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From: SourceForge.net <noreply@so...>  20080331 20:29:12

Bugs item #1930350, was opened at 20080331 19:28 Message generated for change (Comment added) made by andrejv You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1930350&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: 2^2391 does not factorize properly Initial Comment: I TYPED: :lisp (factor (factor ( (expt 2 239) 1))); RESULT: ((MTIMES SIMP FACTORED) 479 1913 5737 168048109206150821918223503032486170915673848376760773023074113) EXPECTED: ((MTIMES SIMP FACTORED)479 1913 5737 176383 134000609 7110008717824458123105014279253754096863768062879) EMAIL: irdaqramo@...  >Comment By: Andrej Vodopivec (andrejv) Date: 20080331 22:29 Message: Logged In: YES user_id=1179910 Originator: NO This working as intended. The simplification routines in maxima sometimes factor integers. For obvious reasons, factoring large integers is disabled by default. This is controlled with the option variable intfaclim. This command gives correct factorization: :lisp (let (($intfaclim nil)) (factor ( (expt 2 239) 1))) This bug should be closed as invalid. I will leave it open for some time in case someone returns to see a reply. Andrej  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1930350&group_id=4933 
From: SourceForge.net <noreply@so...>  20080331 17:28:51

Bugs item #1930350, was opened at 20080331 10:28 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1930350&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: 2^2391 does not factorize properly Initial Comment: I TYPED: :lisp (factor (factor ( (expt 2 239) 1))); RESULT: ((MTIMES SIMP FACTORED) 479 1913 5737 168048109206150821918223503032486170915673848376760773023074113) EXPECTED: ((MTIMES SIMP FACTORED)479 1913 5737 176383 134000609 7110008717824458123105014279253754096863768062879) EMAIL: irdaqramo@...  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1930350&group_id=4933 
From: SourceForge.net <noreply@so...>  20080330 22:49:58

Bugs item #1924460, was opened at 20080324 10:24 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924460&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: Documentation Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Raymond Toy (rtoy) Assigned to: Nobody/Anonymous (nobody) Summary: ordergreat documentation confusing Initial Comment: The documentation for ordergreat is:  Function: ordergreat (<v_1>, ..., <v_n>) Sets up aliases for the variables <v_1>, ..., <v_n> such that <v_1> > <v_2> > ... > <v_n>, and <v_n> > any other variable not mentioned as an argument. I don't understand what it's trying to say. Same goes for the first paragraph for orderless.  >Comment By: Robert Dodier (robert_dodier) Date: 20080330 16:49 Message: Logged In: YES user_id=501686 Originator: NO I;ve revised & expanded ordergreat etc in r1.62 doc/info/Expressions.texi. Probably still confusing, dunno if it can be made much clearer due to inherent Maxima strangeness. Closing this report as fixed anyway.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924460&group_id=4933 
From: SourceForge.net <noreply@so...>  20080330 11:34:51

Bugs item #1929287, was opened at 20080330 06:34 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1929287&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  Simplification Group: None Status: Open Resolution: None Priority: 4 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: 0.0 + [0] > [0] Initial Comment: OK: (%i1) 0.0 + 0; (%o1) 0.0 Not OK; (%o2) should be [0.0], not [0] (%i2) 0.0 + [0]; (%o2) [0] Also, 0.0b0 + [0] > [0]. Matrix addition has the same bug: (%i6) 0.0 + matrix([0,0]); (%o6) matrix([0,0])  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1929287&group_id=4933 
From: SourceForge.net <noreply@so...>  20080330 00:29:32

Bugs item #1904814, was opened at 20080229 09:47 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1904814&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: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: strings in plot2doption `legend' Initial Comment: In my opinion the following example lines f(x):=1/(1+x^2); g(x):=exp(x^2); plot2d([f(x),g(x)],[x,4,4], [legend,"$\\frac{1}{1+x^2}$","$e^{x^2}$"]); plot2d([f(x),g(x)],[x,4,4], [legend,"$\\frac{1}{1+x^2}$","$e^{x^2}$"], [gnuplot_term,"eepic"], [gnuplot_out_file,"bug.tex"]); don't give the expected results: In the displayed graph, and in the eepicoutput, the backslash \ and the beginning dollar $ is missing. For instance, the output in bug.tex contains the line \put(2548,1636){\makebox(0,0)[r]{FRAC{1}{1+X^2}$}} Another problem is that frac and x get capitalized. I have been trying out maxima only for a few hours now, however my understanding of `legend' and the handling of strings let me expect a different result, the above output should be \put(2548,1636){\makebox(0,0)[r]{$\frac{1}{1+x^2}$}} It does not seem to be a gnuplot problem, because gnuplot handles the analogous construct correctly. Maxima version: 5.14.0 Maxima build date: 11:54 2/29/2008 host type: i686pclinuxgnu lispimplementationtype: CLISP lispimplementationversion: 2.39 (20060716) (built 3373656864) (memory 3413271278) Best wishes, Peter Mueller (peter.mueller@...)  >Comment By: Robert Dodier (robert_dodier) Date: 20080329 18:29 Message: Logged In: YES user_id=501686 Originator: NO Resolved by r1.113 src/plot.lisp. Closing this report as fixed. Corrected version will be in next (5.15.0) release. Note that you have to write "$\\\\frac..." to get just \frac in the output. Looks like the string is being processed twice; I would have expected "$\\frac..." should be enough. Not sure if that's a problem.  Comment By: Nobody/Anonymous (nobody) Date: 20080311 23:06 Message: Logged In: NO Problem is due to src/plot.lisp assuming that Maxima strings are implemented as symbols. I have a patch to fix that which I'll commit in a few days. Robert Dodier (not logged in at the moment)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1904814&group_id=4933 
From: SourceForge.net <noreply@so...>  20080329 21:40:13

