extend the definition of q-binomial coefficients to (k > 0, n < 0)

[fchapoton]

This is extending the domain of the q-binomial coefficients.

This is done by polynomiality wrt n, for k >= 0.

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

[tscrim]

LGTM overall. I have one minor code stylistic change, and one question. Should the default ring for the $n &lt; 0$ case be $\mathbb{Z}[q,q^{-1}]$ instead of the fraction field of $\mathbb{Z}[q]$? This has properties closer to the polynomial ring and arithmetic is faster. What do you think?

[fchapoton]

yes, right, this is natural. Done, also for q_int.

[github-actions]

Documentation preview for this PR (built with commit 1e646f1; changes) is ready! 🎉

[tscrim]

Thanks. LGTM.

(Personally, I am not a fan of polygen as it is less explicit, but that's just my preference.)