with respect to x, you are differentiating > with respect to > > (z+conjugate(z))/2 Is that how you propose to define the derivatives for non-analytic functions? I am a little confused what exactly is your proposal. I think one either leaves the derivatives of non analytic functions unevaluated, or defines them in such a way that one recovers the real derivative as a special case, as long as there are no inconsistencies. 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.
