What's the difference in all the polynomial solve/root/zero functions?

[ewjax]

Interesting. I was just playing with that setting, and as you point out, when the i is not checked, solve() and zeros() do not return i or -i in their answer, while the c-versions do, and so does proot().

However, I did notice that if you run cZeros() without i checked, it will be checked after cZeros() runs. That function turns on the i option and doesn't reset it. The csolve() function doesn't commit that error.

But complex numbers aside, I'm still wondering what the conceptual difference is between solve(), zeros(), and proot().

"Solve this polynomial."
"Find the roots of this polynomial."
"Find the zeros of this polynomial."

In my mind at least those are all equivalent sentences, but perhaps there are times when they aren't equivalent?