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From: SourceForge.net <noreply@so...>  20040715 14:45:19

Bugs item #991628, was opened at 20040715 10:45 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^n,x,a,b) wrong for a<0<b Initial Comment: integrate(x^n,x,a,b); Is n positive, negative, or zero? neg; Is n + 1 zero or nonzero? n; Is b  a positive, negative, or zero? pos; => b^(n+1)/(n+1)a^(n+1)/(n+1) (NO!) This is incorrect for (e.g.) n=2, a<0<b: integrate(x^2,x,a,1); Is a  1 positive, negative, or zero? neg; => Integral is divergent (OK) Same thing, but a more dramatic demo: assume(equal(a,1),equal(b,1),equal(n,2)); integrate(x^n,x,a,b) => b^(n+1)/(n+1)a^(n+1)/(n+1) (NO!) vs. integrate(x^2,x,1,1) => Divergent (OK) Also assume(equal(n,2)); integrate(x^n,x,1,1); => (1)^n/(n+1)+1/(n+1) (NO!)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 
From: SourceForge.net <noreply@so...>  20060410 04:09:11

Bugs item #991628, was opened at 20040715 08:45 Message generated for change (Settings changed) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. >Category: Lisp Core  Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^n,x,a,b) wrong for a<0<b Initial Comment: integrate(x^n,x,a,b); Is n positive, negative, or zero? neg; Is n + 1 zero or nonzero? n; Is b  a positive, negative, or zero? pos; => b^(n+1)/(n+1)a^(n+1)/(n+1) (NO!) This is incorrect for (e.g.) n=2, a<0<b: integrate(x^2,x,a,1); Is a  1 positive, negative, or zero? neg; => Integral is divergent (OK) Same thing, but a more dramatic demo: assume(equal(a,1),equal(b,1),equal(n,2)); integrate(x^n,x,a,b) => b^(n+1)/(n+1)a^(n+1)/(n+1) (NO!) vs. integrate(x^2,x,1,1) => Divergent (OK) Also assume(equal(n,2)); integrate(x^n,x,1,1); => (1)^n/(n+1)+1/(n+1) (NO!)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 
From: SourceForge.net <noreply@so...>  20060410 17:33:09

Bugs item #991628, was opened at 20040715 10:45 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^n,x,a,b) wrong for a<0<b Initial Comment: integrate(x^n,x,a,b); Is n positive, negative, or zero? neg; Is n + 1 zero or nonzero? n; Is b  a positive, negative, or zero? pos; => b^(n+1)/(n+1)a^(n+1)/(n+1) (NO!) This is incorrect for (e.g.) n=2, a<0<b: integrate(x^2,x,a,1); Is a  1 positive, negative, or zero? neg; => Integral is divergent (OK) Same thing, but a more dramatic demo: assume(equal(a,1),equal(b,1),equal(n,2)); integrate(x^n,x,a,b) => b^(n+1)/(n+1)a^(n+1)/(n+1) (NO!) vs. integrate(x^2,x,1,1) => Divergent (OK) Also assume(equal(n,2)); integrate(x^n,x,1,1); => (1)^n/(n+1)+1/(n+1) (NO!)  >Comment By: Raymond Toy (rtoy) Date: 20060410 13:33 Message: Logged In: YES user_id=28849 These errors occur because maxima is trying to see if there are any poles on the real axis. It does so by calling polesininterval, which calls realroots on the denominator of the integrand, which is x^(n), since n is negative. But solve thinks this equation has no real roots. This is why x^(2) works. solve wants the roots of x^2, which it can figure out, and thus polesininterval finds poles in the interval.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 
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