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From: SourceForge.net <noreply@so...>  20110811 23:51:50

Bugs item #3387042, was opened at 20110806 00:04 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3387042&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: Pending >Resolution: Works For Me Priority: 5 Private: No Submitted By: Petr Kartsev (kpf) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x exp(x^2)) : strange jump Initial Comment: (%i1) integrate( t*exp((ta)^2), t, inf, x); (%o1) (gamma_incomplete(1/2,x^22*a*x+a^2)*a*x)/(2*abs(xa))+(gamma_incomplete(1/2,x^22*a*x+a^2)*a^2)/(2*abs(xa))gamma_incomplete(1,x^22*a*x+a^2)/2 (1st part on screenshot) why is it so complex? when plotting this integral, it has strange jump at point x=1 (and even becomes negative) while the integrand is smooth and mostly always positive) (%i2) plot2d([x*exp((x1)^2), integrate(t*exp((t1)^2), t, inf,x)], [x,5,5])$ (2nd part on screenshot) However, if I simply add and subtract unity, the actual result is recovered: (%i3) integrate( (t1)*exp((t1)^2), t, inf, x)+ integrate( exp((t1)^2), t, inf, x); (%o3) (sqrt(%pi)*erf(x1))/2%e^(x^2+2*x1)/2+sqrt(%pi)/2 (3rd part on screenshot) Looks like additional signum or abs takes place somewhere? Sorry for not giving solution, I am not that skillful in lisp... Thanks for good system, anyway! :)  Maxima version: 5.24.0 Maxima build date: 10:35 8/1/2011 Host type: x86_64pclinuxgnu Lisp implementation type: SBCL Lisp implementation version: 1.0.19gentoo  PS. Just for information, if this can help, run_testsuite() gives 1 error. May be just my installation is wrong? Running tests in rtest16: ********************** Problem 386 *************** Input: closeto(zeta(%i + 3)  (1.10721440843141  .1482908671781754 %i), 1.e15) Result: 3.3157171357748244e9 This differed from the expected result: true   >Comment By: Dieter Kaiser (crategus) Date: 20110812 01:51 Message: One way to avoid questions is to give Maxima facts which are stored in the assume database, e.g. (%i1) assume(x>1); (%o1) [x > 1] (%i2) res:integrate( t*exp((t1)^2), t,minf,x); (%o2) gamma_incomplete(1/2,x^22*x+1)*x/(2*(1x)) gamma_incomplete(1/2,x^22*x+1)/(2*(1x)) gamma_incomplete(1,x^22*x+1)/2+sqrt(%pi) The result can be transformed to a representation in terms of the erfc function with the option variable gamma_expand: (%i3) res, gamma_expand:true; (%o3) sqrt(%pi)*x*erfc(sqrt(x^22*x+1))/(2*(1x)) sqrt(%pi)*erfc(sqrt(x^22*x+1))/(2*(1x))%e^(x^2+2*x1)/2+sqrt(%pi) In addition it is possible to transform to the erf function when setting the option variable erf_representation: (%i4) res,gamma_expand:true, erf_representation:erf; (%o4) sqrt(%pi)*x*(1erf(sqrt(x^22*x+1)))/(2*(1x)) sqrt(%pi)*(1erf(sqrt(x^22*x+1)))/(2*(1x))%e^(x^2+2*x1)/2 +sqrt(%pi) At this point I think we do not have a bug. I suggest to close this bug report as "works for me". Setting the status to pending. Dieter Kaiser  Comment By: Petr Kartsev (kpf) Date: 20110812 00:30 Message: willisbl, thanks for answer. I upgraded to version 5.25 (appeared in Gentoo Linux repository ) and now the behavior is exactly as you posted! However, my question transforms to the following, may be I should file it as dedicated bug report: Can you remove the question "positive/negative/zero" in this situation, as we can see the result is the same (already known erf+exp) for all cases ? This can be possible, in my opinion, since this question is already removed by simply shifting the variable: (%i6) e1(x): integrate( t*exp((t1)^2), t,minf,x); "Is "x1" positive, negative, or zero?" pos; (%o6) (gamma_incomplete(1/2,x^22*x+1)*x)/(2*(1x))gamma_incomplete(1/2,x^22*x+1)/(2*(1x))gamma_incomplete(1,x^22*x+1)/2+sqrt(%pi) but (%i8) e1: integrate( (t+1)*exp(t^2), t,minf,x1); (%o8) (%e^(x^21)*(sqrt(%pi)*%e^(x^2+1)*erf(x1)%e^(2*x)))/2+sqrt(%pi)/2 (My reason is that in my work I differentiate this function and then do some numerical actions for programmed solution with external parameters. Such automatic analysis would get in trouble if it needs to answer positive/negative) Maybe gamma_incomplete is too universal to let simple erf appear in the formula, but erf is sometimes better, so can some special case be implemented? Sorry if I see something wrong. Thanks for attention and for this good tool! Sincerely, Petr F. Kartsev  Comment By: Barton Willis (willisbl) Date: 20110806 03:25 Message: First, you should check your initialization filemaybe you have set some option variables to non default values ; second try this: (%i23) e1 : integrate( t*exp((t1)^2), t,minf,x); "Is "x1" positive, negative, or zero?"neg; (%o23) (gamma_incomplete(1/2,x^22*x+1)*x)/(2*(1x))+gamma_incomplete(1/2,x^22*x+1)/(2*(1x))gamma_incomplete(1,x^22*x+1)/2 (%i24) e2 : integrate( t*exp((t1)^2), t,minf,x); "Is "x1" positive, negative, or zero?"pos; (%o24) (gamma_incomplete(1/2,x^22*x+1)*x)/(2*(1x))gamma_incomplete(1/2,x^22*x+1)/(2*(1x))gamma_incomplete(1,x^22*x+1)/2+sqrt(%pi) (%i25) plot2d(if x < 1 then ''e1 else ''e2,[x,10,10]); The graph appears to be continuous.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3387042&group_id=4933 
From: SourceForge.net <noreply@so...>  20110811 22:30:46

Bugs item #3387042, was opened at 20110806 02:04 Message generated for change (Comment added) made by kpf You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3387042&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: Petr Kartsev (kpf) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x exp(x^2)) : strange jump Initial Comment: (%i1) integrate( t*exp((ta)^2), t, inf, x); (%o1) (gamma_incomplete(1/2,x^22*a*x+a^2)*a*x)/(2*abs(xa))+(gamma_incomplete(1/2,x^22*a*x+a^2)*a^2)/(2*abs(xa))gamma_incomplete(1,x^22*a*x+a^2)/2 (1st part on screenshot) why is it so complex? when plotting this integral, it has strange jump at point x=1 (and even becomes negative) while the integrand is smooth and mostly always positive) (%i2) plot2d([x*exp((x1)^2), integrate(t*exp((t1)^2), t, inf,x)], [x,5,5])$ (2nd part on screenshot) However, if I simply add and subtract unity, the actual result is recovered: (%i3) integrate( (t1)*exp((t1)^2), t, inf, x)+ integrate( exp((t1)^2), t, inf, x); (%o3) (sqrt(%pi)*erf(x1))/2%e^(x^2+2*x1)/2+sqrt(%pi)/2 (3rd part on screenshot) Looks like additional signum or abs takes place somewhere? Sorry for not giving solution, I am not that skillful in lisp... Thanks for good system, anyway! :)  Maxima version: 5.24.0 Maxima build date: 10:35 8/1/2011 Host type: x86_64pclinuxgnu Lisp implementation type: SBCL Lisp implementation version: 1.0.19gentoo  PS. Just for information, if this can help, run_testsuite() gives 1 error. May be just my installation is wrong? Running tests in rtest16: ********************** Problem 386 *************** Input: closeto(zeta(%i + 3)  (1.10721440843141  .1482908671781754 %i), 1.e15) Result: 3.3157171357748244e9 This differed from the expected result: true   >Comment By: Petr Kartsev (kpf) Date: 20110812 02:30 Message: willisbl, thanks for answer. I upgraded to version 5.25 (appeared in Gentoo Linux repository ) and now the behavior is exactly