On Sunday, January 19, 2014 4:32:38 AM UTC+4, Aaron Meurer wrote:
>
> Oh, and I forgot that another prerequisite is a way for solve() to 
> state that it knows that it has found *all* the solutions. Otherwise, 
> if you code the basic algorithm that finds all the critical points, 
> you may miss some simply by virtue of solve() not finding it, and 
> thereby potentially get wrong answers.


IMHO, it's a solve() problem.  It should return all solutions, or signal
a failure in some conventional way (e.g. raise an error).  In particular,
it can *fail* due to wrong heuristics.  Real issue here - how to represent
some solutions (e.g. sin(x)==0).

Let's document how to detect that solve() was unsuccessful, and then
we can write code that expects solve() works as documented.

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