From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 26 Oct 2012 18:13:03 +0000 (-0400)
Subject: Add the divided_difference_coefficients() function.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=0594e23633dd2088e6ff9b566d86d4618528212f;p=sage.d.git

Add the divided_difference_coefficients() function.
---

diff --git a/mjo/interpolation.py b/mjo/interpolation.py
index 0cafc28..d5011ea 100644
--- a/mjo/interpolation.py
+++ b/mjo/interpolation.py
@@ -73,6 +73,26 @@ def lagrange_polynomial(x, xs, ys):
     return sigma
 
 
+
+def divided_difference_coefficients(xs):
+    """
+    Assuming some function `f`, compute the coefficients of the
+    divided difference f[xs[0], ..., xs[n]].
+
+    TESTS:
+
+        sage: divided_difference_coefficients([0])
+        [1]
+        sage: divided_difference_coefficients([0, pi])
+        [-1/pi, 1/pi]
+        sage: divided_difference_coefficients([0, pi, 2*pi])
+        [1/2/pi^2, -1/pi^2, 1/2/pi^2]
+
+    """
+    coeffs = [ product([ (QQ(1) / (xj - xi)) for xi in xs if xi != xj ])
+               for xj in xs ]
+    return coeffs
+
 def divided_difference(f, xs):
     """
     Return the Newton divided difference of `f` at the points