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From: SourceForge.net <noreply@so...>  20110603 21:20:06

Bugs item #2995089, was opened at 20100501 07:37 Message generated for change (Settings changed) made by sfrobot 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: Closed Resolution: Works For Me 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: SourceForge Robot (sfrobot) Date: 20110603 21:20 Message: This Tracker item was closed automatically by the system. It was previously set to a Pending status, and the original submitter did not respond within 14 days (the time period specified by the administrator of this Tracker).  Comment By: Dan Gildea (dgildea) Date: 20110520 21:06 Message: Seems OK in current git: (%i2) integrate(cos(b*x)*exp(x^2/a^2),x,0,inf); Is a positive or negative? p; Is b positive or negative? p; (%o2) sqrt(%pi)*a*%e^(a^2*b^2/4)/2  Comment By: Dieter Kaiser (crategus) Date: 20100821 12:14 Message: We had a bug fix for the bug ID: 3034140 "incorrect integration of %e^((x^2*a^2))*cos(b*x)". We get the example of this bug report when we set b=1. At first the correct results. We start with the assumption a>0: (%i1) assume(a>0)$ (%i2) integrate(cos(b*x)*exp(x^2/a^2),x,minf,inf); (%o2) sqrt(%pi)*a*%e^(a^2*b^2/4) (%i3) integrate(cos(b*x)*exp(x^2/a^2),x,0,inf); (%o3) sqrt(%pi)*a*%e^(a^2*b^2/4)/2 Both integrals are correct. There is no problem. Now again with no assumption. The first integral again is correct: (%i4) forget(a>0)$ (%i5) integrate(cos(b*x)*exp(x^2/a^2),x,minf,inf); Is a positive or negative? p; (%o5) sqrt(%pi)*a*%e^(a^2*b^2/4) But the following integral gives an extra factor erf(%i*a*b/2). This is wrong: (%i6) integrate(cos(b*x)*exp(x^2/a^2),x,0,inf); Is a positive or negative? p; Is b positive or negative? p; (%o6) sqrt(%pi)*a*%e^(a^2*b^2/4)*erf(%i*a*b/2)/2 By the way: The behavior of Maxima for this integral differs for Maxima 5.21, 5.22 and current CVS. In all versions of Maxima the indefinite integral is the same: (%i7) integrate(cos(b*x)*exp(x^2/a^2),x); (%o7) sqrt(%pi)*%e^(a^2*b^2/4) *(a*erf((2*x+%i*a^2*b)/(2*a))+a*erf((2*x%i*a^2*b)/(2*a))) /4 Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20100709 21:32 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 12:33 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...>  20110603 15:58:38

Bugs item #3311145, was opened at 20110603 10:58 Message generated for change (Tracker Item Submitted) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311145&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^m * exp(x^2),x,minf,inf) > 0 Initial Comment: Bogus: (%i1) integrate(x^m * exp(x^2),x,minf,inf); "Is "m+1" positive, negative, or zero?"pos; "Is "m" an "integer"?"yes; (%o1) 0  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311145&group_id=4933 
From: SourceForge.net <noreply@so...>  20110603 14:05:59

Bugs item #3311100, was opened at 20110603 16:05 Message generated for change (Tracker Item Submitted) made by sergiopesenti You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311100&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  Plotting Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: sergio pesenti (sergiopesenti) Assigned to: Nobody/Anonymous (nobody) Summary: plot2d problem from 5.24.0 Initial Comment: The following plot does not execute in recent releases of MAXIMA. y(x):=log(abs(1/(1+exp(%i*x))))$ plot2d( y(x),[x,0.1,1])$ MAXIMA complains with "sign: argument cannot be imaginary; found %i" but works with MAXIMA 5.20.1  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311100&group_id=4933 
From: SourceForge.net <noreply@so...>  20110603 10:57:02

Bugs item #3311031, was opened at 20110603 05:57 Message generated for change (Tracker Item Submitted) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311031&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: too complicated result with gcd : 'spmod Initial Comment: OK: (%i5) radcan(exp(((t2*%i)*x^2)/(4*t2*%i))), gcd : 'red; (%o5) %e^(((t2*%i)*x^2)/(4*t2*%i)) Too messy: (%i6) radcan(exp(((t2*%i)*x^2)/(4*t2*%i))), gcd : 'spmod; (%o6) %e^(((32*t^6144*%i*t^5240*t^4+200*%i*t^3+90*t^221*%i*t2)*x^2)/(128*t^6384*%i*t^5480*t^4+320*%i*t^3+120*t^224*%i*t2)) See also http://www.math.utexas.edu/pipermail/maxima/2011/025233.html  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311031&group_id=4933 
From: SourceForge.net <noreply@so...>  20110603 10:51:02

Bugs item #3311028, was opened at 20110603 05:51 Message generated for change (Tracker Item Submitted) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311028&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: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: gcd : red bug Initial Comment: (%i1) integrate((sqrt(22*x^2) * (sqrt(2) + sqrt(2) * x^2))/(44*x^2),x,0,1), gcd : red; `quotient' by `zero'  an error. To debug this try: debugmode(true);  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3311028&group_id=4933 