#8390: Find all roots of a trigonometric equation
---------------------------+------------------------------------------------
Reporter: olazo | Owner: olazo
Type: enhancement | Status: new
Priority: minor | Milestone:
Component: algebra | Keywords: trigonometric, roots
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by robert.marik):
Sage interface for Maxima's solver works like this:
We try Maxima's solve function first. It we get empty answer, we try the
to_poly_solve for the same equation.
If the answer is not empty, we pass the answer of solve command to
Maxima's to_poly_solve.
For our equation, solve command in Maxima gives only one solution pi/6
(and probably writes something like "SOLVE is using arc-trig functions to
get a solution. Some solutions will be lost." on terminal).
{{{
[ma...@um-bc107 /opt/sage]$ ./sage
----------------------------------------------------------------------
| Sage Version 4.3.2, Release Date: 2010-02-06 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: eq = sin(2*x-pi/6) == 1/2
sage: eq._maxima_().solve(x)
[x=%pi/6]
sage: eq._maxima_().to_poly_solve(x)
%union([x=-(-2*%pi*%z6-%pi)/2],[x=-(-2*%pi*%z8-%pi/3)/2])
sage:
}}}
I hope this is an explanation. I do not have enough experiences with
to_poly_solve, so my questions are: Is it good idea to skip solve and use
to_poly_solve immediatelly when to_poly_sole = True? Or is it posssible to
check from within Sage, that the warning about arc-trig functions has been
printed? Or introduce to_poly_solve = 'force' to omit solve command?
Now you can use
{{{
sage: eq._maxima_().to_poly_solve(x).sage()
[[x == 1/2*pi + pi*z16], [x == 1/6*pi + pi*z18]]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8390#comment:2>
Sage <http://www.sagemath.org>
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