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From: SourceForge.net <noreply@so...>  20040112 21:30:24

Bugs item #873244, was opened at 20040108 13:15 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: limit(x=0,x,0) wrong Initial Comment: limit(x=0,x,0) => 0=0. limit(equal(x,0),x,0) => equal(x,0) Let's leave aside the fact that 0=0 could simplify to True  that is not a limit issue, but a broader issue in Maxima. The real problem is that limit(x=0,x,0) is in fact FALSE, not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in particular for all 0<x<epsilon. Presumably the problem here is that Limit is assuming that "=" is a continuous function of its arguments. On the other hand, limit is *too* careful with other relationals: limit(x>0,x,0,plus) => noun limit(x>=0,x,0,plus) => noun These could perfectly well return TRUE. But that is a feature request, not a bug.  >Comment By: Barton Willis (willisbl) Date: 20040112 15:30 Message: Logged In: YES user_id=895922 The idom "Take the <limit, derivative, cube, ...> of both sides" is uttered a few thousand times per hour; for that reason, I think mapping limit, diff, and cube over an equality is sensible (not always correct, but GIGO) If, as you suggest (x = x) == true we'd also have to live with diff(x = x,x) > diff(true,x) > huh? I doubt this is what most users expect or want. Polemics aside, Maxima is lackadiasical about mapping functions over mbags. This needs to be cleaned up and (as you and I have discusssed) too much (possibly all) Maxima code assumes that the result of mapping a function over an mbag doesn't need simplification. That's another story. Barton  Comment By: Stavros Macrakis (macrakis) Date: 20040112 13:42 Message: Logged In: YES user_id=588346 Whether 0=0 should simplify to true is a side issue. I don't follow your argument about 0=0 representing the set of all numbers. ANY true statement represents the universal set (if you believe in that), whether it is {x  0=0} or {x  true} or {x  Socrates is mortal}. Note by the way that there is nothing telling you the domain. 0=0 could equally well represent the set of all determinant1 matrices or all the 5th degree polynomials over Z7, if that's the domain of x's you are manipulating.  Comment By: Wolfgang Jenkner (wjenkner) Date: 20040112 13:42 Message: Logged In: YES user_id=581700 > The real problem is that limit(x=0,x,0) is in fact FALSE, > not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in > particular for all 0<x<epsilon. Do you mean that in some punctured neighbourhood of 0, is(limit(x=0,x,0)) == is(0=0) == TRUE, limit(is(x=0),x,0) == limit(FALSE,x,0) == FALSE But this just shows that IS and LIMIT don't commute and, in particular, that IS(? = 0) is not continuous at 0. But... where is Maxima wrong?  Comment By: Stavros Macrakis (macrakis) Date: 20040112 13:37 Message: Logged In: YES user_id=588346 But mapping limit over an *equation* (not a generic mbag) is in general wrong if you consider an equation to be a boolean valued object. Remember, limit is defined for epsilon > 0, not epsilon >= 0. Limit(x=0,x,0) really is false, since x=0 is false for all abs(x)>0. On the other hand, limit(sin(x)=sin(x),x,inf) is true, even though limit(sin(x),x,inf) is ind, and in general ind does not equal ind (like NaN). And limit(x=x^2,x,inf) is false, even though limit(x,x,inf)=limit(x^2,x,inf)=inf.  Comment By: Barton Willis (willisbl) Date: 20040111 15:12 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  Comment By: Barton Willis (willisbl) Date: 20040111 15:11 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 
From: SourceForge.net <noreply@so...>  20040112 19:42:12

Bugs item #873244, was opened at 20040108 14:15 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: limit(x=0,x,0) wrong Initial Comment: limit(x=0,x,0) => 0=0. limit(equal(x,0),x,0) => equal(x,0) Let's leave aside the fact that 0=0 could simplify to True  that is not a limit issue, but a broader issue in Maxima. The real problem is that limit(x=0,x,0) is in fact FALSE, not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in particular for all 0<x<epsilon. Presumably the problem here is that Limit is assuming that "=" is a continuous function of its arguments. On the other hand, limit is *too* careful with other relationals: limit(x>0,x,0,plus) => noun limit(x>=0,x,0,plus) => noun These could perfectly well return TRUE. But that is a feature request, not a bug.  >Comment By: Stavros Macrakis (macrakis) Date: 20040112 14:42 Message: Logged In: YES user_id=588346 Whether 0=0 should simplify to true is a side issue. I don't follow your argument about 0=0 representing the set of all numbers. ANY true statement represents the universal set (if you believe in that), whether it is {x  0=0} or {x  true} or {x  Socrates is mortal}. Note by the way that there is nothing telling you the domain. 0=0 could equally well represent the set of all determinant1 matrices or all the 5th degree polynomials over Z7, if that's the domain of x's you are manipulating.  Comment By: Wolfgang Jenkner (wjenkner) Date: 20040112 14:42 Message: Logged In: YES user_id=581700 > The real problem is that limit(x=0,x,0) is in fact FALSE, > not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in > particular for all 0<x<epsilon. Do you mean that in some punctured neighbourhood of 0, is(limit(x=0,x,0)) == is(0=0) == TRUE, limit(is(x=0),x,0) == limit(FALSE,x,0) == FALSE But this just shows that IS and LIMIT don't commute and, in particular, that IS(? = 0) is not continuous at 0. But... where is Maxima wrong?  Comment By: Stavros Macrakis (macrakis) Date: 20040112 14:37 Message: Logged In: YES user_id=588346 But mapping limit over an *equation* (not a generic mbag) is in general wrong if you consider an equation to be a boolean valued object. Remember, limit is defined for epsilon > 0, not epsilon >= 0. Limit(x=0,x,0) really is false, since x=0 is false for all abs(x)>0. On the other hand, limit(sin(x)=sin(x),x,inf) is true, even though limit(sin(x),x,inf) is ind, and in general ind does not equal ind (like NaN). And limit(x=x^2,x,inf) is false, even though limit(x,x,inf)=limit(x^2,x,inf)=inf.  Comment By: Barton Willis (willisbl) Date: 20040111 16:12 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  Comment By: Barton Willis (willisbl) Date: 20040111 16:11 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 
From: SourceForge.net <noreply@so...>  20040112 19:42:06

