X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Finterpolation.py;h=4be95e2463b7d4b1592a5f4e6cf86ba54e36da7f;hb=eeca2aaf291ef8cb215e277c09c4205be8a84298;hp=393908670054a9740203de64c3e0338e10f689c0;hpb=4a17cddb945c51a206920c5a7a4d5ddce8141af5;p=sage.d.git

diff --git a/mjo/interpolation.py b/mjo/interpolation.py
index 3939086..4be95e2 100644
--- a/mjo/interpolation.py
+++ b/mjo/interpolation.py
@@ -1,5 +1,5 @@
 from sage.all import *
-from misc import product
+product = prod
 
 
 def lagrange_denominator(k, xs):
@@ -48,7 +48,7 @@ def lagrange_coefficient(k, x, xs):
 
         sage: xs = [ -pi/2, -pi/6, 0, pi/6, pi/2 ]
         sage: lagrange_coefficient(0, x, xs)
-        1/8*(pi - 6*x)*(pi - 2*x)*(pi + 6*x)*x/pi^4
+        1/8*(pi + 6*x)*(pi - 2*x)*(pi - 6*x)*x/pi^4
 
     """
     numerator = lagrange_psi(x, xs)/(x - xs[k])
@@ -60,7 +60,7 @@ def lagrange_coefficient(k, x, xs):
 
 def lagrange_polynomial(x, xs, ys):
     """
-    Return the Lagrange form of the interpolation polynomial in `x` of
+    Return the Lagrange form of the interpolating polynomial in `x`
     at the points (xs[k], ys[k]).
 
     INPUT:
@@ -183,10 +183,10 @@ def divided_difference(xs, ys):
 
     We try something entirely symbolic::
 
-        sage: f = function('f', x)
+        sage: f = function('f')(x)
         sage: divided_difference([x], [f(x=x)])
         f(x)
-        sage: x1,x2 = var('x1,x2')
+        sage: x1,x2 = SR.var('x1,x2')
         sage: divided_difference([x1,x2], [f(x=x1),f(x=x2)])
         f(x1)/(x1 - x2) - f(x2)/(x1 - x2)