Bugs item #1921102, was opened at 20080320 15:20 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1921102&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: Includes proposed fix Status: Closed Resolution: Wont Fix Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Test files dont work Initial Comment: I installed now Maxima 5.14.0 with GCL 2.6.6 ANSI on my MS Windows XP system. After installation the test files dont work. I get the error "unexpected end of #(input stream ..." reading the files in test mode. On my system the following extra EOF test in the routine TYIRAW works: (defun tyiraw (&optional (stream *standardinput*) eofoption) ;; added this extra EOF test, because test files generate ;; unexpected end of inputstream on my system (Windows XP, GCL 2.6.6) (when (eq (peekchar nil stream nil eofoption) eofoption) (returnfrom tyiraw eofoption) ) ;; this is the original unchanged code (let ((ch (readcharnohang stream nil eofoption))) (if ch ch (progn (when (and *promptonreadhang* *readhangprompt*) (princ *readhangprompt*) (forceoutput *standardoutput*) ) (readchar stream nil eofoption) ) ) ) ) I had the same problem with the versions 5.13.0 und 5.12.0 of Maxima on my system. Perhaps the bug is in the routine TESTBATCH. A reason may be the different EOF values used in Maxima at different places. Crategus  >Comment By: Crategus (crategus) Date: 20080329 22:40 Message: Logged In: YES user_id=2039760 Originator: YES Thank you very much for your answer. I have installed GCL 2.6.7 too. But this Lisp Version don't work on my Windows XP system. The compiler gives the error message: "undefined __flsbuf ... " loading the binaries. Maxima starts, but the function READCHAR don't work. So I will wait for a next version (I need a executable, I have no experience to build the compiler.) Crategus  Comment By: Robert Dodier (robert_dodier) Date: 20080329 22:11 Message: Logged In: YES user_id=501686 Originator: NO Closing this report as "won't fix". I'm pretty sure the problem is due to a bug in GCL (specifically the function READCHARNOHANG). This bug does not appear in Maxima + GCL 2.6.8pre + Windows XP. Dunno if Maxima + GCL 2.6.7 + Windows is OK. You might consider updating your version of GCL. Unfortunately, I don't know if GCL 2.6.8pre builds from CVS, and as for 2.6.7, I don't know if Maxima + GCL 2.6.7 + Windows XP runs correctly. The maxima5.xx.yy.exe installers which you can download from Sourceforge (https://sourceforge.net/project/showfiles.php?group_id=4933) are built with 2.6.8pre if I am not mistaken.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1921102&group_id=4933 
From: SourceForge.net <noreply@so...>  20080329 21:14:10

Bugs item #1924837, was opened at 20080324 20:25 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924837&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: Includes proposed fix >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integration error Initial Comment: This prob has been discussed in ML.Here it its link: http://www.math.utexas.edu/pipermail/maxima/2008/010566.html Hi,all.I use Maxima 5.14.0 ,and find an error that I think is a bug of Maxima.Hope to FIX IT. Here it is: (%i1) integrate(cos(a*x)/(1+x^2),x,0,inf); Is a positive, negative, or zero? zero; Maxima encountered a Lisp error: Error in PROGN [or a callee]: Caught fatal error [memory may be damaged] Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. The following is a fix from Robert Dodier: It appears that the bug originates from a MRAT expression which some function isn't prepared to handle ... The following patch fixes this bug. Not sure yet what other effect it might have.  src/defint.lisp 17 Feb 2008 20:54:22 0000 1.55 +++ src/defint.lisp 23 Mar 2008 15:59:15 0000 @@ 1015,7 +1015,7 @@ (eq ($sign (m+ (deg (setq nn* ($imagpart (caddr term)))) 2.)) '$neg))  (cond ((eq ($asksign (ratcoef nn* var)) '$pos) + (cond ((eq ($asksign (ratdisrep (ratcoef nn* var))) '$pos) (setq *updn t)) (t (setq *updn nil))) term)  >Comment By: Robert Dodier (robert_dodier) Date: 20080329 15:14 Message: Logged In: YES user_id=501686 Originator: NO Patch applied & committed as src/defint.lisp r1.56. Closing this report as fixed.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924837&group_id=4933 
From: SourceForge.net <noreply@so...>  20080329 21:11:50

Bugs item #1921102, was opened at 20080320 08:20 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1921102&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: Includes proposed fix >Status: Closed >Resolution: Wont Fix Priority: 5 >Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Test files dont work Initial Comment: I installed now Maxima 5.14.0 with GCL 2.6.6 ANSI on my MS Windows XP system. After installation the test files dont work. I get the error "unexpected end of #(input stream ..." reading the files in test mode. On my system the following extra EOF test in the routine TYIRAW works: (defun tyiraw (&optional (stream *standardinput*) eofoption) ;; added this extra EOF test, because test files generate ;; unexpected end of inputstream on my system (Windows XP, GCL 2.6.6) (when (eq (peekchar nil stream nil eofoption) eofoption) (returnfrom tyiraw eofoption) ) ;; this is the original unchanged code (let ((ch (readcharnohang stream nil eofoption))) (if ch ch (progn (when (and *promptonreadhang* *readhangprompt*) (princ *readhangprompt*) (forceoutput *standardoutput*) ) (readchar stream nil eofoption) ) ) ) ) I had the same problem with the versions 5.13.0 und 5.12.0 of Maxima on my system. Perhaps the bug is in the routine TESTBATCH. A reason may be the different EOF values used in Maxima at different places. Crategus  >Comment By: Robert Dodier (robert_dodier) Date: 20080329 15:11 Message: Logged In: YES user_id=501686 Originator: NO Closing this report as "won't fix". I'm pretty sure the problem is due to a bug in GCL (specifically the function READCHARNOHANG). This bug does not appear in Maxima + GCL 2.6.8pre + Windows XP. Dunno if Maxima + GCL 2.6.7 + Windows is OK. You might consider updating your version of GCL. Unfortunately, I don't know if GCL 2.6.8pre builds from CVS, and as for 2.6.7, I don't know if Maxima + GCL 2.6.7 + Windows XP runs correctly. The maxima5.xx.yy.exe installers which you can download from Sourceforge (https://sourceforge.net/project/showfiles.php?group_id=4933) are built with 2.6.8pre if I am not mistaken.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1921102&group_id=4933 
From: SourceForge.net <noreply@so...>  20080329 21:05:44

