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From: SourceForge.net <noreply@so...>  20050615 14:37:16

Bugs item #1192935, was opened at 20050430 05:10 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1192935&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: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: termsubstitution in function sum is too late Initial Comment: (%i1) "Lower RiemannSum, Intervall [0,1], 10 parts"$ (%i2) /*Function*/ f(x):=x^2$ (%i3) /*area width*/ b: 1/10$ (%i4) /*area depending on k=0,...,9*/ Ak: b*f(k*b)$ (%i5) Ak; 2 k (%o5)  1000 (%i6) /* wrong */ sum(Ak,k,0,9); 2 k (%o6)  100 obviously, we first have the summation and then the symbolsubstitution (%i7) sum(''Ak,k,0,9); 57 (%o7)  200 finally, this is ok, but the usage of the doublequote is hard to explain to beginners. it gets even worse, if you use a function A(k):=k*f(k*b)$ for a sum with n partitions: (%i8) "Lower RiemannSum, Intervall [0,1], n parts"$ (%i9) /*area width*/ b:1/n$ (%i10) /*area depending on k=0,...,n1*/ A(k):=k*f(k*b)$ (%i11) A(k); 3 k (%o11)  2 n (%i12) sum(A(k),k,0,n1); n  1 ==== (%o12) > A(k) / ==== k = 0 in that case you need ''(A(k)), a bracket and the doublequote. is it possible to patch the sumfunction in that way, that we first have the term or symbolsubstitution and second the summation?  >Comment By: Robert Dodier (robert_dodier) Date: 20050615 08:37 Message: Logged In: YES user_id=501686 I'm attaching a list of test cases for sum, which can be executed by batch ("rtestsum.mac", test) . Doubtless there will be some discussion as to what the expected output of each test should be. All tests pass after making these 2 changes: ;; ORIGINAL: MEVAL ONCE ;; (mbinding (lind l*i) (meval exp)) ;; TRIED THIS: MEVAL TWICE ;; (mbinding (lind l*i) (meval (meval exp))) ;; THIRD TIME IS A CHARM ?? ($substitute *i ind (mbinding (lind l*i) (meval exp))) ;; ORIGINAL: MEVALATOMS ;; (resimplify (mevalatoms (if (and (not (atom exp)) (resimplify (meval (if (and (not (atom exp))  Comment By: Robert Dodier (robert_dodier) Date: 20050614 08:42 Message: Logged In: YES user_id=501686 OK, here is another attempt. I think I now understand this comment by Stavros in bug report # 740134  "First evaluate foo with i bound to itself, and check if that result is free of i. If so, return the product. If not, *substitute* (don't evaluate) i=lowerlimit, i=lowerlimit+1, etc." ;; ORIGINAL: MEVAL ONCE ;; (mbinding (lind l*i) (meval exp)) ;; TRIED THIS: MEVAL TWICE ;; (mbinding (lind l*i) (meval (meval exp))) ;; THIRD TIME IS A CHARM ?? ($substitute *i ind (mbinding (lind l*i) (meval exp))) This version now yields this result  ex 9: f(x) := sum (x, i, 1, 3); f(x) => 3 x as expected, as well as the same results for ex 1 through ex 8.  Comment By: Robert Dodier (robert_dodier) Date: 20050613 23:00 Message: Logged In: YES user_id=501686 Actually, after looking at the code some more (specifically DOSUM in src/asum.lisp) it looks to me like the intent is indeed to evaluate the summand after binding the summation index to itself. In addition, there is code to assume the index is between its lower and upper limits (although assume/forget is handled incorrectly, see 851765). I believe that the observed behavior is a bug, in the narrow sense that the observed behavior is different from what the code author intended. See also my comments on SF bug # 740134. Here is a different patch. I like this one better than the previous one. In DOSUM: ;; ORIGINAL: MEVAL ONCE ;; (mbinding (lind l*i) (meval exp)) (mbinding (lind l*i) (meval (meval exp))) In MEVALSUMARG: ;; ORIGINAL: MEVALATOMS ;; (resimplify (mevalatoms (if (and (not (atom exp)) (resimplify (meval (if (and (not (atom exp)) With these changes, the results are as expected for the examples