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maxima-bugs

 [Maxima-bugs] [ maxima-Bugs-2989983 ] wrong integration answer From: SourceForge.net - 2010-04-20 16:35:21 ```Bugs item #2989983, was opened at 2010-04-20 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)/1-e^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(1-e^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 ```
 [Maxima-bugs] [ maxima-Bugs-2989983 ] wrong integration answer From: SourceForge.net - 2010-04-20 21:57:04 ```Bugs item #2989983, was opened at 2010-04-20 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)/1-e^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(1-e^2>0) sage: integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*pi) 0 ---------------------------------------------------------------------- Comment By: Aleksas Domarkas (alex108) Date: 2010-04-21 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^2-1.0" 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 non-numeric 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(1-e^2)*cos(w))/(e^4-2*e^2+1) This is same as Maple answer: (%i9) -2*pi*e*cos(w)/(1-e^2)^1.5\$ ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2989983 ] wrong integration answer From: SourceForge.net - 2011-03-15 20:08:04 ```Bugs item #2989983, was opened at 2010-04-20 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)/1-e^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(1-e^2>0) sage: integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*pi) 0 ---------------------------------------------------------------------- >Comment By: Dan Gildea (dgildea) Date: 2011-03-15 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 generate-atan2 flag set to nil for definite integration is incorrect. Expanding before computing the integral works around this problem. ---------------------------------------------------------------------- Comment By: Aleksas Domarkas (alex108) Date: 2010-04-20 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^2-1.0" 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 non-numeric 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(1-e^2)*cos(w))/(e^4-2*e^2+1) This is same as Maple answer: (%i9) -2*pi*e*cos(w)/(1-e^2)^1.5\$ ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&group_id=4933 ```