Bugs item #1920177, was opened at 20080319 22:07 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Crategus (crategus) Date: 20080329 22:05 Message: Logged In: YES user_id=2039760 Originator: YES Next I have added a diff between the orginal and the changed file. Question: Is it possible to attach at once more than one file to a message? Crategus File Added: diff.txt  Comment By: Crategus (crategus) Date: 20080329 22:00 Message: Logged In: YES user_id=2039760 Originator: YES I have put all changes of the code for the Bessel functions in the orginal file bessel.lisp which is distributed with Maxima 5.14.0 and attached this file to this message. I have tested the code with the testsuite and the values of the mytest_bessel.mac. Crategus File Added: besselchanged.lisp  Comment By: Crategus (crategus) Date: 20080329 01:35 Message: Logged In: YES user_id=2039760 Originator: YES Thank you very much for your answer. I have redesigned the following routines: simpbesselj (old name besseljsimp) besselj (old name $bessel) simpbessely (old name besselysimp) bessely simpbesseli (old name besselisimp) besseli simpbesselk (old name besselksimp) besselk The new routines are: $hankel_1 simphankel1 $hankel_2 simphankel2 If have further introduced the nouns %hankel_1 und %hankel_2. I would prefer to call the functions $hankel_1 and $hankel_2 and not bessel_hankel. The reason is that these functions are well known as Hankel functions. Because I have collected the routines in a new file it would be a good idea to do the changes in the orginal file bessel.lisp. Than it easier to produce a diff for you. I do this the next time. But first, I would like to have a second look at the global arrays $besselarray, $yarray and $iarray. I think it is not so easy to manage these global arrays in a consistent and predictable way for the user. One reason is, that the code for the numerical calculations use the other functions too (i.e. to calculate bessely we need besselj or for the calculation of besseli we need besselj and besselk). So $besselarray can be destroyed when calculating besseli. It might be possible to prevent this effect by introducing a global flag which signals the internal call of one of the routines. A second point is, that we often dont't use the numerical slatec routines directly. In this case it is necessary to do a lot of extra calculations to obtain the values for the arrays. Perhaps it is useful to decide to fill the global arrays only for the case when we can use the values of the slatec routines directly. This is possible for positive order and argument or positiv order and complex argument of the Bessel functions. Further, an additional flag could be introduced to switch the filling of the arrays on and off. It is also to decide what we do when the user calculate a new value for a Bessel function and the calculation don't fill the global array. In this case, the user may be confused by the fact that the global arrays still hold old values. But for which order and argument? For this case it may be helpful to invalidate the array every time we calculate a new value or to store additionally the order and argument for which the values in the global array are calculated. All these problems with the global arrays arise because of the extension of the routines to negative arguments and orders. In my opinion it would be the best to use the concept of the global arrays no longer. The code becomes much more complicated and the benefit for the user might be small. Crategus  Comment By: Raymond Toy (rtoy) Date: 20080328 17:37 Message: Logged In: YES user_id=28849 Originator: NO First, thank you very much for the fixes to the Bessel routines. I'm sure we all want the routines to be correct! Second, about $besselarray. I see the documentation for that is gone, but I think the intent for besselarray was to let the user have access to all the computed values, since some algorithms end up computing all the intermediate orders to get to the desired order. We need to think if this should go away or not. Third, it would certainly help me a lot if you actually produced a diff between your new code and the existing code. Right now, I have to go look at every single function in different places to figure out what's changed. Trying to minimize the changes would help. I know this is a lot of work for you too. Just identifying which function you actually changed would help a lot too. About the specific changes you mention in the comments. No problem with changing besselxsimp to simpbesselx. (I think most of the code uses simpbesselx, but that's too messy for my tastes.) Extending the range is very, very good. Not sure about the special tests for pure real or imaginary answers. Need to look at that some more. Definitions for Hankel functions are good. May want to name them bessel_hankel_1 to be consistent with other Bessel functions. Certainly want to add some properties like derivatives, but that can wait. All in all, I would very much like to take in your very nice changes.  Comment By: Crategus (crategus) Date: 20080327 17:50 Message: Logged In: YES user_id=2039760 Originator: YES I have tested the Bessel functions with the numerical data attached to this message. For the tests I used a function TEST_BESSEL(value, result, digits) which allow to compare the value with the result within the specified digits. Crategus File Added: mytest_bessel.mac  Comment By: Crategus (crategus) Date: 20080327 17:21 Message: Logged In: YES user_id=2039760 Originator: YES I have finished a first redesign of the code for the numerical calculation of the Bessel functions. I have extended the calculation to or changed parts of the calculation to negative orders and arguments. Perhaps the ideas and the code are interesting for the project. I have added the code to this message. A short description of the changes can be find in the header of the file. Crategus File Added: besselnew.lisp  Comment By: Crategus (crategus) Date: 20080323 18:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 
From: SourceForge.net <noreply@so...>  20080329 21:00:21

