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From: SourceForge.net <noreply@so...>  20100525 13:55:43

Bugs item #3006875, was opened at 20100525 17:55 Message generated for change (Tracker Item Submitted) made by aleckalinin You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&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: akalinin (aleckalinin) Assigned to: Nobody/Anonymous (nobody) Summary: ldefint() integration seems to be not correct Initial Comment: The ldefint() integration seems to be not correct. I compared Maxima results with Maple results. I tried to integrate "Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);" function and I got three strange results in Maxima: 1. Too many terms in sum after integration. 2. Some terms have strange "false" factor in numerator. 3. Several terms have the singularity 1/epsilon, epsilon > 0. The Maple integration produces less terms and no 1/epsilon singularity. Please, see attachments for details. I put the Maxima "false" strange term and singular term in double bar.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&group_id=4933 
From: SourceForge.net <noreply@so...>  20100525 20:34:20

Bugs item #3006875, was opened at 20100525 13:55 Message generated for change (Comment added) made by You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&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: akalinin (aleckalinin) Assigned to: Nobody/Anonymous (nobody) Summary: ldefint() integration seems to be not correct Initial Comment: The ldefint() integration seems to be not correct. I compared Maxima results with Maple results. I tried to integrate "Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);" function and I got three strange results in Maxima: 1. Too many terms in sum after integration. 2. Some terms have strange "false" factor in numerator. 3. Several terms have the singularity 1/epsilon, epsilon > 0. The Maple integration produces less terms and no 1/epsilon singularity. Please, see attachments for details. I put the Maxima "false" strange term and singular term in double bar.  Comment By: l_butler () Date: 20100525 20:34 Message: Hi, Thanks for the report. A few comments: 1. Rather than using expand, try ratsimp. This produces a relatively compact expression. 2. I can confirm there is a bug in Maxima's integral with v5.21.1: false appears as a term. When a1=0, this term disappears. 3. If you look at your integrand, when epsilon=0 (a1 is irrelevant), you are computing the integral of 1/x from 0 to QL, which diverges. From that, one expects that the integral will have a singularity at epsilon=0. If Maple doesn't produce such a result, this is a bug in Maple. Please report your version of Maxima when filing a bug report. Just copy the output of the 'build_info' command into your report.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&group_id=4933 
From: SourceForge.net <noreply@so...>  20100526 08:22:03

Bugs item #3006875, was opened at 20100525 17:55 Message generated for change (Comment added) made by aleckalinin You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&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: akalinin (aleckalinin) Assigned to: Nobody/Anonymous (nobody) Summary: ldefint() integration seems to be not correct Initial Comment: The ldefint() integration seems to be not correct. I compared Maxima results with Maple results. I tried to integrate "Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);" function and I got three strange results in Maxima: 1. Too many terms in sum after integration. 2. Some terms have strange "false" factor in numerator. 3. Several terms have the singularity 1/epsilon, epsilon > 0. The Maple integration produces less terms and no 1/epsilon singularity. Please, see attachments for details. I put the Maxima "false" strange term and singular term in double bar.  >Comment By: akalinin (aleckalinin) Date: 20100526 12:22 Message: Thanks for comments. Version of maxima: Maxima version: 5.21.0 Maxima build date: 8:38 4/12/2010 Host type: i686pcmingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 About the divergence. It should be log(epsilon) but not 1/epsilon. And after integration I manually separate this log(epsilon) term. Without a1 coefficient Maxima works correct, see maximaresults2.pdf and maximascript2.mac in attachment. In this case both Maxima and Maple produces the same results. But when the a1 term is present, Maxima produces 1/epsilon divergence. I think this is not right, because a1 term cannot change the behavior of the integral.  Comment By: l_butler () Date: 20100526 00:34 Message: Hi, Thanks for the report. A few comments: 1. Rather than using expand, try ratsimp. This produces a relatively compact expression. 2. I can confirm there is a bug in Maxima's integral with v5.21.1: false appears as a term. When a1=0, this term disappears. 3. If you look at your integrand, when epsilon=0 (a1 is irrelevant), you are computing the integral of 1/x from 0 to QL, which diverges. From that, one expects that the integral will have a singularity at epsilon=0. If Maple doesn't produce such a result, this is a bug in Maple. Please report your version of Maxima when filing a bug report. Just copy the output of the 'build_info' command into your report.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&group_id=4933 
From: SourceForge.net <noreply@so...>  20100526 10:42:50