as you posted! However, my question transforms to the following, may be I should file it as dedicated bug report: Can you remove the question "positive/negative/zero" in this situation, as we can see the result is the same (already known erf+exp) for all cases ? This can be possible, in my opinion, since this question is already removed by simply shifting the variable: (%i6) e1(x): integrate( t*exp((t1)^2), t,minf,x); "Is "x1" positive, negative, or zero?" pos; (%o6) (gamma_incomplete(1/2,x^22*x+1)*x)/(2*(1x))gamma_incomplete(1/2,x^22*x+1)/(2*(1x))gamma_incomplete(1,x^22*x+1)/2+sqrt(%pi) but (%i8) e1: integrate( (t+1)*exp(t^2), t,minf,x1); (%o8) (%e^(x^21)*(sqrt(%pi)*%e^(x^2+1)*erf(x1)%e^(2*x)))/2+sqrt(%pi)/2 (My reason is that in my work I differentiate this function and then do some numerical actions for programmed solution with external parameters. Such automatic analysis would get in trouble if it needs to answer positive/negative) Maybe gamma_incomplete is too universal to let simple erf appear in the formula, but erf is sometimes better, so can some special case be implemented? Sorry if I see something wrong. Thanks for attention and for this good tool! Sincerely, Petr F. Kartsev  Comment By: Barton Willis (willisbl) Date: 20110806 05:25 Message: First, you should check your initialization filemaybe you have set some option variables to non default values ; second try this: (%i23) e1 : integrate( t*exp((t1)^2), t,minf,x); "Is "x1" positive, negative, or zero?"neg; (%o23) (gamma_incomplete(1/2,x^22*x+1)*x)/(2*(1x))+gamma_incomplete(1/2,x^22*x+1)/(2*(1x))gamma_incomplete(1,x^22*x+1)/2 (%i24) e2 : integrate( t*exp((t1)^2), t,minf,x); "Is "x1" positive, negative, or zero?"pos; (%o24) (gamma_incomplete(1/2,x^22*x+1)*x)/(2*(1x))gamma_incomplete(1/2,x^22*x+1)/(2*(1x))gamma_incomplete(1,x^22*x+1)/2+sqrt(%pi) (%i25) plot2d(if x < 1 then ''e1 else ''e2,[x,10,10]); The graph appears to be continuous.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3387042&group_id=4933 
From: SourceForge.net <noreply@so...>  20110811 19:29:38

Bugs item #3389830, was opened at 20110811 00:19 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3389830&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 Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Error break in rtest15 with linear display Initial Comment: I have run the testfile rtest15.mac in linear display and with display_all=true and I have got an error break. (%i1) display2d:false; (%o1) false (%i2) run_testsuite(display_all=true, tests=[rtest15]); Running tests in rtest15: [...] ********************** Problem 203 *************** Input: Caused an error break: rtest15 Error summary: Error found in rtest15, problem: (error break) 0 tests failed out of 0 total tests. This is a short example to show the problem: (%i1) display2d:false; (%o1) false (%i2) postfix("f"); (%o2) "f" (%i3) "f"(x) := x; (%o3) Maxima encountered a Lisp error: The value #\x is not of type LIST. Automatically continuing. To enable the Lisp debugger set *debuggerhook* to nil. Maxima can not display the definition in (%i3) for a postfixoperator in linear display. It works in 2ddisplay. It is an old bug. I have observed it in all Maxima versions since 5.9. Dieter Kaiser  >Comment By: Dieter Kaiser (crategus) Date: 20110811 21:29 Message: Fixed in grind.lisp revision 11.08.2011. The function mszmdef has been extended to handle prefix and postfix operators. Closing this bug report as fixed. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3389830&group_id=4933 