Bugs item #1920177, was opened at 20080319 22:07 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Crategus (crategus) Date: 20080329 22:00 Message: Logged In: YES user_id=2039760 Originator: YES I have put all changes of the code for the Bessel functions in the orginal file bessel.lisp which is distributed with Maxima 5.14.0 and attached this file to this message. I have tested the code with the testsuite and the values of the mytest_bessel.mac. Crategus File Added: besselchanged.lisp  Comment By: Crategus (crategus) Date: 20080329 01:35 Message: Logged In: YES user_id=2039760 Originator: YES Thank you very much for your answer. I have redesigned the following routines: simpbesselj (old name besseljsimp) besselj (old name $bessel) simpbessely (old name besselysimp) bessely simpbesseli (old name besselisimp) besseli simpbesselk (old name besselksimp) besselk The new routines are: $hankel_1 simphankel1 $hankel_2 simphankel2 If have further introduced the nouns %hankel_1 und %hankel_2. I would prefer to call the functions $hankel_1 and $hankel_2 and not bessel_hankel. The reason is that these functions are well known as Hankel functions. Because I have collected the routines in a new file it would be a good idea to do the changes in the orginal file bessel.lisp. Than it easier to produce a diff for you. I do this the next time. But first, I would like to have a second look at the global arrays $besselarray, $yarray and $iarray. I think it is not so easy to manage these global arrays in a consistent and predictable way for the user. One reason is, that the code for the numerical calculations use the other functions too (i.e. to calculate bessely we need besselj or for the calculation of besseli we need besselj and besselk). So $besselarray can be destroyed when calculating besseli. It might be possible to prevent this effect by introducing a global flag which signals the internal call of one of the routines. A second point is, that we often dont't use the numerical slatec routines directly. In this case it is necessary to do a lot of extra calculations to obtain the values for the arrays. Perhaps it is useful to decide to fill the global arrays only for the case when we can use the values of the slatec routines directly. This is possible for positive order and argument or positiv order and complex argument of the Bessel functions. Further, an additional flag could be introduced to switch the filling of the arrays on and off. It is also to decide what we do when the user calculate a new value for a Bessel function and the calculation don't fill the global array. In this case, the user may be confused by the fact that the global arrays still hold old values. But for which order and argument? For this case it may be helpful to invalidate the array every time we calculate a new value or to store additionally the order and argument for which the values in the global array are calculated. All these problems with the global arrays arise because of the extension of the routines to negative arguments and orders. In my opinion it would be the best to use the concept of the global arrays no longer. The code becomes much more complicated and the benefit for the user might be small. Crategus  Comment By: Raymond Toy (rtoy) Date: 20080328 17:37 Message: Logged In: YES user_id=28849 Originator: NO First, thank you very much for the fixes to the Bessel routines. I'm sure we all want the routines to be correct! Second, about $besselarray. I see the documentation for that is gone, but I think the intent for besselarray was to let the user have access to all the computed values, since some algorithms end up computing all the intermediate orders to get to the desired order. We need to think if this should go away or not. Third, it would certainly help me a lot if you actually produced a diff between your new code and the existing code. Right now, I have to go look at every single function in different places to figure out what's changed. Trying to minimize the changes would help. I know this is a lot of work for you too. Just identifying which function you actually changed would help a lot too. About the specific changes you mention in the comments. No problem with changing besselxsimp to simpbesselx. (I think most of the code uses simpbesselx, but that's too messy for my tastes.) Extending the range is very, very good. Not sure about the special tests for pure real or imaginary answers. Need to look at that some more. Definitions for Hankel functions are good. May want to name them bessel_hankel_1 to be consistent with other Bessel functions. Certainly want to add some properties like derivatives, but that can wait. All in all, I would very much like to take in your very nice changes.  Comment By: Crategus (crategus) Date: 20080327 17:50 Message: Logged In: YES user_id=2039760 Originator: YES I have tested the Bessel functions with the numerical data attached to this message. For the tests I used a function TEST_BESSEL(value, result, digits) which allow to compare the value with the result within the specified digits. Crategus File Added: mytest_bessel.mac  Comment By: Crategus (crategus) Date: 20080327 17:21 Message: Logged In: YES user_id=2039760 Originator: YES I have finished a first redesign of the code for the numerical calculation of the Bessel functions. I have extended the calculation to or changed parts of the calculation to negative orders and arguments. Perhaps the ideas and the code are interesting for the project. I have added the code to this message. A short description of the changes can be find in the header of the file. Crategus File Added: besselnew.lisp  Comment By: Crategus (crategus) Date: 20080323 18:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 
From: SourceForge.net <noreply@so...>  20080329 00:35:05

Bugs item #1920177, was opened at 20080319 22:07 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Crategus (crategus) Date: 20080329 01:35 Message: Logged In: YES user_id=2039760 Originator: YES Thank you very much for your answer. I have redesigned the following routines: simpbesselj (old name besseljsimp) besselj (old name $bessel) simpbessely (old name besselysimp) bessely simpbesseli (old name besselisimp) besseli simpbesselk (old name besselksimp) besselk The new routines are: $hankel_1 simphankel1 $hankel_2 simphankel2 If have further introduced the nouns %hankel_1 und %hankel_2. I would prefer to call the functions $hankel_1 and $hankel_2 and not bessel_hankel. The reason is that these functions are well known as Hankel functions. Because I have collected the routines in a new file it would be a good idea to do the changes in the orginal file bessel.lisp. Than it easier to produce a diff for you. I do this the next time. But first, I would like to have a second look at the global arrays $besselarray, $yarray and $iarray. I think it is not so easy to manage these global arrays in a consistent and predictable way for the user. One reason is, that the code for the numerical calculations use the other functions too (i.e. to calculate bessely we need besselj or for the calculation of besseli we need besselj and besselk). So $besselarray can be destroyed when calculating besseli. It might be possible to prevent this effect by introducing a global flag which signals the internal call of one of the routines. A second point is, that we often dont't use the numerical slatec routines directly. In this case it is necessary to do a lot of extra calculations to obtain the values for the arrays. Perhaps it is useful to decide to fill the global arrays only for the case when we can use the values of the slatec routines directly. This is possible for positive order and argument or positiv order and complex argument of the Bessel functions. Further, an additional flag could be introduced to switch the filling of the arrays on and off. It is also to decide what we do when the user calculate a new value for a Bessel function and the calculation don't fill the global array. In this case, the user may be confused by the fact that the global arrays still hold old values. But for which order and argument? For this case it may be helpful to invalidate the array every time we calculate a new value or to store additionally the order and argument for which the values in the global array are calculated. All these problems with the global arrays arise because of the extension of the routines to negative arguments and orders. In my opinion it would be the best to use the concept of the global arrays no longer. The code becomes much more complicated and the benefit for the user might be small. Crategus  Comment By: Raymond Toy (rtoy) Date: 20080328 17:37 Message: Logged In: YES user_id=28849 Originator: NO First, thank you very much for the fixes to the Bessel routines. I'm sure we all want the routines to be correct! Second, about $besselarray. I see the documentation for that is gone, but I think the intent for besselarray was to let the user have access to all the computed values, since some algorithms end up computing all the intermediate orders to get to the desired order. We need to think if this should go away or not. Third, it would certainly help me a lot if you actually produced a diff between your new code and the existing code. Right now, I have to go look at every single function in different places to figure out what's changed. Trying to minimize the changes would help. I know this is a lot of work for you too. Just identifying which function you actually changed would help a lot too. About the specific changes you mention in the comments. No problem with changing besselxsimp to simpbesselx. (I think most of the code uses simpbesselx, but that's too messy for my tastes.) Extending the range is very, very good. Not sure about the special tests for pure real or imaginary answers. Need to look at that some more. Definitions for Hankel functions are good. May want to name them bessel_hankel_1 to be consistent with other Bessel functions. Certainly want to add some properties like derivatives, but that can wait. All in all, I would very much like to take in your very nice changes.  Comment By: Crategus (crategus) Date: 20080327 17:50 Message: Logged In: YES user_id=2039760 Originator: YES I have tested the Bessel functions with the numerical data attached to this message. For the tests I used a function TEST_BESSEL(value, result, digits) which allow to compare the value with the result within the specified digits. Crategus File Added: mytest_bessel.mac  Comment By: Crategus (crategus) Date: 20080327 17:21 Message: Logged In: YES user_id=2039760 Originator: YES I have finished a first redesign of the code for the numerical calculation of the Bessel functions. I have extended the calculation to or changed parts of the calculation to negative orders and arguments. Perhaps the ideas and the code are interesting for the project. I have added the code to this message. A short description of the changes can be find in the header of the file. Crategus File Added: besselnew.lisp  Comment By: Crategus (crategus) Date: 20080323 18:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 
From: SourceForge.net <noreply@so...>  20080328 17:37:11

