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From: SourceForge.net <noreply@so...>  20120901 22:24:26

Bugs item #3558096, was opened at 20120815 17:46 Message generated for change (Comment added) made by jyoberle You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3558096&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: 5 Private: No Submitted By: JeanYves (jyoberle) Assigned to: Nobody/Anonymous (nobody) Summary: to_poly_solve gives a wrong solution for cos(x)=sin(3x) Initial Comment: Hi, When doing: load(to_poly_solve); algexact:true; to_poly_solve(cos(x)sin(3*x),x); I get: to_poly_solve: to_poly_solver.mac is obsolete; I'm loading to_poly_solve.mac instead. %union([x=(4*%pi*%z0+%pi)/4],[x=(4*%pi*%z1+%pi)/8]) But I think that the first solution should be (based on hand solving): (4*%pi*%z0+%pi)/4 (no minus sign). For example: if we consider %z0 = 0 in the to_poly_solve solution, we get x=%pi/4 which is not a solution of the equation cos(x)sin(3*x). On the other hand, if we set %z0 = 0 in the hand found solution, we get x=%pi/4 which is a solution. The build_info is: build_info("5.27.0","20120508 11:27:57","i686pcmingw32","GNU Common Lisp (GCL)","GCL 2.6.8"). Best regards, JeanYves  >Comment By: JeanYves (jyoberle) Date: 20120901 15:24 Message: Aleksasd, I agree with you regarding your calculations. However, when I apply the function "trigsolve" to the equation, I get: trigsolve(cos(x)sin(3*x),%pi,%pi); {(7*%pi)/8,(3*%pi)/8,%pi/8,(5*%pi)/8} Several solutions are missing (e.g. %pi/4) because of the bug I highlighted. Best regards, JeanYves  Comment By: Aleksas (aleksasd) Date: 20120831 08:03 Message: To finding all solutions of trigonometric equation eq from interval [a, b] we define function "trigsolve": (%i1) trigsolve(eq,a,b):=block([s,i,ats,algebraic], algebraic:true, to_poly_solve([eq], [x],'simpfuncs = ['rootscontract,'expand,'radcan,'nicedummies]), s:makelist(rhs(part(%%,k)[1]),k,1,length(%%)), ats:[], for i:1 thru length(s) do (makelist(ev(s[i],%z0=k),k,10,10), ats:append(ats,%%)), sublist(ats,lambda([e],e>=a and e<=b and float(ev(abs(lhs(eq)rhs(eq)),x=e))<ratepsilon)), sort(%%), setify(%%) )$ Example: solve cos(x)sin(3*x)=0 (%i2) eq:cos(x)sin(3*x)=0$ (%i3) cos(x)cos(y)=2*sin(1/2*x+1/2*y)*sin(1/2*x1/2*y)$ (%i4) subst(y=3*x%pi/2,%),expand; (%o4) cos(x)sin(3*x)=2*sin(x%pi/4)*sin(2*x%pi/4) (%i5) eq1:sin(x%pi/4)=0$ (%i6) eq2:sin(2*x%pi/4)=0$ (%i7) S1:trigsolve(eq1,%pi,%pi); to_poly_solve: to_poly_solver.mac is obsolete; I'm loading to_poly_solve.mac instead. Loading maximagrobner $Revision: 1.6 $ $Date: 20090602 07:49:49 $ (%o7) {(3*%pi)/4,%pi/4} (%i8) S2:trigsolve(eq2,%pi,%pi); (%o8) {(7*%pi)/8,(3*%pi)/8,%pi/8,(5*%pi)/8} (%i9) S:union(S1,S2); (%o9) {(7*%pi)/8,(3*%pi)/4,(3*%pi)/8,%pi/8,%pi/4,(5*%pi)/8} (%i10) float(%), numer; (%o10) {2.748893571891069,2.356194490192345,1.178097245096172,0.39269908169872,0.78539816339745,1.963495408493621} Answer: x=a+2*%pi*k, where a  any from S, k  any integer (%i11) plot2d([cos(x)sin(3*x)], [x,%pi,%pi])$  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3558096&group_id=4933 