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.