Bugs item #1928142, was opened at 20080328 18:37 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1928142&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  Simplification Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Harald Geyer (hgeyer) Assigned to: Nobody/Anonymous (nobody) Summary: keepfloat breaks ratsubst() in some cases Initial Comment: ratsubst returns incorrect results when keepfloat==true and the substitution causes the expression to contain both floats and rationals at the same time. See the following example session for things that don't work as well as for some things that do work. I can reproduce the problem from at least 5.11.0 up to current cvs with clisp and gcl. Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp CLISP 2.41 (20061013) 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) batch(ratsubstbug.mac) batching /home/rld/ratsubstbug.mac (%i2) keepfloat : true (%i3) display2d : false (%i4) cos(%pi/3) (%o4) 1/2 (%i5) subst(%pi/3,th,1.2*cos(th)) (%o5) 0.6 (%i6) ratsubst(%pi/3,th,1.2*cos(th)) (%o6) 1.2 (%i7) cos(%pi) (%o7) 1 (%i8) subst(%pi,th,1.2*cos(th)) (%o8) 1.2 (%i9) ratsubst(%pi,th,1.2*cos(th)) (%o9) 1.2 (%i10) sqrt(1/4) (%o10) 1/2 (%i11) subst(4,th,1.2*sqrt(1/th)) (%o11) 0.6 (%i12) ratsubst(4,th,1.2*sqrt(1/th)) Maxima encountered a Lisp error: COMMONLISP:GCD: 1.2 is not an integer Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. (%i13) subst(9,th,1.2*sqrt(1/th)) (%o13) 0.4 (%i14) ratsubst(9,th,1.2*sqrt(1/th)) Maxima encountered a Lisp error: COMMONLISP:GCD: 1.2 is not an integer Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. (%i15) ratsubst(9,th,1.2*sqrt(th)) (%o15) 3.6 (%i16) ratsubst(4,th,1.2/sqrt(th)) Maxima encountered a Lisp error: COMMONLISP:GCD: 1.2 is not an integer Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. (%i17) log(%e^(1/2)) (%o17) 1/2 (%i18) subst(%e^(1/2),th,1.2*log(th)) (%o18) 0.6 (%i19) ratsubst(%e^(1/2),th,1.2*log(th)) (%o19) 1.2 (%i20) ratsubst(%e^(1/3), th, 1.2*log(th)); (%o20) 1.2 (%i21) subst(%e^2,th,1.2*log(th)) (%o21) 2.4 (%i22) ratsubst(%e^2,th,1.2*log(th)) (%o22) 2.4  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1928142&group_id=4933 
From: SourceForge.net <noreply@so...>  20080328 16:43:07

Bugs item #721575, was opened at 20030414 23:45 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=721575&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  Simplification Group: None Status: Open Resolution: None Priority: 8 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: 2/sqrt(2) doesn\'t simplify Initial Comment: 2/sqrt(2) doesn't simplify. Similarly for 2/2^(2/3). On the other hand, x/sqrt(x) => sqrt(x). And of course sqrt(2) simplifies to itself  it doesn't become 2/sqrt(2)!! I believe the original examples should simplify to sqrt(2) and 2^(1/3). Note that 2^(4/3) => 2*2^(1/3) (the current behavior) is probably CORRECT, in order to make things like 10^(10/3) intelligible. Or is there something I'm missing? Maxima 5.9.0 gcl 2.5.0 mingw32 Windows 2000 Athlon  >Comment By: Raymond Toy (rtoy) Date: 20080328 12:42 Message: Logged In: YES user_id=28849 Originator: NO The issue appears to be in timesin. The basic issue is that timesin isn't commutative, as dgildea shows. I have a partial fix for this which fixes this particular issue, but it causes many failures in the testsuite, mostly due to a different ordering of the answer. But some tests now cause errors to be signaled, and some are no longer simplified as before or not simplified at all. Bummer.  Comment By: Dan Gildea (dgildea) Date: 20080111 07:55 Message: Logged In: YES user_id=1797506 Originator: NO (%i6) (1/2)*sqrt(2); (%o6) sqrt(2)/2 (%i7) sqrt(2)*(1/2); (%o7) 1/sqrt(2)  Comment By: Stavros Macrakis (macrakis) Date: 20071219 09:59 Message: Logged In: YES user_id=588346 Originator: YES I have raised the priority of this bug, because it is very close to the surface (i.e. easy for just about any user to run into). See also 1853191, where algebraic gives strange results...  Comment By: Stavros Macrakis (macrakis) Date: 20031008 23:21 Message: Logged In: YES user_id=588346 More examples. Righthand side is after ratsimp/algebraic. I believe the general simplifier should be giving those forms. 1/(2*2^(2/3)) 2^(1/3)/4 1/2^(2/3) 2^(1/3)/2 1/(2*SQRT(2)) SQRT(2)/4 1/SQRT(2) SQRT(2)/2 1/(2*2^(1/3)) 2^(2/3)/4 1/2^(1/3) 2^(2/3)/2 Things get worse with nonnumeric contents. In the following, each group of expressions denotes the same thing, but none simplifies to the others. I have put *** next to those forms which are the results of ratsimp/algebraic. Note that in several cases, there is more than one equivalent ratsimp'ed form.... 1/(a*b)^(5/2) 1/(a^2*b^2*SQRT(a*b)) *** SQRT(a*b)/(a^3*b^3) *** 1/(a*b)^(3/2) 1/(a*b*SQRT(a*b)) *** SQRT(a*b)/(a^2*b^2) *** 1/(a*b)^(7/6) 1/(a^(2/3)*b^(2/3)*SQRT(a*b)) *** SQRT(a*b)/(a^(5/3)*b^(5/3)) *** (a*b)^(5/6)/(a^2*b^2) *** 1/(a*b)^(5/6) *** 1/(a^(1/3)*b^(1/3)*SQRT(a*b)) *** (a*b)^(1/6)/(a*b) *** SQRT(a*b)/(a^(4/3)*b^(4/3)) *** 1/SQRT(a*b) *** SQRT(a*b)/(a*b) *** a^(1/3)*b^(1/3)/SQRT(a*b) *** 1/(a*b)^(1/6) *** SQRT(a*b)/(a^(2/3)*b^(2/3)) *** (a*b)^(5/6)/(a*b) *** Now it is true that these expressions are in fact not all equivalent as to principal value, but I will leave that exercise for later. Many of them are, and they are not being canonicalized.  Comment By: Stavros Macrakis (macrakis) Date: 20030417 14:53 Message: Logged In: YES user_id=588346 Yes, of course there are ways within Maxima to perform this simplification. But it should be the default in the general simplifer. The logic already appears to be in the general simplifier, but there is a bug in this particular case. If the general simplifier's philosophy were to leave such things untouched, why does it simplify x/sqrt(x) and the like?  Comment By: Barton Willis (willisb) Date: 20030417 14:44 Message: Logged In: YES user_id=570592 Try ratsimp with algebraic : true (C1) z : 2/sqrt(2); (D1) 2/SQRT(2) (C2) ratsimp(z); (D2) 2/SQRT(2) (C3) ratsimp(z),algebraic; (D3) SQRT(2) (C4) z : 2/2^(2/3); (D4) 2/2^(2/3) (C5) ratsimp(z); (D5) 2/2^(2/3) (C6) ratsimp(z),algebraic; (D6) 2^(1/3) (C7)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=721575&group_id=4933 
From: SourceForge.net <noreply@so...>  20080328 16:37:43