cited by the original poster, and also the example about the translated function produces the correct result, and some examples adapted from another bug report (740134) yield correct results. ex 1: f(x):=x^2$ b: 1/10$ Ak: b*f(k*b)$ sum(Ak,k,0,9); => 57/200 ex 2: A(k):=k*f(k*b)$ b:1/n$ A(k) => k^3/n^2 sum(A(k),k,0,n1) => ('sum(k^3,k,0,n1))/n^2 sum(A(k),k,0,n1), simpsum => ((n1)^4 + 2*(n1)^3 + (n1)^2) / (4*n^2) ex 3: ak : k^2$ g(a,n) := sum(a,k,1,n)$ g(ak,5) => 55 translate (g)$ g(ak,5) => 55 some other examples, adapted from bug # 740134: ex 4: sum (print (i), i, 1, 3) => prints 1, 2, 3 then returns 6 ex 5: sum (integrate (x^i ,x), i, 0, 2) => x^3/3 + x^2/2 + x ex 6: sum (integrate (1/(x^i + 1), x), i, 0, 1) => log(x+1) + x/2 ex 7: f[i](x):=x^i$ g[i](x):=x^i$ h[i](x):=x^i$ /* reference f[i] and g[i]  see 740134 for the effect this has on previous defn of sum */ f[i]$ g[i](t)$ sum (f[i](x), i, 0, n) => 'sum (x^i, i, 0, n) sum (g[i](x), i, 0, n) => 'sum (x^i, i, 0, n) sum (h[i](x), i, 0, n) => 'sum (x^i, i, 0, n) ex 8: sum (integrate (x^i, x), i, 0, n) => 'sum (x^(i+1) / (i+1), i, 0, n)  Comment By: Barton Willis (willisbl) Date: 20050613 05:30 Message: Logged In: YES user_id=895922 If we decide to use Robert's $sum function, the translate property for sum will need to be changed. Consider: (1) Redefine $sum as Robert suggested. (2) Try this: (%i1) ak : k^2$ (%i2) g(a,n) := sum(a,k,1,n)$ (%i3) g(ak,5); (%o3) 55 < correct for Robert's $sum function (%i4) translate(g); (%o4) [g] (%i5) g(ak,5); (%o5) 5*k^2 < yeech There might be other things that need fixing: (%i8) properties(sum); (%o8) [Special Evaluation Form,OUTATIVE,NOUN,RULE] Barton  Comment By: Robert Dodier (robert_dodier) Date: 20050612 20:34 Message: Logged In: YES user_id=501686 OK, for the record, here is a definition of $sum which implements one of the ideas that has been proposed, namely this policy: evaluate the summand after binding the summation variable to itself. (defmspec $sum (l) (setq l (cdr l)) (if (= (length l) 4) (progv (list (cadr l)) (list (cadr l)) (dosum (meval (car l)) (cadr l) (meval (caddr l)) (meval (cadddr l)) t)) (wnaerr '$sum))) This version yields the results expected by the person who originated this bug report, and yields the results predicted by S Macrakis in the email referenced below (http://www.math.utexas.edu/pipermail/maxima/2003/004869.html), and run_testsuite() runs to completion with no errors. I'm in favor of making this change, but I'm just recording this code snippet here for future reference; no changes planned at the moment. For comparison here is the current version of $sum: (defmspec $sum (l) (setq l (cdr l)) (if (= (length l) 4) (dosum (car l) (cadr l) (meval (caddr l)) (meval (cadddr l)) t) (wnaerr '$sum)))  Comment By: Barton Willis (willisbl) Date: 20050501 06:09 Message: Logged In: YES user_id=895922 We've discussed this before; see http://www.math.utexas.edu/pipermail/maxima/2003/004869.html http://www.math.utexas.edu/pipermail/maxima/2003/004870.html Maybe a simple workaround such as mysum(f,v,lo,hi):=block([acc:0], if integerp(lo) and integerp(hi) then for i from lo thru hi do acc:acc+substitute(i,v,f) else acc:funmake('mysum,[f,v,lo,hi]), acc) or mysum(f,lo,hi):= block([acc:0], if integerp(lo) and integerp(hi) then for i : lo thru hi do acc : acc + apply(f,[i]) else acc : funmake('mysum,[f,lo,hi]), acc); might work for you, Barton  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1192935&group_id=4933 
From: SourceForge.net <noreply@so...>  20050615 07:18:06

Bugs item #1220979, was opened at 20050615 00:18 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=1220979&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 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Taylor Initial Comment: M : MATRIX([a,b],[b,c]); L : eigenvalues(M) Tc : taylor(L[1][1],c,0,2); Ta : taylor(L[1][1],a,0,2); But "a" and "c" is simmetric. it work for Tc, but don't work for Ta.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1220979&group_id=4933 
