Abs[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg5418] Abs[]*From*: fast at magellan.Colorado.EDU (Bruce Alan Fast)*Date*: Sat, 7 Dec 1996 00:25:47 -0500*Organization*: University of Colorado at Boulder*Sender*: owner-wri-mathgroup at wolfram.com

robpeterson at sprintmail.com writes > I may not understand the limitations of Abs[]. > ...... > This works just fine: > s[L_]=I/(L+1/L);(* a complex function *) > Plot[Evaluate[D[Abs[s[L]],L]],{L,1,2}] > (*The Abs[] of a complex function, which is real, apparently > has a real derivative and it is plotted.*) Bad news: Abs[] is not analytic -- i.e., as a function of complex values it does not have a derivative. So a lot of attempts to get numerical values or plots of derivatives of Abs[Anything] are doomed. I tried your example and it did *not* work --- which is good, because it would be in error. If f[x] is a real function of real values x, then it's possible to make sense of D[Abs[f[x],x]], but not if f is complex.