Bugs item #1920177, was opened at 20080319 17:07 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Raymond Toy (rtoy) Date: 20080328 12:37 Message: Logged In: YES user_id=28849 Originator: NO First, thank you very much for the fixes to the Bessel routines. I'm sure we all want the routines to be correct! Second, about $besselarray. I see the documentation for that is gone, but I think the intent for besselarray was to let the user have access to all the computed values, since some algorithms end up computing all the intermediate orders to get to the desired order. We need to think if this should go away or not. Third, it would certainly help me a lot if you actually produced a diff between your new code and the existing code. Right now, I have to go look at every single function in different places to figure out what's changed. Trying to minimize the changes would help. I know this is a lot of work for you too. Just identifying which function you actually changed would help a lot too. About the specific changes you mention in the comments. No problem with changing besselxsimp to simpbesselx. (I think most of the code uses simpbesselx, but that's too messy for my tastes.) Extending the range is very, very good. Not sure about the special tests for pure real or imaginary answers. Need to look at that some more. Definitions for Hankel functions are good. May want to name them bessel_hankel_1 to be consistent with other Bessel functions. Certainly want to add some properties like derivatives, but that can wait. All in all, I would very much like to take in your very nice changes.  Comment By: Crategus (crategus) Date: 20080327 12:50 Message: Logged In: YES user_id=2039760 Originator: YES I have tested the Bessel functions with the numerical data attached to this message. For the tests I used a function TEST_BESSEL(value, result, digits) which allow to compare the value with the result within the specified digits. Crategus File Added: mytest_bessel.mac  Comment By: Crategus (crategus) Date: 20080327 12:21 Message: Logged In: YES user_id=2039760 Originator: YES I have finished a first redesign of the code for the numerical calculation of the Bessel functions. I have extended the calculation to or changed parts of the calculation to negative orders and arguments. Perhaps the ideas and the code are interesting for the project. I have added the code to this message. A short description of the changes can be find in the header of the file. Crategus File Added: besselnew.lisp  Comment By: Crategus (crategus) Date: 20080323 13:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 
From: SourceForge.net <noreply@so...>  20080328 01:51:39

Bugs item #1927346, was opened at 20080327 13:31 Message generated for change (Settings changed) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1927346&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  Simplification Group: None Status: Open >Resolution: Duplicate Priority: 3 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: sqrt(2) ./ 2 vs 1/sqrt(2) Initial Comment: It's not wrong, but it's not right either: (%i3) integrate(sin(t),t,%pi/4,3*%pi/4); (%o3) sqrt(2)/2+1/sqrt(2)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1927346&group_id=4933 
From: SourceForge.net <noreply@so...>  20080327 18:31:08

Bugs item #1927346, was opened at 20080327 13:31 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1927346&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  Simplification Group: None Status: Open Resolution: None Priority: 3 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: sqrt(2) ./ 2 vs 1/sqrt(2) Initial Comment: It's not wrong, but it's not right either: (%i3) integrate(sin(t),t,%pi/4,3*%pi/4); (%o3) sqrt(2)/2+1/sqrt(2)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1927346&group_id=4933 
From: SourceForge.net <noreply@so...>  20080327 16:50:51

Bugs item #1920177, was opened at 20080319 22:07 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Crategus (crategus) Date: 20080327 17:50 Message: Logged In: YES user_id=2039760 Originator: YES I have tested the Bessel functions with the numerical data attached to this message. For the tests I used a function TEST_BESSEL(value, result, digits) which allow to compare the value with the result within the specified digits. Crategus File Added: mytest_bessel.mac  Comment By: Crategus (crategus) Date: 20080327 17:21 Message: Logged In: YES user_id=2039760 Originator: YES I have finished a first redesign of the code for the numerical calculation of the Bessel functions. I have extended the calculation to or changed parts of the calculation to negative orders and arguments. Perhaps the ideas and the code are interesting for the project. I have added the code to this message. A short description of the changes can be find in the header of the file. Crategus File Added: besselnew.lisp  Comment By: Crategus (crategus) Date: 20080323 18:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 
From: SourceForge.net <noreply@so...>  20080327 16:22:00

