[MUG] Integration bug, i think

[MUG] Re: Integration bug, i think
Author: Maple Group    Posted: 29/11/2000 15:23:47 GMT
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 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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 **************************************************************************** -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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 ________________________________________________________________________________ _____ Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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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