Re: confused!
- To: mathgroup at smc.vnet.net
- Subject: [mg78962] Re: [mg78900] confused!
- From: anguzman at ing.uchile.cl
- Date: Fri, 13 Jul 2007 06:16:26 -0400 (EDT)
- References: <200707120920.FAA08316@smc.vnet.net>
Hello:
I think the limits should be different. But there is something strange
about your limits (I got them too, don't know why), because g[z] is
always real, and the limits have big imaginary parts. However,
FullSimplify delivers an expression for the limit from the left:
Limit[g[z], z -> disc] // FullSimplify // N
0.951755 + 0. \[ImaginaryI]
Unfortunately, with no discrimination between the Directions.
The above, with no FullSimplify, gives the other limit:
Limit[g[z], z -> disc] // N
-4.817368722651279`\ - 1.1102230246251565`*^-16\ \[ImaginaryI]\)
Obviously this is not a satisfactory behavior. But you know if the
expression MUST give a discontinuity?. I couldn't find a simpler
example where this behavior in Limit could be reproduced...
Atte. Andres Guzman
dimitris <dimmechan at yahoo.com> ha escrito:
> Hello.
>
> (version 5.2)
>
> Say
>
> In[201]:=
> g[z_] := RootSum[1 + #1^2 + #1^3 & , (Log[-I + z]*Log[1 - (-I + z)/(-I
> + #1)] + PolyLog[2, (-I + z)/(-I + #1)])/
> (2*#1 + 3*#1^2) & ] + RootSum[1 + #1^2 + #1^3 & , (Log[I +
> z]*Log[1 - (I + z)/(I + #1)] + PolyLog[2, (I + z)/(I + #1)])/(2*#1 +
> 3*#1^2) & ]
>
> Then
>
> In[208]:=
> Plot[g[z], {z, 0, 10}]
>
> In[209]:=
> disc =
> z /. ToRadicals[ToRules[Reduce[Im[1 - (I + z)/((-(1/3) + I) +
> (1/6)*(1 + I*Sqrt[3])*((1/2)*(29 - 3*Sqrt[93]))^(1/3) +
> (1 - I*Sqrt[3])/(3*2^(2/3)*(29 - 3*Sqrt[93])^(1/3)))] == 0
> && Im[z] == 0, z]]]
>
> Out[209]=
> (4 - 2*(29/2 + (3*Sqrt[93])/2)^(1/3) - 2*(2/(29 + 3*Sqrt[93]))^(1/3))/
> (-12 + 2*Sqrt[3]*(29/2 + (3*Sqrt[93])/2)^(1/3) -
> 2*Sqrt[3]*(2/(29 + 3*Sqrt[93]))^(1/3))
>
> Should the following limits be different?
>
> In[235]:=
> (Limit[g[z],z\[Rule]disc,Direction\[Rule]#]&)/@{-1,1}//N[#,120]&
>
> Out[235]=
> {-1.9328068705851854459133332334109901866262538160640608787226290809426162=
3587\
> 579018111126672955973274498162595572599953216-0.\
> 35279992963649906574293634280225311905963597342346263276877540034102588143=
0703\
> 16101859237983014877085731418268885248465 \
> \[ImaginaryI],-1.\
> 93280687058518544591333323341099018662625381606406087872262908094261623587=
5790\
> 18111126672955973274498162595572599953216-0.\
> 35279992963649906574293634280225311905963597342346263276877540034102588143=
0703\
> 16101859237983014877085731418268885248465 \[ImaginaryI]}
>
> Dimitris
>
>
>
----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.
- References:
- confused!
- From: dimitris <dimmechan@yahoo.com>
- confused!