Bugs item #1920177, was opened at 20080319 22:07 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Crategus (crategus) Date: 20080327 17:21 Message: Logged In: YES user_id=2039760 Originator: YES I have finished a first redesign of the code for the numerical calculation of the Bessel functions. I have extended the calculation to or changed parts of the calculation to negative orders and arguments. Perhaps the ideas and the code are interesting for the project. I have added the code to this message. A short description of the changes can be find in the header of the file. Crategus File Added: besselnew.lisp  Comment By: Crategus (crategus) Date: 20080323 18:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 
From: SourceForge.net <noreply@so...>  20080327 15:00:42

Bugs item #1927178, was opened at 20080327 10:00 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1927178&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  Simplification Group: None Status: Open Resolution: None Priority: 3 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: sqrt(2) ./ 2 vs 1/sqrt(2) Initial Comment: It's not wrong, but it's not right either: (%i3) integrate(sin(t),t,%pi/4,3*%pi/4); (%o3) sqrt(2)/2+1/sqrt(2)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1927178&group_id=4933 
From: SourceForge.net <noreply@so...>  20080326 01:29:14

Bugs item #580721, was opened at 20020712 14:38 Message generated for change (Comment added) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=580721&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  Trigonometry Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Raymond Toy (rtoy) Assigned to: Nobody/Anonymous (nobody) Summary: trigexpand bug Initial Comment: Consider this: (C1) display2d:false; (D1) FALSE (C2) tan(%pi/2+x); (D2) COT(x) (C3) tan(%pi/2+%pi*x); (D3) TAN(%PI*x+%PI/2) (C4) %,trigexpand; Division by 0  an error. Quitting. To debug this try DEBUGMODE(TRUE);) d3 should have been expanded into cot(%pi*x) instead of getting a division by zero error.  >Comment By: Dan Gildea (dgildea) Date: 20080325 21:29 Message: Logged In: YES user_id=1797506 Originator: NO The proposed patch disables the following simplification: (%i1) declare(n, integer); (%o1) done (%i2) tan(n*2*%pi); (%o2) 0 However, it almost fixes bugs 903190, 1553866 and 1755550.  Comment By: Rupert Swarbrick (rswarbrick) Date: 20071228 12:15 Message: Logged In: YES user_id=1673565 Originator: NO I think I've posted a patch onto the mailing list that fixes this. I can't work out how to attach files here, so the link is: http://thread.gmane.org/gmane.comp.mathematics.maxima.general/19076  Comment By: Rupert Swarbrick (rswarbrick) Date: 20071226 21:38 Message: Logged In: YES user_id=1673565 Originator: NO So the first thing that's wrong is that %piargstan/cot shouldn't return nonnil for stuff like tan(pi/2) as they aren't defined, let alone simplifiable. Here's an amended and reformatted version with variables renamed and a possible bug due to reuse of variable names eliminated too (I think) (defun %piargstan/cot (x) (displa x) (let ((coeff (linearize (coefficient x '$%pi 1))) (zlrem (coefficient x '$%pi 0)) (sinofcoeffpi) (cosofcoeffpi)) (cond ((and (zerop1 zlrem) (setq sinofcoeffpi (%piargs coeff nil)) (not (zerop1 (setq cosofcoeffpi (%piargs (cons (car coeff) (rplus 1//2 (cdr coeff))) nil))))) ;; sinofcoeffpi and cosofcoeffpi are only nonnil if they ;; are constants that %piargsoffset could compute, and we just ;; checked that cosofcoeffpi was nonzero. Thus we can just ;; return their quotient. (div sinofcoeffpi cosofcoeffpi)) ((not (mevenp (car coeff))) nil) ((integerp (setq x (mmod (cdr coeff) 2))) (consexp '%tan zlrem)) ((or (alike1 1//2 x) (alike1 '((rat) 3 2) x)) (neg (consexp '%cot zlrem))))))  Comment By: Rupert Swarbrick (rswarbrick) Date: 20071226 21:29 Message: Logged In: YES user_id=1673565 Originator: NO Ah. Of course tan(pi/2) = infinity ...  Comment By: Rupert Swarbrick (rswarbrick) Date: 20071225 20:10 Message: Logged In: YES user_id=1673565 Originator: NO Hi, a bit more information: the error's caused by a (div 1 0) which gets returned in %piargstan/cot, called by simp%tan. You can reproduce more simply by just calling tan(%pi/2), trigexpand; I'm trying to work out what the functions are _supposed_ to do. Maybe then I'll be able to fix it!  Comment By: Robert Dodier (robert_dodier) Date: 20060326 18:40 Message: Logged In: YES user_id=501686 For the record, same problem observed in maxima 5.9.3.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=580721&group_id=4933 
From: SourceForge.net <noreply@so...>  20080325 03:00:49

Bugs item #887646, was opened at 20040130 15:49 Message generated for change (Comment added) made by hgeyer You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=887646&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: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: bogus PV integral [defint(exp(a*x),x,0,inf)] Initial Comment: (C1) defint(exp(a*x),x,0,inf); Is a positive, negative, or zero? zero;Principal Value (D1) 0 This isn't a PV integral; the integral diverges when a == 0. (C2) build_info(); Maxima version: 5.9.0 Maxima build date: 19:10 2/9/2003 host type: i686pcmingw32 lispimplementationtype: Kyoto Common Lisp lispimplementationversion: GCL25.0  >Comment By: Harald Geyer (hgeyer) Date: 20080325 04:00 Message: Logged In: YES user_id=929336 Originator: NO Still observed in 5.14.0 and cvs HEAD from 20080325  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=887646&group_id=4933 
From: SourceForge.net <noreply@so...>  20080325 02:58:07

Bugs item #1309432, was opened at 20050930 14:19 Message generated for change (Comment added) made by hgeyer You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1309432&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(1/cosh(a*x)^2,x,inf,inf); Initial Comment:  Maxima version: 5.9.1 Maxima build date: 16:35 2/10/2005 host type: i686pclinuxgnu lispimplementationtype: GNU Common Lisp (GCL) lispimplementationversion: GCL 2.6.6  integrate(1/cosh(a*x)^2,x,inf,inf); Is a positive, negative, or zero? p; (%o3) 0 Correct answer is 2/a.  >Comment By: Harald Geyer (hgeyer) Date: 20080325 03:58 Message: Logged In: YES user_id=929336 Originator: NO Still observed in 5.14.0 and cvs HEAD from 20080325  Comment By: Raymond Toy (rtoy) Date: 20060215 21:23 Message: Logged In: YES user_id=28849 I think this integral fails because polelist is unable to find the roots of z^(4*a)+2*z^(2*a)+1.  Comment By: Stavros Macrakis (macrakis) Date: 20051109 20:39 Message: Logged In: YES user_id=588346 Interestingly, if you exponentialize the expression first, it gets the right answer. But still asks, unnecessarily, the sign of 'a'.  Comment By: Stavros Macrakis (macrakis) Date: 20051109 20:34 Message: Logged In: YES user_id=588346 Interestingly, if you exponentialize the expression first, it gets the right answer. But still asks, unnecessarily, the sign of 'a'.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1309432&group_id=4933 
From: SourceForge.net <noreply@so...>  20080325 02:25:49

