[Maxima-bugs] [ maxima-Bugs-3322221 ] Lost solutions in to_poly_solve

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Bugs item #3322221, was opened at 2011-06-19 08:43
Message generated for change (Comment added) made by aleksasd
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Category: Lisp Core - Solving equations
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Aleksas (aleksasd)
Assigned to: Nobody/Anonymous (nobody)
Summary: Lost solutions in to_poly_solve

Initial Comment:
 Lost solutions in to_poly_solve

(%i1) eq:sin(2*x)=cos(x);
(%o1) sin(2*x)=cos(x)
(%i2) eq1:trigexpand(eq);
(%o2) 2*cos(x)*sin(x)=cos(x)

 Lost solutions:
(%i3) to_poly_solve([eq], [x]);
Loading maxima-grobner $Revision: 1.6 $ $Date: 2009/06/02 07:49:49 $
(%o3) %union([x=-(4*%pi*%z0+%pi)/2],[x=(4*%pi*%z1+%pi)/6])

 Correct:
(%i4) to_poly_solve([eq1], [x]);
(%o4) %union([x=2*%pi*%z15-%pi/2],[x=2*%pi*%z17+%pi/2],
      [x=2*%pi*%z19+%pi/6],[x=2*%pi*%z21+(5*%pi)/6])

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>Comment By: Aleksas (aleksasd)
Date: 2011-06-19 09:28

Message:
 In to_poly_solve equation is not equivalent to 
lhs(equation)-rhs(equation)=0.

For example:
(%i1) eq:sin(2*x)=cos(x);
(%o1) sin(2*x)=cos(x)
(%i2) to_poly_solve([eq], [x]);
Loading maxima-grobner $Revision: 1.6 $ $Date: 2009/06/02 07:49:49 $
(%o2) %union([x=-(4*%pi*%z0+%pi)/2],[x=(4*%pi*%z1+%pi)/6])
(%i3) to_poly_solve([lhs(eq)-rhs(eq)=0], [x]);
(%o3)
%union([x=2*%pi*%z15-%pi/2],[x=2*%pi*%z17+%pi/2],[x=2*%pi*%z19+%pi/6],[x=2*%pi*%z21+(5*%pi)/6])

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