Bugs item #3006875, was opened at 20100525 17:55 Message generated for change (Comment added) made by aleckalinin You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&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: akalinin (aleckalinin) Assigned to: Nobody/Anonymous (nobody) Summary: ldefint() integration seems to be not correct Initial Comment: The ldefint() integration seems to be not correct. I compared Maxima results with Maple results. I tried to integrate "Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);" function and I got three strange results in Maxima: 1. Too many terms in sum after integration. 2. Some terms have strange "false" factor in numerator. 3. Several terms have the singularity 1/epsilon, epsilon > 0. The Maple integration produces less terms and no 1/epsilon singularity. Please, see attachments for details. I put the Maxima "false" strange term and singular term in double bar.  Comment By: akalinin (aleckalinin) Date: 20100526 14:42 Message: Some additional information. I tried to use integrate(...) instead of ldefint(...) and got the incorrect results. The coefficient a1 change the behavior of the integral:  Maxima script  logexpand : all; logarc : true; assume(epsilon > 0); assume(a1 > 0); assume(a1  2.0 > 0); kern1 : Lambda^4 / (Lambda^2 + epsilon * Lambda + epsilon^2 )^(5/2); kern2 : Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2); phi1 : integrate(kern1, Lambda); phi2 : integrate(kern2, Lambda); phi2 : subst(a1 = 1, phi2); res : phi2  phi1;  The res is not zero!  Comment By: akalinin (aleckalinin) Date: 20100526 12:22 Message: Thanks for comments. Version of maxima: Maxima version: 5.21.0 Maxima build date: 8:38 4/12/2010 Host type: i686pcmingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 About the divergence. It should be log(epsilon) but not 1/epsilon. And after integration I manually separate this log(epsilon) term. Without a1 coefficient Maxima works correct, see maximaresults2.pdf and maximascript2.mac in attachment. In this case both Maxima and Maple produces the same results. But when the a1 term is present, Maxima produces 1/epsilon divergence. I think this is not right, because a1 term cannot change the behavior of the integral.  Comment By: l_butler () Date: 20100526 00:34 Message: Hi, Thanks for the report. A few comments: 1. Rather than using expand, try ratsimp. This produces a relatively compact expression. 2. I can confirm there is a bug in Maxima's integral with v5.21.1: false appears as a term. When a1=0, this term disappears. 3. If you look at your integrand, when epsilon=0 (a1 is irrelevant), you are computing the integral of 1/x from 0 to QL, which diverges. From that, one expects that the integral will have a singularity at epsilon=0. If Maple doesn't produce such a result, this is a bug in Maple. Please report your version of Maxima when filing a bug report. Just copy the output of the 'build_info' command into your report.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&group_id=4933 
From: SourceForge.net <noreply@so...>  20100710 14:08:52

