## [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero

 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2006-11-18 19:52:37 ```Bugs item #1504146, was opened at 2006-06-10 17:59 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&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 - Assume Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- >Comment By: Stavros Macrakis (macrakis) Date: 2006-11-18 14:52 Message: Logged In: YES user_id=588346 Originator: YES > Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! This is because of rounding errors. To see clearly how small these errors are, try plot2d(sin(x)^2+cos(x)^2-1,[x,0,6]); This gives you a useful scale for the y axis. Unfortunately, plot2d(sin(x)^2+cos(x)^2,...) does not -- it shows the min and max values as 1, where it is in fact 0.999999999999999 -> 1.000000000000001 or something. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-11-18 11:16 Message: Logged In: NO Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! S.Sangwal sangwal77 AT yahoo.com ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-11 14:47 Message: Logged In: YES user_id=588346 It would be OK if taylor/asksign asked if the expression was pnz, because the user could answer z (there will always be some cases that asksign can't handle, after all). The problem is that taylor/asksign is asking if it is pn, not giving the user the possibility of answering z. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-11 14:30 Message: Logged In: YES user_id=501686 I don't think the bug is in taylor; reassigning the category to "Lisp Core - Assume". Feel free to change the category again. asksign (sin(x)^2+cos(x)^2-1); => Is sin(x)^2+cos(x)^2-1 pnz ? is(equal(sin(x)^2+cos(x)^2-1,0)); => Maxima was unable to evaluate the predicate I don't know how hard asksign and/or is and/or mevalp should try to simplify. trigsimp(sin(x)^2+cos(x)^2-1); => 0 but trigsimp isn't applied automatically. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2006-06-10 21:59:49 ```Bugs item #1504146, was opened at 2006-06-10 17:59 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=1504146&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 - Taylor Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2006-06-11 18:30:09 ```Bugs item #1504146, was opened at 2006-06-10 15:59 Message generated for change (Settings changed) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&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 - Assume Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- >Comment By: Robert Dodier (robert_dodier) Date: 2006-06-11 12:30 Message: Logged In: YES user_id=501686 I don't think the bug is in taylor; reassigning the category to "Lisp Core - Assume". Feel free to change the category again. asksign (sin(x)^2+cos(x)^2-1); => Is sin(x)^2+cos(x)^2-1 pnz ? is(equal(sin(x)^2+cos(x)^2-1,0)); => Maxima was unable to evaluate the predicate I don't know how hard asksign and/or is and/or mevalp should try to simplify. trigsimp(sin(x)^2+cos(x)^2-1); => 0 but trigsimp isn't applied automatically. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2006-06-11 18:47:04 ```Bugs item #1504146, was opened at 2006-06-10 17:59 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&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 - Assume Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- >Comment By: Stavros Macrakis (macrakis) Date: 2006-06-11 14:47 Message: Logged In: YES user_id=588346 It would be OK if taylor/asksign asked if the expression was pnz, because the user could answer z (there will always be some cases that asksign can't handle, after all). The problem is that taylor/asksign is asking if it is pn, not giving the user the possibility of answering z. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-11 14:30 Message: Logged In: YES user_id=501686 I don't think the bug is in taylor; reassigning the category to "Lisp Core - Assume". Feel free to change the category again. asksign (sin(x)^2+cos(x)^2-1); => Is sin(x)^2+cos(x)^2-1 pnz ? is(equal(sin(x)^2+cos(x)^2-1,0)); => Maxima was unable to evaluate the predicate I don't know how hard asksign and/or is and/or mevalp should try to simplify. trigsimp(sin(x)^2+cos(x)^2-1); => 0 but trigsimp isn't applied automatically. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2006-11-18 16:16:47 ```Bugs item #1504146, was opened at 2006-06-10 14:59 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&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 - Assume Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-11-18 08:16 Message: Logged In: NO Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! S.Sangwal sangwal77 AT yahoo.com ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-11 11:47 Message: Logged In: YES user_id=588346 It would be OK if taylor/asksign asked if the expression was pnz, because the user could answer z (there will always be some cases that asksign can't handle, after all). The problem is that taylor/asksign is asking if it is pn, not giving the user the possibility of answering z. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-11 11:30 Message: Logged In: YES user_id=501686 I don't think the bug is in taylor; reassigning the category to "Lisp Core - Assume". Feel free to change the category again. asksign (sin(x)^2+cos(x)^2-1); => Is sin(x)^2+cos(x)^2-1 pnz ? is(equal(sin(x)^2+cos(x)^2-1,0)); => Maxima was unable to evaluate the predicate I don't know how hard asksign and/or is and/or mevalp should try to simplify. trigsimp(sin(x)^2+cos(x)^2-1); => 0 but trigsimp isn't applied automatically. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2006-11-18 19:52:37 ```Bugs item #1504146, was opened at 2006-06-10 17:59 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&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 - Assume Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- >Comment By: Stavros Macrakis (macrakis) Date: 2006-11-18 14:52 Message: Logged In: YES user_id=588346 Originator: YES > Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! This is because of rounding errors. To see clearly how small these errors are, try plot2d(sin(x)^2+cos(x)^2-1,[x,0,6]); This gives you a useful scale for the y axis. Unfortunately, plot2d(sin(x)^2+cos(x)^2,...) does not -- it shows the min and max values as 1, where it is in fact 0.999999999999999 -> 1.000000000000001 or something. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-11-18 11:16 Message: Logged In: NO Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! S.Sangwal sangwal77 AT yahoo.com ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-11 14:47 Message: Logged In: YES user_id=588346 It would be OK if taylor/asksign asked if the expression was pnz, because the user could answer z (there will always be some cases that asksign can't handle, after all). The problem is that taylor/asksign is asking if it is pn, not giving the user the possibility of answering z. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-11 14:30 Message: Logged In: YES user_id=501686 I don't think the bug is in taylor; reassigning the category to "Lisp Core - Assume". Feel free to change the category again. asksign (sin(x)^2+cos(x)^2-1); => Is sin(x)^2+cos(x)^2-1 pnz ? is(equal(sin(x)^2+cos(x)^2-1,0)); => Maxima was unable to evaluate the predicate I don't know how hard asksign and/or is and/or mevalp should try to simplify. trigsimp(sin(x)^2+cos(x)^2-1); => 0 but trigsimp isn't applied automatically. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504146 ] taylor asks pn? when expr is zero From: SourceForge.net - 2008-11-30 22:03:05 ```Bugs item #1504146, was opened at 2006-06-10 17:59 Message generated for change (Comment added) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&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 - Assume Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) >Assigned to: Dan Gildea (dgildea) Summary: taylor asks pn? when expr is zero Initial Comment: taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2) asks whether sin(x)^2+cos(x)^2-1 is positive or negative, where of course it is identically zero. ---------------------------------------------------------------------- >Comment By: Dan Gildea (dgildea) Date: 2008-11-30 17:03 Message: as of comm2.lisp rev 1.22, simpatan2 no longer asks questions: (%i8) taylor( asin( ( cos(x+a)^2 + sin(x)^2-1 ) / a), a, 0, 2); (%o8) %i*log(a)+(-log(abs(2*sin(x)^2+2*cos(x)^2-2))*%i +atan2(2*sin(x)^2+2*cos(x)^2-2,0)) +2*%i*cos(x)*sin(x)*a/(sin(x)^2+cos(x)^2-1) -(4*%i*sin(x)^4+(-8*%i*cos(x)^2-4*%i)*sin(x)^2-4*%i*cos(x)^4 +4*%i*cos(x)^2-%i) *a^2 /(4*sin(x)^4+(8*cos(x)^2-8)*sin(x)^2+4*cos(x)^4-8*cos(x)^2+4) (%i9) trigsimp(%); atan2(0,0) has been generated. (oops) ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-11-18 14:52 Message: Logged In: YES user_id=588346 Originator: YES > Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! This is because of rounding errors. To see clearly how small these errors are, try plot2d(sin(x)^2+cos(x)^2-1,[x,0,6]); This gives you a useful scale for the y axis. Unfortunately, plot2d(sin(x)^2+cos(x)^2,...) does not -- it shows the min and max values as 1, where it is in fact 0.999999999999999 -> 1.000000000000001 or something. ---------------------------------------------------------------------- Comment By: Nobody/Anonymous (nobody) Date: 2006-11-18 11:16 Message: Logged In: NO Also, the graph (2d!) of sin(x)^2+cos(x)^2 is not a straight line! S.Sangwal sangwal77 AT yahoo.com ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-11 14:47 Message: Logged In: YES user_id=588346 It would be OK if taylor/asksign asked if the expression was pnz, because the user could answer z (there will always be some cases that asksign can't handle, after all). The problem is that taylor/asksign is asking if it is pn, not giving the user the possibility of answering z. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-11 14:30 Message: Logged In: YES user_id=501686 I don't think the bug is in taylor; reassigning the category to "Lisp Core - Assume". Feel free to change the category again. asksign (sin(x)^2+cos(x)^2-1); => Is sin(x)^2+cos(x)^2-1 pnz ? is(equal(sin(x)^2+cos(x)^2-1,0)); => Maxima was unable to evaluate the predicate I don't know how hard asksign and/or is and/or mevalp should try to simplify. trigsimp(sin(x)^2+cos(x)^2-1); => 0 but trigsimp isn't applied automatically. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504146&group_id=4933 ```