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## [Maxima-bugs] [ maxima-Bugs-2815766 ] strange results from eigenvalues

 [Maxima-bugs] [ maxima-Bugs-2815766 ] strange results from eigenvalues From: SourceForge.net - 2009-07-22 02:20:20 ```Bugs item #2815766, was opened at 2009-07-02 12:57 Message generated for change (Comment added) made by sf-robot You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&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 - Solving equations Group: None >Status: Closed Resolution: Invalid Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: strange results from eigenvalues Initial Comment: large matrices like matrix([72126.5,-25007.8,7670.53],[-25007.8,8670.74,-2659.53],[7670.53,-2659.53,818.809]) produce strange outputs: (%i32) eigenvalues(T); rat: replaced 25007.8 by 125039/5 = 25007.8 rat: replaced 2.0400004650900003E+7 by 20400005/1 = 2.0400005E+7 rat: replaced -25007.8 by -125039/5 = -25007.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 7670.53 by 767053/100 = 7670.53 rat: replaced 6.6508994334000006E+7 by 66508994/1 = 6.6508994E+7 rat: replaced -7670.53 by -767053/100 = -7670.53 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced -7073099.8209 by -35365499/5 = -7073099.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced 72126.5 by 144253/2 = 72126.5 (%o32) [[(-(sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*((sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*(-(sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+58619247149883207/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225],[1,1,1]] ovtave gives followin: octave.exe:3> t = >[72126.5, -25007.8, 7670.53; > -25007.8, 8670.74, -2659.53; > 7670.53, -2659.53, 818.809]; octave.exe:4> eig(t) ans = 8.2521e-004 3.0311e+000 8.1613e+004 ---------------------------------------------------------------------- >Comment By: SourceForge Robot (sf-robot) Date: 2009-07-22 02:20 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: Raymond Toy (rtoy) Date: 2009-07-07 18:24 Message: Marking as pending/invalid so this will be closed automatically in two weeks. I don't think there's anything wrong here. If you disagree, please comment on this. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2009-07-02 13:30 Message: In what way is the result strange? Eigenvalues the floats to rationals and does a symbolic calculation. Hence the long answer. If you want a float result, you can use float and rectform to get [[6.912159733474255e-11 %i + 2.999728814902483, .03218669009947916 - 6.548361852765083e-11 %i, 81613.01707325905 - 2.442490654175344e-15 %i], [1.0, 1.0, 1.0]] (These aren't quite the same as octave.) If you numeric results, you can try dgeev. This produces [81613.01707247499, 8.252057359223741e-4, 3.031102319243371] This is probably the same routine that octave uses to find eigenvalues. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&group_id=4933 ```

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 [Maxima-bugs] [ maxima-Bugs-2815766 ] strange results from eigenvalues From: SourceForge.net - 2009-07-02 12:57:24 ```Bugs item #2815766, was opened at 2009-07-02 12:57 Message generated for change (Tracker Item Submitted) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&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 - Solving equations Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: strange results from eigenvalues Initial Comment: large matrices like matrix([72126.5,-25007.8,7670.53],[-25007.8,8670.74,-2659.53],[7670.53,-2659.53,818.809]) produce strange outputs: (%i32) eigenvalues(T); rat: replaced 25007.8 by 125039/5 = 25007.8 rat: replaced 2.0400004650900003E+7 by 20400005/1 = 2.0400005E+7 rat: replaced -25007.8 by -125039/5 = -25007.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 7670.53 by 767053/100 = 7670.53 rat: replaced 6.6508994334000006E+7 by 66508994/1 = 6.6508994E+7 rat: replaced -7670.53 by -767053/100 = -7670.53 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced -7073099.8209 by -35365499/5 = -7073099.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced 72126.5 by 144253/2 = 72126.5 (%o32) [[(-(sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*((sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*(-(sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+58619247149883207/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225],[1,1,1]] ovtave gives followin: octave.exe:3> t = >[72126.5, -25007.8, 7670.53; > -25007.8, 8670.74, -2659.53; > 7670.53, -2659.53, 818.809]; octave.exe:4> eig(t) ans = 8.2521e-004 3.0311e+000 8.1613e+004 ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2815766 ] strange results from eigenvalues From: SourceForge.net - 2009-07-02 13:30:41 ```Bugs item #2815766, was opened at 2009-07-02 08:57 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&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 - Solving equations Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: strange results from eigenvalues Initial Comment: large matrices like matrix([72126.5,-25007.8,7670.53],[-25007.8,8670.74,-2659.53],[7670.53,-2659.53,818.809]) produce strange outputs: (%i32) eigenvalues(T); rat: replaced 25007.8 by 125039/5 = 25007.8 rat: replaced 2.0400004650900003E+7 by 20400005/1 = 2.0400005E+7 rat: replaced -25007.8 by -125039/5 = -25007.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 7670.53 by 767053/100 = 7670.53 rat: replaced 6.6508994334000006E+7 by 66508994/1 = 6.6508994E+7 rat: replaced -7670.53 by -767053/100 = -7670.53 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced -7073099.8209 by -35365499/5 = -7073099.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced 72126.5 by 144253/2 = 72126.5 (%o32) [[(-(sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*((sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*(-(sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+58619247149883207/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225],[1,1,1]] ovtave gives followin: octave.exe:3> t = >[72126.5, -25007.8, 7670.53; > -25007.8, 8670.74, -2659.53; > 7670.53, -2659.53, 818.809]; octave.exe:4> eig(t) ans = 8.2521e-004 3.0311e+000 8.1613e+004 ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2009-07-02 09:30 Message: In what way is the result strange? Eigenvalues the floats to rationals and does a symbolic calculation. Hence the long answer. If you want a float result, you can use float and rectform to get [[6.912159733474255e-11 %i + 2.999728814902483, .03218669009947916 - 6.548361852765083e-11 %i, 81613.01707325905 - 2.442490654175344e-15 %i], [1.0, 1.0, 1.0]] (These aren't quite the same as octave.) If you numeric results, you can try dgeev. This produces [81613.01707247499, 8.252057359223741e-4, 3.031102319243371] This is probably the same routine that octave uses to find eigenvalues. