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From: SourceForge.net <noreply@so...>  20030808 23:50:22

Bugs item #776441, was opened at 20030723 20:25 Message generated for change (Comment added) made by wjenkner You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=776441&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: orderlessp not transitive Initial Comment: l: [z+x*(x+2)+v+1,z+x^2+x+v+1,z+(x+1)^2+v]; orderlessp(l[1],l[2]) => True orderlessp(l[2],l[3]) => True orderlessp(l[1],l[3]) => False !!! More concise example: q: x^2; r: (x+1)^2; s: x*(x+2); orderlessp(q,r) => true orderlessp(r,s) => true orderlessp(s,q) => true That is, s<q<r<s. The problem is somewhere in the internal great function, which by the way does some strange things, in particular: why does ordlist have an explicit check for mplus: (RETURN (COND ((= L2 0) (EQ CX 'MPLUS)) (Thanks to Barton for his contributions to tracking this down.) Maxima 5.9.0 GCL 2.5.0  >Comment By: Wolfgang Jenkner (wjenkner) Date: 20030809 01:50 Message: Logged In: YES user_id=581700 This one doesn't even involve MEXPT (I found it while checking one of the cases needed for proving that ORDLIST implements a consistent way of extending a given total order on a set of simplified expressions to their simplified sums and products. So it doesn't...) (C1) orderlessp(t/2,t); (D1) TRUE (C2) orderlessp(t,t+1/4); (D2) TRUE (C3) orderlessp(t/2,t+1/4); (D3) FALSE The point is that t/2 is ((MTIMES SIMP) ((RAT SIMP) 1 2) $t) and, lexicographically, we have (t, 1/2) < (t, 1), (t, 0) < (t, 1/4) and (t, 1/2, *) > (t, 1/4, +). So t corresponds to (t, 1) in the first comparison and to (t, 0) in the second comparison. Trouble. Floats instead of rational numbers give the same results, by the way. This one is more like Stavros's examples. (C1) orderlessp((x+1)^2,x^21); (D1) TRUE (C2) orderlessp(x^21,x^2); (D2) TRUE (C3) orderlessp((x+1)^2,x^2); (D3) FALSE Maybe powers whose exponents are positive integers should be treated like products. Actually, ORDMEXPT does this already but it isn't always called by ORDFN, for whatever reason. Anyway, here is the patch I'm currently experimenting with (it solves all the issues reported by Stavros and also the last example above, but in light of the other example it is certainly far from being a complete solution. It might even be totally wrong since I have no reason to believe that it is more than a simple palliative and that it would make things more consistent). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cut ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Index: simp.lisp =================================================================== RCS file: /cvsroot/maxima/maxima/src/simp.lisp,v retrieving revision 1.5 diff C2 r1.5 simp.lisp *** simp.lisp 5 Mar 2003 01:36:26 0000 1.5  simp.lisp 8 Aug 2003 19:10:57 0000 *************** *** 1848,1854 **** ((MEMQ CX '(MPLUS MTIMES)) (COND ((MEMQ CY '(MPLUS MTIMES)) (ORDLIST (CDR X) (CDR Y) CX CY)) ! ((ALIKE1 (SETQ U (CAR (LAST X))) Y) (NOT (ORDHACK X))) ! ((AND (EQ CX 'MPLUS) (EQ CY 'MEXPT) (MPLUSP (CADR Y))) (NOT (ORDMEXPT Y X))) (T (GREAT U Y)))) ((MEMQ CY '(MPLUS MTIMES)) (NOT (ORDFN Y X)))  1848,1854  ((MEMQ CX '(MPLUS MTIMES)) (COND ((MEMQ CY '(MPLUS MTIMES)) (ORDLIST (CDR X) (CDR Y) CX CY)) ! ((AND (EQ CX 'MPLUS) (EQ CY 'MEXPT)) (NOT (ORDMEXPT Y X))) + ((ALIKE1 (SETQ U (CAR (LAST X))) Y) (NOT (ORDHACK X))) (T (GREAT U Y)))) ((MEMQ CY '(MPLUS MTIMES)) (NOT (ORDFN Y X))) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cut ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  Comment By: Stavros Macrakis (macrakis) Date: 20030805 06:35 Message: Logged In: YES user_id=588346 More amusing consequences: q+r+s => (x+1)^2+x^2+x*(x+2) expand(%,0,0) => x^2+x*(x+2)+(x+1)^2 expand(%,0,0) => x*(x+2)+(x+1)^2+x^2 expand(%,0,0) => (x+1)^2+x^2+x*(x+2) q+r+srqs => (x+1)^2+x^2+x*(x+2)(x+1)^2x^2x* (x+2) expand(%,0,0) => x^2x^2 expand(%,0,0) => 0 I haven't found an example where simptimes fails, though. Fateman reports that this bug is also found in commercial Macsyma 2.4, and calls it a Methuselah bug because it has persisted for so long  presumably it has been around for 30+ years.  Comment By: Stavros Macrakis (macrakis) Date: 20030725 16:26 Message: Logged In: YES user_id=588346 This not only screws up SORT etc., but even basic simplification, since simplus, simptimes, etc. depend on great: q+r+s => (x+1)^2+x^2+x*(x+2) q+s+r => x^2+x*(x+2)+(x+1)^2 (q+s+r)(q+s+r) => x^2x^2 (q+s+r)(s+q+r) => x^2x^2 (q+r+s)(q+s+r) => x (x + 2)  x (x + 2)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=776441&group_id=4933 