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[MUG] Re: Integration bug, i think
| [MUG] Re: Integration bug, i think |
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Author: Maple Group
Posted: 29/11/2000 15:23:47 GMT
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Subject: Integration bug, i think
Yes, it's a bug. It shows up in a simpler form here:
> f:= exp(-t)*ln(exp(t/2)/(1+exp(1)));
int(f,t);
2 2
- 1/2 exp(- 1/2 t) + 2 exp(- 1/2 t) ln(1 + exp(1))
2
- 1/2 t exp(- 1/2 t)
The 2 in front of the second term should be 1.
The bug seems to be new in Maple 6: it doesn't affect
Maple V Releases 4 to 5.1.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
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Date: Tue, 28 Nov 2000 09:55:03 +0900
To:
From: tanaka
Subject: Integration bug, i think
"a2" in "b1"should read "a1" and "a1" in "b2" should read "a2".
>a1 := .9*(.9+8.*exp(-1))*exp(.1*tt)/(1+8*exp(-1)):
>b1:=int(exp(-tt)*ln(a1),tt=t..1):
>c1:=evalf(subs(t=0.5,b1));
>a2:=simplify(a1):
>b2:=int(exp(-tt)*ln(a2),tt=t..1):
>c2:=evalf(subs(t=0.5,b2));
Evaluating the above procedure by Maple V release 5.1, we have
c1 := -.01387125141
c2 := -.01387124687
Evaluating the above by Maple V release 4, we have
c1 := -.013871277
c2 := -.013871131
Therefore, I am sure that integrations in Maple 6 has some bugs.
Dr.TANAKA, Kazuo,
Canon Inc., Tokyo, JAPAN
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Date: Mon, 27 Nov 2000 17:03:31 -0800
Subject: Integration bug, i think
From: Don Hartig
To:
Halvor,
I assume that the a2 appearing in the expression for b1 should actually be
a1. If that is the case, then I get the same values for c1 and c2. I also
get the same values for b1 and b2.
I am running Maple 6.1 on a Macintosh G4.
regards,
Don Hartig
****************************************************************************
Donald Hartig | Telephone: (805) 756 1684
Professor of Mathematics | Fax: (805) 756 6537
Mathematics Department | e-mail:
California Polytechnic State U. |
San Luis Obispo, CA 93407 |
USA |
Web page: http://www.calpoly.edu/~dhartig
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From: "Nathan Sokalski"
To:
Subject: Integration bug, i think
Date: Mon, 27 Nov 2000 23:08:56 -0500
In b1 you are using a2 before it is defined. Therefore, the first time
through b1 will involve the variable a2. However, if you enter each equation
a second time (in order), you will recieve the same value, because a2 has
already been defined.
Nathan Sokalski
________________________________________________________________________________
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Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com
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Date: Tue, 28 Nov 2000 11:03:40 +0100
From: Heike Koch-Beuttenmueller
To:
Subject: Integration bug, i think
Things seems to be even much stranger:
I tried the following on Compac Alpha:
d1 := 9/10*(9/10+8*exp(-1))*exp(1/10*tt)/(1+8*exp(-1));
int(exp(-tt)*log(d1),tt=1/2..1);
-1/5*exp(-1)-2*exp(-1)*ln(3)+3*exp(-1)*ln(2)+3*exp(-1)*ln(5)-2*exp(-1)
*ln(9+80*exp(-1))+2*exp(-1)*ln(1+8*exp(-1))+3/20*exp(-1/2)+2*exp(-1/2)
*ln(3)-3*exp(-1/2)*ln(2)-3*exp(-1/2)*ln(5)+2*exp(-1/2)*ln(9+80*exp(-1)
evalf(%,30);
-.02000179714067499958474512972
int(exp(-tt)*log(d1),tt=0.5..1);
-.01387125093
Mathematica gives the last result. Numerical integration with Maple as
well
--
Mit freundlichen Gruessen
Heike Koch-Beuttenmueller
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