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Removed[] pop-visiting explanation?

• To: mathgroup at smc.vnet.net
• Subject: [mg34265] Removed[] pop-visiting explanation?
• From: Vladimir Bondarenko <vvb at mail.strace.net>
• Date: Sun, 12 May 2002 03:26:42 -0400 (EDT)
• Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

In Mathematica 4.1, the answers to several thousands of
integrals involve  Removed["$$Failure"] . For example,
you can see it in the following simplest inputs

Integrate[Log[1 - z^2] Cos[Sqrt[z]], {z, -1, 1}]// InputForm

(-8*E^2 + 4*(-2 + EulerGamma - CosIntegral[-1 + I] + 2*CosIntegral[I] -
CosIntegral[1 + I] - 2*ExpIntegralEi[1] + ExpIntegralEi[2] - Log[4] +
I*SinIntegral[-1 + I] - (2*I)*SinIntegral[I] + I*SinIntegral[1 + I]) +

E*(Removed["$$Failure"]         - 4*(EulerGamma*(Cos[1] + Sin[1]) + Sin[1]*(-

2*CosIntegral[1] + CosIntegral[2] - Log[4] - 2*SinIntegral[1] +
SinIntegral[2]) - Cos[1]*(4 + 2*CosIntegral[1] - CosIntegral[2] +
Log[4] - 2*SinIntegral[1] + SinIntegral[2]))))/(2*E)


Integrate[Log[1 - z^2] Sin[Sqrt[z]], {z, -1, 1}]
Integrate[Log[1 - z^2] Cosh[Sqrt[z]], {z, -1, 1}]
Integrate[Log[1 - z^2] Sinh[Sqrt[z]], {z, -1, 1}]
Integrate[Log[1 - z^2] Sinh[Sqrt[-z]], {z, -1, 1}]
.......................................................................
.......................................................................
.......................................................................

I tried to ferret out more about it, but the Help Browser does not
include it, and I found only

?? Removed

"Removed[string] is printed to indicate a symbol that has been removed."

Attributes[Removed] = {Protected}


Why this unusual bug occurs? I mean, what language constructions might
be involved in or responsible for it?

How can I get more information about the stuff like this?

What is the simplest way to program in Mathematica this case?


Can anybody drop me at least a couple of words?


Thanks in advance!


Vladimir Bondarenko

• Follow-Ups:
  • Re: Removed[] pop-visiting explanation?
    • From: Daniel Lichtblau <danl@wolfram.com>