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From: SourceForge.net <noreply@so...>  20100420 16:35:21

Bugs item #2989983, was opened at 20100420 16:35 Message generated for change (Tracker Item Submitted) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&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 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: wrong integration answer Initial Comment: When using sage, and thus Maxima, for the integration of: Cos(T + w) / (1+e cos(T)^2 from 0 to 2*pi, sage (and thus maxima?) gives 0 as answer. There maple gives the answer: 2*pi*e*cos(w)/1e^2)^1.5 the correct commands in sage 4.3.5 are (don't know them in maxima): sage: e = var('e') sage: w = var('w') sage: T = var('T') sage: assume(1e^2>0) sage: integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*pi) 0  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&group_id=4933 
From: SourceForge.net <noreply@so...>  20100420 21:57:04

Bugs item #2989983, was opened at 20100420 19:35 Message generated for change (Comment added) made by alex108 You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&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 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: wrong integration answer Initial Comment: When using sage, and thus Maxima, for the integration of: Cos(T + w) / (1+e cos(T)^2 from 0 to 2*pi, sage (and thus maxima?) gives 0 as answer. There maple gives the answer: 2*pi*e*cos(w)/1e^2)^1.5 the correct commands in sage 4.3.5 are (don't know them in maxima): sage: e = var('e') sage: w = var('w') sage: T = var('T') sage: assume(1e^2>0) sage: integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*pi) 0  Comment By: Aleksas Domarkas (alex108) Date: 20100421 00:57 Message: Solving with maxima 5.21.0 : (%i1) S: 'integrate(cos(T+w)/(1+e*cos(T))^2, T, 0, 2*%pi)$ (%i2) first(%)$ (%i3) expand(%)$ (%i4) f:trigexpand(%)$ (%i5) F:integrate(f,T)$ "Is "e^21.0" positive or negative?"negative; Antiderivative F is discontinous at T=%pi. For example (%i6) wxplot2d([F], [T,0,2*%pi]),e=1/2,w=1$ plot2d: expression evaluates to nonnumeric value somewhere in plotting range. (%t6) << Graphics >> Then integral is equal (%i7) limit(F,T,%pi,minus)ev(F,T=0)+ev(F,T=2*%pi)limit(F,T,%pi,plus)$ (%i8) sol:ratsimp(%); (%o8) (2*%pi*e*sqrt(1e^2)*cos(w))/(e^42*e^2+1) This is same as Maple answer: (%i9) 2*pi*e*cos(w)/(1e^2)^1.5$  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&group_id=4933 
From: SourceForge.net <noreply@so...>  20110315 20:08:04

Bugs item #2989983, was opened at 20100420 12:35 Message generated for change (Comment added) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&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: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: wrong integration answer Initial Comment: When using sage, and thus Maxima, for the integration of: Cos(T + w) / (1+e cos(T)^2 from 0 to 2*pi, sage (and thus maxima?) gives 0 as answer. There maple gives the answer: 2*pi*e*cos(w)/1e^2)^1.5 the correct commands in sage 4.3.5 are (don't know them in maxima): sage: e = var('e') sage: w = var('w') sage: T = var('T') sage: assume(1e^2>0) sage: integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*pi) 0  >Comment By: Dan Gildea (dgildea) Date: 20110315 16:08 Message: Fixed in defint.lisp rev 1.86. o dintegrate: try trigexpand for cases when arg of trig function is of form x+c. fixes integrate(cos(T+w)/(1+1/2*cos(T))^2, T, 0, 2*%pi) In this integral, the antideriv computed with the generateatan2 flag set to nil for definite integration is incorrect. Expanding before computing the integral works around this problem.  Comment By: Aleksas Domarkas (alex108) Date: 20100420 17:57 Message: Solving with maxima 5.21.0 : (%i1) S: 'integrate(cos(T+w)/(1+e*cos(T))^2, T, 0, 2*%pi)$ (%i2) first(%)$ (%i3) expand(%)$ (%i4) f:trigexpand(%)$ (%i5) F:integrate(f,T)$ "Is "e^21.0" positive or negative?"negative; Antiderivative F is discontinous at T=%pi. For example (%i6) wxplot2d([F], [T,0,2*%pi]),e=1/2,w=1$ plot2d: expression evaluates to nonnumeric value somewhere in plotting range. (%t6) << Graphics >> Then integral is equal (%i7) limit(F,T,%pi,minus)ev(F,T=0)+ev(F,T=2*%pi)limit(F,T,%pi,plus)$ (%i8) sol:ratsimp(%); (%o8) (2*%pi*e*sqrt(1e^2)*cos(w))/(e^42*e^2+1) This is same as Maple answer: (%i9) 2*pi*e*cos(w)/(1e^2)^1.5$  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&group_id=4933 
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