Bugs item #3006875, was opened at 20100525 15:55 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&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: akalinin (aleckalinin) Assigned to: Nobody/Anonymous (nobody) Summary: ldefint() integration seems to be not correct Initial Comment: The ldefint() integration seems to be not correct. I compared Maxima results with Maple results. I tried to integrate "Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);" function and I got three strange results in Maxima: 1. Too many terms in sum after integration. 2. Some terms have strange "false" factor in numerator. 3. Several terms have the singularity 1/epsilon, epsilon > 0. The Maple integration produces less terms and no 1/epsilon singularity. Please, see attachments for details. I put the Maxima "false" strange term and singular term in double bar.  >Comment By: Dieter Kaiser (crategus) Date: 20100710 16:08 Message: It is easier to see the problem of this bug report, when we reduce the problem to the following integrand: x^4 * (a*x^2 + b*x + c)^(5/2) When we assume a>0, b>0, c>0 and b^24*a*c>0 and try to get the integral integrate(x^4*(a*x^2+b*x+x)^(5/2), x) we get a wrong answer which includes a term 9*false. We can further simplify the example and set a=1. Then we have the integrand x^4 * (x^2 + b*x +c)^(5/2) When we assume again b>0, c>0, and b^24*c>0 then we get a wrong answer too (%i1) assume(b>0,c>0,b^24*c>0)$ (%i2) integrate(x^4*(x^2+b*x+c)^(5/2),x); (%o2) 7*false+log(2*sqrt(x^2+b*x+c)+2*x+b) +x*(32*b*c*x/(3*(4*cb^2)^2*sqrt(x^2+b*x+c)) +2*b*(4*c+b^2)*x/(3*(4*cb^2)^2*sqrt(x^2+b*x+c)) 16*b^2*c/(3*(4*cb^2)^2*sqrt(x^2+b*x+c)) +b^2*(4*c+b^2)/(3*(4*cb^2)^2*sqrt(x^2+b*x+c)) x^2/(x^2+b*x+c)^(3/2)2*b*c*x/((4*cb^2)*(x^2+b*x+c)^(3/2)) +b^3*x/(3*(4*cb^2)*(x^2+b*x+c)^(3/2)) b^2*c/(3*(4*cb^2)*(x^2+b*x+c)^(3/2)) 2*c/(3*(x^2+b*x+c)^(3/2))) 4*c*x/(3*(4*cb^2)*sqrt(x^2+b*x+c)) +2*b^2*x/((4*cb^2)*sqrt(x^2+b*x+c)) +10*b*c/(3*(4*cb^2)*sqrt(x^2+b*x+c)) For this case we get an answer with a term 7*false. The problem occurs in the routine INTIRA in the file irinte.lisp. This routine detects correctly a integration problem of the type (1) d*p(x)*x^m*(a*x^2+b*x+x)^n I have not analyzed the integration process in detail, but the algorithm produces a list of subproblems which are passed again to the routine INTIRA. For our example from above, the algorithm founds 7 subproblems. Furthermore, the algorithm assumes that all subproblems are again of the type (1) and have a solution. But the routine INTIRA does not return a solution, the answer for this subproblems is false. These false terms are added up. I think the problem is, that the expression which are passed again to the routine INTIRA are of the type (1), but the routine INTIRA does not recognize it. The following expression is one of the seven subproblems INTIRA has to solve: b^3*x/(12*c*(x^2+b*x+c)^(3/2)3*b^2*(x^2+b*x+c)^(3/2)) It is difficult to see in linear display, but this expression is of the type INTIRA can solve, but INTIRA does not match it, because the root (x^2+b*x+c)^(3/2) is distributed over two terms. To see that INTIRA in principle can solve the problem we can rewrite the expression from above the following way b^3*(12*c3*b^2)^1 * x * (x^2+b*x+c)^(3/2) The problem is that the root is distributed over the constant term (12*c3*b^2)^1 It might be difficult to solve this problem in general, but at least, the algorithm should recognize that a subproblem was not solved. A correct answer would be a noun form for the integral for this case. Dieter Kaiser  Comment By: akalinin (aleckalinin) Date: 20100526 12:42 Message: Some additional information. I tried to use integrate(...) instead of ldefint(...) and got the incorrect results. The coefficient a1 change the behavior of the integral:  Maxima script  logexpand : all; logarc : true; assume(epsilon > 0); assume(a1 > 0); assume(a1  2.0 > 0); kern1 : Lambda^4 / (Lambda^2 + epsilon * Lambda + epsilon^2 )^(5/2); kern2 : Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2); phi1 : integrate(kern1, Lambda); phi2 : integrate(kern2, Lambda); phi2 : subst(a1 = 1, phi2); res : phi2  phi1;  The res is not zero!  Comment By: akalinin (aleckalinin) Date: 20100526 10:22 Message: Thanks for comments. Version of maxima: Maxima version: 5.21.0 Maxima build date: 8:38 4/12/2010 Host type: i686pcmingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 About the divergence. It should be log(epsilon) but not 1/epsilon. And after integration I manually separate this log(epsilon) term. Without a1 coefficient Maxima works correct, see maximaresults2.pdf and maximascript2.mac in attachment. In this case both Maxima and Maple produces the same results. But when the a1 term is present, Maxima produces 1/epsilon divergence. I think this is not right, because a1 term cannot change the behavior of the integral.  Comment By: l_butler () Date: 20100525 22:34 Message: Hi, Thanks for the report. A few comments: 1. Rather than using expand, try ratsimp. This produces a relatively compact expression. 2. I can confirm there is a bug in Maxima's integral with v5.21.1: false appears as a term. When a1=0, this term disappears. 3. If you look at your integrand, when epsilon=0 (a1 is irrelevant), you are computing the integral of 1/x from 0 to QL, which diverges. From that, one expects that the integral will have a singularity at epsilon=0. If Maple doesn't produce such a result, this is a bug in Maple. Please report your version of Maxima when filing a bug report. Just copy the output of the 'build_info' command into your report.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3006875&group_id=4933 