[3.11] Add polynomial_from_roots() to the itertools recipes (GH-96102)

[miss-islington]

(cherry picked from commit 0e28a3a)

Co-authored-by: Raymond Hettinger rhettinger@users.noreply.github.com

[miss-islington]

@rhettinger: Status check is done, and it's a failure ❌ .

[miss-islington]

Status check is done, and it's a success ✅ .

[mdickinson]

@rhettinger It may be worth adding a caveat that this approach should only be used for small inputs. While it's an interesting demonstration of pieces of itertools, it's also inefficient (exponential time) for large inputs, compared to the obvious multiply-the-linear-terms quadratic-time algorithm:

def polynomial_from_roots(roots):
    poly = [1]
    for root in roots:
        poly = [a + b for a, b in zip([0] + [c * -root for c in poly], poly + [0])]
    return poly