From: SourceForge.net <noreply@so...>  20080730 02:12:33

Bugs item #2032110, was opened at 20080729 20:12 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=2032110&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  Solving equations Group: None Status: Open Resolution: None Priority: 7 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: spurious solution of trig equation, missed actual solution Initial Comment: (sin(x)  8*cos(x)*sin(x))*(sin(x)^2 + cos(x))  (2*cos(x)*sin(x)  sin(x))*(2*sin(x)^2 + 2*cos(x)^2  cos(x)); solve (%, x); `solve' is using arctrig functions to get a solution. Some solutions will be lost. => [x = %pi,x = %pi/2,x = 0] x = %pi and x = 0 are bona fide solutions, x = %pi/2 is spurious. A plot shows a root near 1.9 which find_root says is 1.9106.... Forwarded from sagedevel 20080729.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2032110&group_id=4933 
From: SourceForge.net <noreply@so...>  20080730 02:33:10

Bugs item #2032110, was opened at 20080729 21:12 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2032110&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  Solving equations Group: None Status: Open Resolution: None Priority: 7 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: spurious solution of trig equation, missed actual solution Initial Comment: (sin(x)  8*cos(x)*sin(x))*(sin(x)^2 + cos(x))  (2*cos(x)*sin(x)  sin(x))*(2*sin(x)^2 + 2*cos(x)^2  cos(x)); solve (%, x); `solve' is using arctrig functions to get a solution. Some solutions will be lost. => [x = %pi,x = %pi/2,x = 0] x = %pi and x = 0 are bona fide solutions, x = %pi/2 is spurious. A plot shows a root near 1.9 which find_root says is 1.9106.... Forwarded from sagedevel 20080729.  >Comment By: Barton Willis (willisbl) Date: 20080729 21:33 Message: Logged In: YES user_id=895922 Originator: NO Of course, Maxima should solve this equation without help. At least Maxima has the tools to solve it: (%o45) (sin(x)8*cos(x)*sin(x))*(sin(x)^2+cos(x))(2*cos(x)*sin(x)sin(x))*(2*sin(x)^2+2*cos(x)^2cos(x)) (%i46) exponentialize(%)$ (%i47) ratsubst(z, exp(%i*x),%)$ (%i48) solve(%,z)$ (%i49) subst(exp(%i*x),z,%)$ (%i50) map(lambda([s], solve(s,x)),%); (%o50) [[x=%i*log((2*sqrt(2)*%i)/31/3)],[x=%i*log((2*sqrt(2)*%i)/31/3)],[x=0],[x=%i*log(1)]]  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2032110&group_id=4933 
From: SourceForge.net <noreply@so...>  20090303 09:22:30

Bugs item #2032110, was opened at 20080729 21:12 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2032110&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  Solving equations Group: None Status: Open Resolution: None Priority: 7 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: spurious solution of trig equation, missed actual solution Initial Comment: (sin(x)  8*cos(x)*sin(x))*(sin(x)^2 + cos(x))  (2*cos(x)*sin(x)  sin(x))*(2*sin(x)^2 + 2*cos(x)^2  cos(x)); solve (%, x); `solve' is using arctrig functions to get a solution. Some solutions will be lost. => [x = %pi,x = %pi/2,x = 0] x = %pi and x = 0 are bona fide solutions, x = %pi/2 is spurious. A plot shows a root near 1.9 which find_root says is 1.9106.... Forwarded from sagedevel 20080729.  >Comment By: Barton Willis (willisbl) Date: 20090303 03:22 Message: The new to_poly_solver solves this equation: (%i7) eq : (sin(x)  8*cos(x)*sin(x))*(sin(x)^2 + cos(x))  (2*cos(x)*sin(x)  sin(x))*(2*sin(x)^2 + 2*cos(x)^2  cos(x)); (%o7) (sin(x)8*cos(x)*sin(x))*(sin(x)^2+cos(x))(2*cos(x)*sin(x)sin(x))*(2*sin(x)^2+2*cos(x)^2cos(x)) (%i8) sol : to_poly_solve(eq,x); (%o8) %union([x=2*%pi*%z22+%pi],[x=2*%pi*%z24],[x=2*%pi*%z26atan(2*sqrt(2))+%pi],[x=2*%pi*%z28+atan(2*sqrt(2))%pi]) (%i9) makelist(sublis(s,eq),s,args(sol)); (%o9) [0,0,0,0]  Comment By: Barton Willis (willisbl) Date: 20080729 21:33 Message: Logged In: YES user_id=895922 Originator: NO Of course, Maxima should solve this equation without help. At least Maxima has the tools to solve it: (%o45) (sin(x)8*cos(x)*sin(x))*(sin(x)^2+cos(x))(2*cos(x)*sin(x)sin(x))*(2*sin(x)^2+2*cos(x)^2cos(x)) (%i46) exponentialize(%)$ (%i47) ratsubst(z, exp(%i*x),%)$ (%i48) solve(%,z)$ (%i49) subst(exp(%i*x),z,%)$ (%i50) map(lambda([s], solve(s,x)),%); (%o50) [[x=%i*log((2*sqrt(2)*%i)/31/3)],[x=%i*log((2*sqrt(2)*%i)/31/3)],[x=0],[x=%i*log(1)]]  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2032110&group_id=4933 