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2815766 ] strange results from eigenvalues From: SourceForge.net - 2009-07-07 18:24:17 ```Bugs item #2815766, was opened at 2009-07-02 08:57 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&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 - Solving equations Group: None >Status: Pending >Resolution: Invalid Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: strange results from eigenvalues Initial Comment: large matrices like matrix([72126.5,-25007.8,7670.53],[-25007.8,8670.74,-2659.53],[7670.53,-2659.53,818.809]) produce strange outputs: (%i32) eigenvalues(T); rat: replaced 25007.8 by 125039/5 = 25007.8 rat: replaced 2.0400004650900003E+7 by 20400005/1 = 2.0400005E+7 rat: replaced -25007.8 by -125039/5 = -25007.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 7670.53 by 767053/100 = 7670.53 rat: replaced 6.6508994334000006E+7 by 66508994/1 = 6.6508994E+7 rat: replaced -7670.53 by -767053/100 = -7670.53 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced -7073099.8209 by -35365499/5 = -7073099.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced 72126.5 by 144253/2 = 72126.5 (%o32) [[(-(sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*((sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*(-(sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+58619247149883207/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225],[1,1,1]] ovtave gives followin: octave.exe:3> t = >[72126.5, -25007.8, 7670.53; > -25007.8, 8670.74, -2659.53; > 7670.53, -2659.53, 818.809]; octave.exe:4> eig(t) ans = 8.2521e-004 3.0311e+000 8.1613e+004 ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2009-07-07 14:24 Message: Marking as pending/invalid so this will be closed automatically in two weeks. I don't think there's anything wrong here. If you disagree, please comment on this. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2009-07-02 09:30 Message: In what way is the result strange? Eigenvalues the floats to rationals and does a symbolic calculation. Hence the long answer. If you want a float result, you can use float and rectform to get [[6.912159733474255e-11 %i + 2.999728814902483, .03218669009947916 - 6.548361852765083e-11 %i, 81613.01707325905 - 2.442490654175344e-15 %i], [1.0, 1.0, 1.0]] (These aren't quite the same as octave.) If you numeric results, you can try dgeev. This produces [81613.01707247499, 8.252057359223741e-4, 3.031102319243371] This is probably the same routine that octave uses to find eigenvalues. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2815766 ] strange results from eigenvalues From: SourceForge.net - 2009-07-22 02:20:20 ```Bugs item #2815766, was opened at 2009-07-02 12:57 Message generated for change (Comment added) made by sf-robot You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&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 - Solving equations Group: None >Status: Closed Resolution: Invalid Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: strange results from eigenvalues Initial Comment: large matrices like matrix([72126.5,-25007.8,7670.53],[-25007.8,8670.74,-2659.53],[7670.53,-2659.53,818.809]) produce strange outputs: (%i32) eigenvalues(T); rat: replaced 25007.8 by 125039/5 = 25007.8 rat: replaced 2.0400004650900003E+7 by 20400005/1 = 2.0400005E+7 rat: replaced -25007.8 by -125039/5 = -25007.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 7670.53 by 767053/100 = 7670.53 rat: replaced 6.6508994334000006E+7 by 66508994/1 = 6.6508994E+7 rat: replaced -7670.53 by -767053/100 = -7670.53 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced -7073099.8209 by -35365499/5 = -7073099.8 rat: replaced 818.809 by 72874/89 = 818.8089887640449 rat: replaced 8670.74 by 433537/50 = 8670.74 rat: replaced 72126.5 by 144253/2 = 72126.5 (%o32) [[(-(sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*((sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((sqrt(3)*%i)/2-1/2)*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+(58619247149883207*(-(sqrt(3)*%i)/2-1/2))/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225,((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3)+58619247149883207/(79210000*((3*sqrt(12608488167242884134811801138679920231)*%i)/(3960500000*sqrt(2))+2838509476210882261900497/140993800000)^(1/3))+60531903/2225],[1,1,1]] ovtave gives followin: octave.exe:3> t = >[72126.5, -25007.8, 7670.53; > -25007.8, 8670.74, -2659.53; > 7670.53, -2659.53, 818.809]; octave.exe:4> eig(t) ans = 8.2521e-004 3.0311e+000 8.1613e+004 ---------------------------------------------------------------------- >Comment By: SourceForge Robot (sf-robot) Date: 2009-07-22 02:20 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: Raymond Toy (rtoy) Date: 2009-07-07 18:24 Message: Marking as pending/invalid so this will be closed automatically in two weeks. I don't think there's anything wrong here. If you disagree, please comment on this. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2009-07-02 13:30 Message: In what way is the result strange? Eigenvalues the floats to rationals and does a symbolic calculation. Hence the long answer. If you want a float result, you can use float and rectform to get [[6.912159733474255e-11 %i + 2.999728814902483, .03218669009947916 - 6.548361852765083e-11 %i, 81613.01707325905 - 2.442490654175344e-15 %i], [1.0, 1.0, 1.0]] (These aren't quite the same as octave.) If you numeric results, you can try dgeev. This produces [81613.01707247499, 8.252057359223741e-4, 3.031102319243371] This is probably the same routine that octave uses to find eigenvalues. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2815766&group_id=4933 ```