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From: SourceForge.net <noreply@so...>  20100709 21:32:58

Bugs item #2995089, was opened at 20100501 09:37 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2995089&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: Sam Hagen (neanderslob) Assigned to: Nobody/Anonymous (nobody) Summary: arbitrary constant exponent seems to confound integration Initial Comment: It can best be explained by a look at the HTML file attached, I have comments in there as well to point out what to look at. It appears that the power of an arbitrary constant will affect the outcome of an integration.  >Comment By: Dieter Kaiser (crategus) Date: 20100709 23:32 Message: The problem of this bug report is caused by the behavior of Maxima to return INFINITY for the following limit: limit(r/a, r, inf) > infinity If the sign of the parameter a is known to be positive Maxima gives limit(r/a, r, inf) > inf This is related to the problem of this bug report the following way. The indefinite integral is (%i1) integrate(cos(r)*exp(r^2/a^2),r),factor; (%o1) sqrt(%pi)*a*%e^(a^2/4) *(erf((2*r+%i*a^2)/(2*a))+erf((2*r%i*a^2)/(2*a))) /4 This answer is correct. It contains two erf terms. The problem is the limit of the erf function for r > inf. We take one of the terms: (%i2) limit(erf((2*r+%i*a^2)/(2*a)), r, inf); (%o2) und The realpart of the argument is r/a. Maxima returns INFINITY for the limit of the argument because the sign of r/a is not known. This gives UND as the result for the erf function and as a consequence UND as the result for the definite integral. So the problem of this bug report is, that Maxima returns immediately INFINITY for the limit of r/a and does not ask for the sign of the parameter a. Of course, Maxima gets the correct answer, if we assume the parameter a to be positive, but the user might not recognize that this information is necessary, because a limit has to be evaluated for an expression r/a. (%i6) assume(a>0)$ (%i7) integrate(cos(r)*exp(r^2/a^2),r,0,inf),factor; (%o7) sqrt(%pi)*a*%e^(a^2/4)/2 Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20100501 14:33 Message: Thank you very much for the report. The underlying problem of this bug report is the following definite integral. We have a constant a in the exponent of the exp function: (%i1) integrate(cos(r)*exp(r^2/a),r,0,inf); Is a positive or negative? p; (%o1) sqrt(%pi)*sqrt(a)*%e^(a/4)/2 When we take the square of the constant, Maxima no longer gets a result: (%i2) integrate(cos(r)*exp(r^2/a^2),r,0,inf); (%o2) und It works again if we assume a to be positive. This is a bit strange, because a^2 is known to be positive too: (%i3) assume(a>0)$ (%i4) integrate(cos(r)*exp(r^2/a^2),r,0,inf); (%o4) sqrt(%pi)*a*%e^(a^2/4)/2 There is a second problem. The derivative of 'und gives 0. 'und is the intermediate result of the integration of the example of this bug report: (%i2) diff(und,q); (%o2) 0 Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2995089&group_id=4933 
From: SourceForge.net <noreply@so...>  20100709 19:08:05