From: SourceForge.net <noreply@so...>  20050615 04:28:00

Bugs item #1220649, was opened at 20050614 13:41 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1220649&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: Closed Resolution: None Priority: 5 Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: empty sums Initial Comment: The user documentation says that an empty sum should evaluate to 0. But ... This is OK (%i1) sum(k,k,0,1); (%o1) 0 while this isn't (%i2) sum(k,k,0,2); Lower bound to SUM: 0 is greater than the upper bound:  2  an error. Quitting. To debug this try DEBUGMODE(TRUE); Barton  >Comment By: Barton Willis (willisbl) Date: 20050614 23:27 Message: Logged In: YES user_id=895922 When reading the user documentation, I skipped over the word 'one.' (I'd guess that other readers might skip it too.) So I agree, this isn't a bug. But it is weird that not every empty sum evaluates to 0 (when sumhack is false). Sometimes an empty sum might indicate a programming error. Something like (%i1) sum(i,i,5,1), sumhack : false; Warning: empty sum  returning 0 (%o1) 0 might make me happier. I'll close the bug. Barton  Comment By: Robert Dodier (robert_dodier) Date: 20050614 22:57 Message: Logged In: YES user_id=501686 Well, the documentation is not entirely clear on this point, but it looks to me like sum is behaving according to spec. The current documentation for sum in doc/info/Expressions.texi (restated from the old documentation) says If <i_1> is one less than <i_0>, the sum is a considered an "empty sum" and `sum' returns 0 rather than reporting an error. See also `sumhack'. The implication is that one less is OK, but anything else is an error. Probably I should clarify that. The flag sumhack causes sum to return something other than an error when the the second index is less than the first index. (Likewise prodhack for prod.) The behavior of sum is fairly strange, but I don't know if this should be called a bug.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1220649&group_id=4933 
From: SourceForge.net <noreply@so...>  20050615 03:57:50

Bugs item #1220649, was opened at 20050614 12:41 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1220649&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 Submitted By: Barton Willis (willisbl) Assigned to: Nobody/Anonymous (nobody) Summary: empty sums Initial Comment: The user documentation says that an empty sum should evaluate to 0. But ... This is OK (%i1) sum(k,k,0,1); (%o1) 0 while this isn't (%i2) sum(k,k,0,2); Lower bound to SUM: 0 is greater than the upper bound:  2  an error. Quitting. To debug this try DEBUGMODE(TRUE); Barton  >Comment By: Robert Dodier (robert_dodier) Date: 20050614 21:57 Message: Logged In: YES user_id=501686 Well, the documentation is not entirely clear on this point, but it looks to me like sum is behaving according to spec. The current documentation for sum in doc/info/Expressions.texi (restated from the old documentation) says If <i_1> is one less than <i_0>, the sum is a considered an "empty sum" and `sum' returns 0 rather than reporting an error. See also `sumhack'. The implication is that one less is OK, but anything else is an error. Probably I should clarify that. The flag sumhack causes sum to return something other than an error when the the second index is less than the first index. (Likewise prodhack for prod.) The behavior of sum is fairly strange, but I don't know if this should be called a bug.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1220649&group_id=4933 