Add support for different `show`s about polynomials.jl

[jverzani]

Implementing this first would likely involve just generalizing printpoly and then figuring out the proper way to call it. I'm not sure how that should be done.

As for the second, I have a new package PolynomialFactors that can factor over the integers modest-sized polynomials. I show the factors in a dictionary so it is clear to a user how to manipulate them, maybe in factored form would be more suitable and not much trouble. But that doesn't really help you, as your polynomials aren't restricted to integer or rational coefficients, so even the act of factoring isn't so easy if multiple roots are common.

[martinholters]

I'd actually like to see printpoly be made part of the public API to be able to show a polynomial (or convert it to a string) without the surrounding Poly(...), and with the possibility to request reverse ordering. (And also an option to appreciate any powers part of the variable, e.g. printpoly(Poly([1,2,3], "z^-1"), collapse_powers=true) should give "1 + 2*z^-1 + 3*z^-2".)

Unless this is considered a bad idea (or someone happens to be working on it already), I'd be willing to tackle it. Should I?

[aytekinar]

Correct. In our case, since we are dealing polynomials having real coefficients, we have roots in conjugate pairs. I am planning to keep one of the pairs (in this case, the one with the positive imaginary part, for example). Then, at least, I would not need to care much about pairing them.

As for the first (reversed order printing), I would be more than happy seeing such an option. (Maybe I can also come up with a PR if needed).

[aytekinar]

Actually, I would like to have the representation without the Poly(...) surrounding 👍
Reverse ordering also sounds great!

[jverzani]

The only reason I worked on this was to have the printed output be copy-and-pasteable and to have printing work with some other number types (like the GF(2) example). I'm not sure who is wed to the enclosing Poly or the ordering, though I would think the default should match that expected by the constructor. Looking forward to what you come up with.