Bugs item #1924837, was opened at 20080324 19:25 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924837&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integration error Initial Comment: This prob has been discussed in ML.Here it its link: http://www.math.utexas.edu/pipermail/maxima/2008/010566.html Hi,all.I use Maxima 5.14.0 ,and find an error that I think is a bug of Maxima.Hope to FIX IT. Here it is: (%i1) integrate(cos(a*x)/(1+x^2),x,0,inf); Is a positive, negative, or zero? zero; Maxima encountered a Lisp error: Error in PROGN [or a callee]: Caught fatal error [memory may be damaged] Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. The following is a fix from Robert Dodier: It appears that the bug originates from a MRAT expression which some function isn't prepared to handle ... The following patch fixes this bug. Not sure yet what other effect it might have.  src/defint.lisp 17 Feb 2008 20:54:22 0000 1.55 +++ src/defint.lisp 23 Mar 2008 15:59:15 0000 @@ 1015,7 +1015,7 @@ (eq ($sign (m+ (deg (setq nn* ($imagpart (caddr term)))) 2.)) '$neg))  (cond ((eq ($asksign (ratcoef nn* var)) '$pos) + (cond ((eq ($asksign (ratdisrep (ratcoef nn* var))) '$pos) (setq *updn t)) (t (setq *updn nil))) term)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924837&group_id=4933 
From: SourceForge.net <noreply@so...>  20080324 16:24:42

Bugs item #1924460, was opened at 20080324 12:24 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924460&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: Documentation Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Raymond Toy (rtoy) Assigned to: Nobody/Anonymous (nobody) Summary: ordergreat documentation confusing Initial Comment: The documentation for ordergreat is:  Function: ordergreat (<v_1>, ..., <v_n>) Sets up aliases for the variables <v_1>, ..., <v_n> such that <v_1> > <v_2> > ... > <v_n>, and <v_n> > any other variable not mentioned as an argument. I don't understand what it's trying to say. Same goes for the first paragraph for orderless.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1924460&group_id=4933 
From: SourceForge.net <noreply@so...>  20080323 17:16:39

Bugs item #1920177, was opened at 20080319 22:07 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with the bessel functions Initial Comment: There are several problems with the bessel functions. The problems I have found can be divided in the following categories: 1. Inconsistent use of the internal arrays $besselarray, $yarray and $iarray. Example: Restart Maxima and Enter bessel_y(2,1.0). You get an Lisp error. Try first bessel_y(2,1.0) and then repeat bessel_y(2,1.0). Now you get the correct result 1.65...  %i * 3,30... Try bessel_j(2,1.0), you get 0.1149...  %i*2.8142... Next enter bessel_y(2,1.0), you get a Lisp error. The reason for the problems is that the routine bessely uses the global array $YARRAY to store values, but uses also the array $BESSELARRAY to calculate the answer. This is an error. I think the best is to eliminate the use of the global arrays completly. 2. Problematic roundoff errors: Try bessel_j(2,1.0). The result is 0,114903...  %i* 2.8142... e17. The correct result is pure real. The problem is the use of the transformation j[n]=exp(n*%pi*%i)*j[n](x) in the code which produce a small imaginary part. This is a roundoff error for an integer order. In the case of non integer values the imaginary part is correct. So you can not cut off the imaginary part in general. Here is a piece of code which will return an answer which is pure real when the order is an integer (I started to rewrite the code, introduced a function besselj and eliminated the use of the global arrays): (if (integerp order) (if (evenp order) (aref jvals n) ( (aref jvals n)) ) (let ((v (* (cis (* order pi)) (aref jvals n)))) (simplifya `((mplus) ,(realpart v) ((mtimes) $%i ,(imagpart v))) nil ) ) ) 3. Wrong mathematic: Try bessel_j(2.5,1,0). You get 0.04949... Correct is the result 2.8763... * %i Or bessel_j(3,2.0). You get 0,128943... Correct is the result 0.128943... The calculation of the bessel function j[n](x) for real argument x and negativ order n as (realpart (hankel1 order arg)) is not correct. The correct result can be obtained with the formula j[n](x) = 1/2 * (H1[n](x) + H2[n](x)). I tried the following code: (let ((result (* 0.5d0 (+ (hankel1 order arg) (hankel2 order arg))))) (complexify result) ; Problem: you get a small imaginary part ;in the case of a real result (like Problem 2) ; An alternative with a function fpround which round the result ; so that a small imaginary part will vanish ; ; (simplifya ; `((mplus) ; ,(fpround (realpart result) 14) ; ((mtimes) ; ,(fpround (imagpart result) 14) ; $%i ; ) ; ) ; nil ; ) ) This is the definition of the function fpround: (defun fpround (x &optional (digits 1)) (let ((fac (expt 10 digits))) (/ (round x (/ 1 fac)) (float fac)) ) ) I have redesigned a lot of the code for the bessel functions but the work is not finished. Is the work interesting for the project? I use GCL 2.6.6 on Windows XP for programing. Crategus  >Comment By: Crategus (crategus) Date: 20080323 18:16 Message: Logged In: YES user_id=2039760 Originator: YES I have added to this posting the code for a routine besselj which handles the above problems. The global array $BESSELARRAY is not used. Futher, I added numerical test values for the the special cases in the code. I used Maxima 5.14.0 and GCL 2.6.6 ANSI to compile the code. The testsuite runs with no unexpected errors found. 22 of the 29 numerical tests I have added give the result within a presision of 16 digits. 7 results have a precision of about 14 to 15 digits. Perhaps, the code is interesting enough for further investigation of the numerical evaluation of the Bessel functions. Crategus File Added: besselj.lisp  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933 