Bugs item #873244, was opened at 20040108 20:15 Message generated for change (Comment added) made by wjenkner You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: limit(x=0,x,0) wrong Initial Comment: limit(x=0,x,0) => 0=0. limit(equal(x,0),x,0) => equal(x,0) Let's leave aside the fact that 0=0 could simplify to True  that is not a limit issue, but a broader issue in Maxima. The real problem is that limit(x=0,x,0) is in fact FALSE, not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in particular for all 0<x<epsilon. Presumably the problem here is that Limit is assuming that "=" is a continuous function of its arguments. On the other hand, limit is *too* careful with other relationals: limit(x>0,x,0,plus) => noun limit(x>=0,x,0,plus) => noun These could perfectly well return TRUE. But that is a feature request, not a bug.  >Comment By: Wolfgang Jenkner (wjenkner) Date: 20040112 20:42 Message: Logged In: YES user_id=581700 > The real problem is that limit(x=0,x,0) is in fact FALSE, > not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in > particular for all 0<x<epsilon. Do you mean that in some punctured neighbourhood of 0, is(limit(x=0,x,0)) == is(0=0) == TRUE, limit(is(x=0),x,0) == limit(FALSE,x,0) == FALSE But this just shows that IS and LIMIT don't commute and, in particular, that IS(? = 0) is not continuous at 0. But... where is Maxima wrong?  Comment By: Stavros Macrakis (macrakis) Date: 20040112 20:37 Message: Logged In: YES user_id=588346 But mapping limit over an *equation* (not a generic mbag) is in general wrong if you consider an equation to be a boolean valued object. Remember, limit is defined for epsilon > 0, not epsilon >= 0. Limit(x=0,x,0) really is false, since x=0 is false for all abs(x)>0. On the other hand, limit(sin(x)=sin(x),x,inf) is true, even though limit(sin(x),x,inf) is ind, and in general ind does not equal ind (like NaN). And limit(x=x^2,x,inf) is false, even though limit(x,x,inf)=limit(x^2,x,inf)=inf.  Comment By: Barton Willis (willisbl) Date: 20040111 22:12 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  Comment By: Barton Willis (willisbl) Date: 20040111 22:11 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 
From: SourceForge.net <noreply@so...>  20040112 19:37:40

Bugs item #873244, was opened at 20040108 14:15 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: limit(x=0,x,0) wrong Initial Comment: limit(x=0,x,0) => 0=0. limit(equal(x,0),x,0) => equal(x,0) Let's leave aside the fact that 0=0 could simplify to True  that is not a limit issue, but a broader issue in Maxima. The real problem is that limit(x=0,x,0) is in fact FALSE, not TRUE. Since x=0 is FALSE for all x#0, it is FALSE in particular for all 0<x<epsilon. Presumably the problem here is that Limit is assuming that "=" is a continuous function of its arguments. On the other hand, limit is *too* careful with other relationals: limit(x>0,x,0,plus) => noun limit(x>=0,x,0,plus) => noun These could perfectly well return TRUE. But that is a feature request, not a bug.  >Comment By: Stavros Macrakis (macrakis) Date: 20040112 14:37 Message: Logged In: YES user_id=588346 But mapping limit over an *equation* (not a generic mbag) is in general wrong if you consider an equation to be a boolean valued object. Remember, limit is defined for epsilon > 0, not epsilon >= 0. Limit(x=0,x,0) really is false, since x=0 is false for all abs(x)>0. On the other hand, limit(sin(x)=sin(x),x,inf) is true, even though limit(sin(x),x,inf) is ind, and in general ind does not equal ind (like NaN). And limit(x=x^2,x,inf) is false, even though limit(x,x,inf)=limit(x^2,x,inf)=inf.  Comment By: Barton Willis (willisbl) Date: 20040111 16:12 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  Comment By: Barton Willis (willisbl) Date: 20040111 16:11 Message: Logged In: YES user_id=895922 I think mapping limit over an mbag is sensible and consistent with much of Maxima. 0 = 0 could reasonally simplify to true, but it could just as well represent the set of all real (or complex) numbers. [ If 0 = 0, then 0 x = 0; the solution set of 0 x = 0 is everything.] I think Maxima shouldn't simplify 0 = 0 to true or anything else. Barton  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=873244&group_id=4933 