Bugs item #2977217, was opened at 20100326 19:58 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2977217&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: maxima can not integrate x*exp(1/2*(xm)^2) Initial Comment: Maxima can not integrate the function x*exp(1/2*(xm)^2) Maxima 5.20.1 http://maxima.sourceforge.net using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) integrate(x*exp(1/2*(xm)^2),x); 2 (x  m) /   [ 2 (%o1) I x %e dx ] / The correct solution would be (%i2) diff(exp(1/2*x^2+m*x1/2*m^2)+1/2*m*sqrt(%pi)*sqrt(2)*erf(1/2*sqrt(2)*x1/2*m*sqrt(2)),x); 2 2 x m 2 x m  (  )   + m x   sqrt(2) sqrt(2) 2 2 (%o2) m %e  (m  x) %e  >Comment By: Dieter Kaiser (crategus) Date: 20100709 21:08 Message: Fixed in sin.lisp revision 1.67. Maxima can now calculate the integral of this bug report. 'The result is not as nice as the expected result, but can be shown to be equivalent up to a constant: (%i48) multthru(integrate(x*exp(1/2*(xm)^2),x)),gamma_expand:true,erf_representation:erf; (%o48) sqrt(%pi)*m*(mx)*(1erf(abs(xm)/sqrt(2)))/(sqrt(2)*abs(xm)) (mx)^2*%e^((mx)^2/2)/(xm)^2 Closing this bug report as fixed. Dieter Kaiser  Comment By: Robert Dodier (robert_dodier) Date: 20100605 19:01 Message: Wow, that's pretty surprising. Maxima can solve integrate(exp((1/2)*(x  m)^2), x) so why not this one?  Comment By: uhlst (uhlst) Date: 20100327 15:45 Message: Thank you for showing this "trick" with changevar. Is there a way that Maxima automatically does the correct substitution without giving it a hint with changevar? If e.g. the "1/2" in the exponent is removed, then Maxima has no problem to do the integration. Does Maxima not try itself some substitutions if integrate is called?  Comment By: Aleksas Domarkas (alex108) Date: 20100326 21:40 Message: (%i1) S:'integrate(x*exp(1/2*(xm)^2),x); (%o1) integrate(x*%e^((xm)^2/2),x) (%i2) changevar(S, y=xm, y, x); (%o2) integrate((y+m)*%e^(y^2/2),y) (%i3) ev(%, nouns); (%o3) (sqrt(%pi)*m*erf(y/sqrt(2)))/sqrt(2)%e^(y^2/2) Solution: (%i4) sol:subst(y=xm,%),rootscontract; (%o4) sqrt(%pi/2)*m*erf((xm)/sqrt(2))%e^((xm)^2/2) Test: (%i5) diff(sol,x)first(S)$ (%i6) expand(%); (%o6) 0  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2977217&group_id=4933 
From: SourceForge.net <noreply@so...>  20100709 18:59:43

Bugs item #3027529, was opened at 20100709 20:57 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3027529&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: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) >Summary: integrate(logarc(atan2(y,x)),y) > Divison by zero Initial Comment: When we try to integrate the equivalent logarithmic expression for atan2 we get an error: (%i34) integrate(logarc(atan2(y,x)),x); Division by 0  an error. To debug this try: debugmode(true); (%i35) integrate(logarc(atan2(y,x)),y); Division by 0  an error. To debug this try: debugmode(true); The error occurs in ratint. ratint tries to integrate the following expression: (%i36) expr; (%o36) x^3/(%i*y^3+x*y^2+%i*x^2*y+x^3) (%i37) integrate(expr,x); 0: (RATINT ((MTIMES SIMP) ((MEXPT SIMP) $X 3) ((MEXPT SIMP) ((MPLUS SIMP) ((MEXPT SIMP) $X 3) ((MTIMES SIMP) $%I ((MEXPT SIMP) $X 2) $Y) ((MTIMES SIMP) $X ((MEXPT SIMP) $Y 2)) ((MTIMES SIMP) $%I ((MEXPT SIMP) $Y 3))) 1)) $X) Division by 0  an error. To debug this try: debugmode(true); Dieter Kaiser  >Comment By: Dieter Kaiser (crategus) Date: 20100709 20:59 Message: Correcting the title.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3027529&group_id=4933 
From: SourceForge.net <noreply@so...>  20100709 18:57:27

Bugs item #3027529, was opened at 20100709 20:57 Message generated for change (Tracker Item Submitted) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3027529&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: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(logarc(atan2(y,x),y) > Divison by zero Initial Comment: When we try to integrate the equivalent logarithmic expression for atan2 we get an error: (%i34) integrate(logarc(atan2(y,x)),x); Division by 0  an error. To debug this try: debugmode(true); (%i35) integrate(logarc(atan2(y,x)),y); Division by 0  an error. To debug this try: debugmode(true); The error occurs in ratint. ratint tries to integrate the following expression: (%i36) expr; (%o36) x^3/(%i*y^3+x*y^2+%i*x^2*y+x^3) (%i37) integrate(expr,x); 0: (RATINT ((MTIMES SIMP) ((MEXPT SIMP) $X 3) ((MEXPT SIMP) ((MPLUS SIMP) ((MEXPT SIMP) $X 3) ((MTIMES SIMP) $%I ((MEXPT SIMP) $X 2) $Y) ((MTIMES SIMP) $X ((MEXPT SIMP) $Y 2)) ((MTIMES SIMP) $%I ((MEXPT SIMP) $Y 3))) 1)) $X) Division by 0  an error. To debug this try: debugmode(true); Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3027529&group_id=4933 