solve() can return undefined points as "solutions"
|Reported by:||cwitty||Owned by:||was|
|Report Upstream:||N/A||Work issues:|
Consider the following examples (reported by Dean Moore here: http://groups.google.com/group/sage-support/browse_thread/thread/5555e780a76b3343#)
sage: solve(sin(x^2)/x == 0) [x == 0] sage: solve(sin(x^2)/x^2 == 0) [x == 0] sage: solve(sin(x^2)/x^3 == 0) [x == 0]
None of these functions are even defined at x=0, so that should not be returned as a solution. (The first two functions can be extended to x=0 by taking limits, in which case x=0 is a solution to the first one but not the second; the third function has a vertical asymptote at x=0.)