id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
3745,calculus -- bugs in solve,was,gfurnish,"We get a ""solution"" from `solve()` that isn't actually a solution:
{{{
sage: f(x) = (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))
sage: solve(f(x), x)
[x == pi, x == 1/2*pi, x == 0]
sage: f(pi/2)
-1
}}}
The following is correct:
{{{
sage: solve(f(x).simplify_trig(), x)
[x == 0, x == pi - arccos(1/3), x == pi]
}}}
Reduced example (after manually removing the factor `sin(x)`):
{{{
sage: g(x) = (1 - 8*cos(x))*(sin(x)^2 + cos(x)) - (2*cos(x) - 1)*(-2*sin(x)^2 + 2*cos(x)^2 - cos(x))
sage: solve(g(x), x)
[x == pi, x == 1/2*pi]
sage: g(pi/2)
-1
}}}",defect,new,major,sage-6.4,calculus,,,,,,,Reported upstream. No feedback yet.,,,,,todo