From 0214c7ad90b0afc3d1491c96e22e48d426caf5e2 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Tue, 21 Mar 2023 13:21:57 -0500 Subject: [PATCH] Tweak polynomial itertool recipes (GH-102880) --- Doc/library/itertools.rst | 27 +++++++++++++-------------- 1 file changed, 13 insertions(+), 14 deletions(-) diff --git a/Doc/library/itertools.rst b/Doc/library/itertools.rst index 38bc369d410dda..5daadfd3759f4b 100644 --- a/Doc/library/itertools.rst +++ b/Doc/library/itertools.rst @@ -866,6 +866,17 @@ which incur interpreter overhead. window.append(x) yield math.sumprod(kernel, window) + def polynomial_from_roots(roots): + """Compute a polynomial's coefficients from its roots. + + (x - 5) (x + 4) (x - 3) expands to: x³ -4x² -17x + 60 + """ + # polynomial_from_roots([5, -4, 3]) --> [1, -4, -17, 60] + expansion = [1] + for r in roots: + expansion = convolve(expansion, (1, -r)) + return list(expansion) + def polynomial_eval(coefficients, x): """Evaluate a polynomial at a specific value. @@ -876,20 +887,8 @@ which incur interpreter overhead. n = len(coefficients) if n == 0: return x * 0 # coerce zero to the type of x - powers = map(pow, repeat(x), range(n)) - return math.sumprod(reversed(coefficients), powers) - - def polynomial_from_roots(roots): - """Compute a polynomial's coefficients from its roots. - - (x - 5) (x + 4) (x - 3) expands to: x³ -4x² -17x + 60 - """ - # polynomial_from_roots([5, -4, 3]) --> [1, -4, -17, 60] - roots = list(map(operator.neg, roots)) - return [ - sum(map(math.prod, combinations(roots, k))) - for k in range(len(roots) + 1) - ] + powers = map(pow, repeat(x), reversed(range(n))) + return math.sumprod(coefficients, powers) def iter_index(iterable, value, start=0): "Return indices where a value occurs in a sequence or iterable."