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From: SourceForge.net <noreply@so...>  20100418 19:45:11

Bugs item #2989076, was opened at 20100418 14:45 Message generated for change (Tracker Item Submitted) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989076&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: 1 Private: No Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: error message from determinant Initial Comment: The error message has the number of rows and columns off by one: (%i30) determinant(matrix([1,2,3],[4,5,6])); determinant: matrix must be square; found 3 rows, 4 columns.  an error. To debug this try: debugmode(true);  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989076&group_id=4933 
From: SourceForge.net <noreply@so...>  20100418 17:30:58

Bugs item #635627, was opened at 20021108 19:35 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=635627&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: subst([...] is orderdependent Initial Comment: I would have expected subst([a=...,b=...],...) to substitute a and b simultaneously (like Lisp Sublis), but it does not, and it simplifies along the way. Here are some cases where it matters. The most obvious case is subst([b=c,a=b],b) => c This means that subst cannot be used to permute variables, e.g. subst([x=y,y=x],...) That is not good.  But there are other cases:  subst([a=0,b=0],atan2(a,b)) Depending on the answers to a>0 etc., this can return 0 or %pi, whereas subst([b=0,a=0],...) can return pi/2 or  pi/2. I believe that it should give the error: atan2(0.0) has been generated.  subst(["="="+","["="*"],[x=1,x=2]); gives (x+1) * (x+2) as expected, but subst(["["="*","="="+"],[x=1,x=2]); gives x^2+2 ((It would have been nice if minus were nary, so that I could use "="=""...))  These two cases can be worked around by turning simp off temporarily, e.g. subst(["["="*","="="+"],[x=1,x=2]), simp:false; but the workaround for the first case is much clumsier: subst([x=x0,y=x,x0=y],...)  >Comment By: Dieter Kaiser (crategus) Date: 20100418 19:30 Message: A function psubst has been added in comm.lisp revision 1.41. This function does the desired parallel substitutions: (%i1) psubst ([a=b,b=a], sin(a)+sin(b)); (%o1) sin(b)+sin(a) (%i2) psubst([a=0,b=0],atan2(a,b)); atan2: atan2(0,0) is undefined.  an error. To debug this try: debugmode(true); (%i3) psubst(["="="+","["="*"],[x=1,x=2]); (%o3) (x+1)*(x+2) (%i5) psubst(["["="*","="="+"],[x=1,x=2]); (%o5) (x+1)*(x+2) (%i6) psubst([a=[1,2],b=[3,4]],a+b); (%o6) [4,6] In addition to the function sublis psubst can do parallel substitution not only for atoms on the left hand side, but for expressions too: (%i7) psubst([x^2=y^2,y^2=x^2],exp(x^2)+sin(y^2)); (%o7) %e^y^2+sin(x^2) The function subst is not changed. Closing this bug report as fixed. Dieter Kaiser  Comment By: Stavros Macrakis (macrakis) Date: 20030712 22:23 Message: Logged In: YES user_id=588346 Another case where simultaneous substitution is necessary... subst([a=[1,2],b=[3,4]],a+b) => [[4,5],[5,6]] instead of the expected [4,6] because [1,2]+b => [1+b,2+b], then 1+[3,4] => = [4,5] etc. I am arguing that simultaneous substitution is the only reasonable default behavior.  Comment By: Stavros Macrakis (macrakis) Date: 20021119 20:48 Message: Logged In: YES user_id=588346 Sublis is broken for operators, e.g. sublis(["+"="*"],x+y) And the online documentation (describe) of subst does not mention the parallel substitution issue. I do not think we need both subst([...]) and sublis([...]...). My guess is that sublis was defined before subst was extended to cover the multiple substitution case.  Comment By: Nobody/Anonymous (nobody) Date: 20021116 17:43 Message: Logged In: NO The info tells you to use SUBLIS if you want to do substitution in parallel.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=635627&group_id=4933 
From: SourceForge.net <noreply@so...>  20100418 13:23:17

Bugs item #2988546, was opened at 20100416 22:37 Message generated for change (Comment added) made by andrejv You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2988546&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: Fixed Priority: 5 Private: No Submitted By: Mitch Richling (richmit) Assigned to: Nobody/Anonymous (nobody) Summary: primep can be wrong for n<10^16 Initial Comment: The documentation for primep located at http://maxima.sourceforge.net/docs/manual/en/maxima_31.html#Item_003aprimep Says: For n less than 10^16 a deterministic version of MillerRabin's test is used. So primep should always work for n<10^16  i.e. never falsely think a composite number is prime. But: ================================================================================ Maxima 5.19.1 http://maxima.sourceforge.net Using Lisp SBCL 1.0.23 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) primep(2974861 * 5949721); (%o1) true <=== Thinks that it is prime (%i2) 10^16  (2974861 * 5949721); (%o2) 9982300407036219 <=== It is much less than 10^16. :) ================================================================================ I tracked down the offending code in ifactor.lisp: ================================================================================ (defun primep (n) (cond ((= n 1) nil) ((evenp n) (= n 2)) ((member n *smallprimes*) t) ((< n 9080191) (primepsmall n '(31 73))) ((< n 4759123141) (primepsmall n '(2 7 61))) ((< n 2152302898747) (primepsmall n '(2 3 5 7 11))) ((= n 46856248255981) nil) ((< n 10000000000000000) (primepsmall n '(2 3 7 61 24251))) ((member n *largeprimes*) t) (t (primepprob n)))) ;;; millerrabin test is deterministic for small n ;;; if we test for small bases ;;; Reference: ;;; [1] G. Jaeschke, On Strong Pseudoprimes to Several Bases, ;;; Math. Comp., 61 (1993), 915926. ;;; [2] http://primes.utm.edu/prove/prove2_3.html ================================================================================ The second reference [2] doesn't provide much insight, but it looks like the code makes the assumption that if n<10^16, n is not 46856248255981, and n is a strong psudoprime to the basis {2, 3, 7, 61, 24251} then it is prime. This assumption is false. As far as I know, the best PUBLISHED result is probably still Jaeschke (a few "Internet sources" claim better, but have not been verified near as I can tell). Switching the code to use Jaeschke would lower the maximum number for which primep would prove primality  and you would need to change the documentation too. That said, I'm reasonably sure the following code works for n<341550071728321: ================================================================================ (defun primep (n) (cond ((= n 1) nil) ((evenp n) (= n 2)) ((member n *smallprimes*) t) ((< n 9080191) (primepsmall n '(31 73))) ((< n 4759123141) (primepsmall n '(2 7 61))) ((< n 2152302898747) (primepsmall n '(2 3 5 7 11))) ((< n 3474749660383) (primepsmall n '(2 3 5 7 11 13))) ((< n 341550071728321) (primepsmall n '(2 3 5 7 11 13 17))) ((member n *largeprimes*) t) (t (primepprob n)))) ;;; millerrabin test is deterministic for small n ;;; if we test for small bases ;;; Reference: ;;; [1] G. Jaeschke, On Strong Pseudoprimes to Several Bases, ;;; Math. Comp., 61 (1993), 915926. ================================================================================  >Comment By: Andrej Vodopivec (andrejv) Date: 20100418 15:23 Message: Thank you for reporting this bug. primep from cvs now uses the Jaeschke's result.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2988546&group_id=4933 