From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 4 Nov 2012 21:12:17 +0000 (-0500)
Subject: Add the lagrange_psi function.
X-Git-Url: http://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=03f0629ed5ea048ba00751d72e8508868b48fb66;p=sage.d.git

Add the lagrange_psi function.
---

diff --git a/mjo/interpolation.py b/mjo/interpolation.py
index 70c35c1..8c3936e 100644
--- a/mjo/interpolation.py
+++ b/mjo/interpolation.py
@@ -93,6 +93,7 @@ def divided_difference_coefficients(xs):
                for xj in xs ]
     return coeffs
 
+
 def divided_difference(xs, ys):
     """
     Return the Newton divided difference of the points (xs[k],
@@ -269,3 +270,25 @@ def hermite_interpolant(x, xs, ys, y_primes):
                for k in range(0, len(xs)) ])
 
     return (s1 + s2)
+
+
+def lagrange_psi(x, xs):
+    """
+    The function,
+
+      Psi(x) = (x - xs[0])*(x - xs[1])* ... *(x - xs[-1])
+
+    used in Lagrange and Hermite interpolation.
+
+    INPUT:
+
+      - ``x`` -- The independent variable of the resulting expression.
+
+      - ``xs`` -- A list of points.
+
+    OUTPUT:
+
+    A symbolic expression in one variable, `x`.
+    """
+
+    return product([ (x - xj) for xj in xs ])