Updates:
Labels: EasyToFix
Comment #1 on issue 716 by [email protected]: either tangent_line or
is_tangent is wrong
http://code.google.com/p/sympy/issues/detail?id=716
In the branch (geometry2) that I am on, the tangent_line for a random_point
cannot be solved but the tangent for an arbitrary point can be. So using
that we can find the problem:
h[14] >>> e = Ellipse(Point(0,0), 3, 2)
h[14] >>> a=e.arbitrary_point().subs(t, 1)
h[14] >>> l=e.tangent_lines(a)[0]
h[14] >>> i=e.intersection(l)
h[14] >>> len(i)
2
So there are apparently two intersection points. Let's see if the x and y
values of the intersections are the same or not:
h[15] >>> trigsimp(factor(i[0][0] - i[1][0]))
0
h[15] >>> trigsimp(factor(i[0][1] - i[1][1]))
0
They aren't different from each other. Issue 1562 identified the need of
trigsimp to use factoring. That would solve this problem since the
determination of being tangent depends on determining how many intersection
points there are. Without factor the x and y values of the coordinate *do*
appear different i.e. nonzero:
h[15] >>> trigsimp((i[0][0] - i[1][0]))
-(36 - 72*cos(1)**2 - 36*sin(1)**4 + 36*cos(1)**4)**(1/2)*sin(1)
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