On 14 November 2014 14:29, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > > On Nov 14, 2014 11:30 AM, "Bill Page" <bill.p...@newsynthesis.org> wrote: >> >> 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. >
It seems to me that the concept of "real axis" is rather foreign to the algebra. Assuming conjugate is implemented properly, i.e. "algebraically", what you are actually saying is just that z = conjugate(z) > ... >> 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 am sorry for the confusion. What I am proposing is that the Wirtinger derivative(s) be considered the fundamental case (valid for complex or even quaternion variables). As you noted previously this is fine and doesn't change anything for the case of analytic functions. If someone wants the derivative of a non-analytic function over a given domain that should be called something else. > I think one either leaves the derivatives of non analytic functions > unevaluated, No, this is just giving up. We should be able to do much better than that. > or defines them in such a way that one recovers the real derivative > as a special case, as long as there are no inconsistencies. > Yes exactly, the concept of "real derivative" is a special case. 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.
