X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Forthogonal_polynomials.py;h=7544f65c048c72662ff72c40bbcb1197a98382a7;hb=852c32e6db3d27310489abd9e23787a1b7d068ad;hp=fd5fd75317b9f07b9108dd41ebd74d6606f9fd12;hpb=5f0f517a80ae4f3e12bf4d3a84ea3d182cb96e70;p=sage.d.git

diff --git a/mjo/orthogonal_polynomials.py b/mjo/orthogonal_polynomials.py
index fd5fd75..7544f65 100644
--- a/mjo/orthogonal_polynomials.py
+++ b/mjo/orthogonal_polynomials.py
@@ -1,7 +1,7 @@
 from sage.all import *
 
 def legendre_p(n, x, a = -1, b = 1):
-    """
+    r"""
     Returns the ``n``th Legendre polynomial of the first kind over the
     interval [a, b] with respect to ``x``.
 
@@ -72,15 +72,12 @@ def legendre_p(n, x, a = -1, b = 1):
         sage: a = -pi
         sage: b = pi
         sage: def inner_product(v1, v2):
-        ...       return integrate(v1*v2, x, a, b)
-        ...
+        ....:     return integrate(v1*v2, x, a, b)
         sage: def norm(v):
-        ...       return sqrt(inner_product(v,v))
-        ...
+        ....:     return sqrt(inner_product(v,v))
         sage: def project(basis, v):
-        ...       return sum([ inner_product(v, b)*b/norm(b)**2
-        ...                    for b in basis])
-        ...
+        ....:     return sum( inner_product(v, b)*b/norm(b)**2
+        ....:                 for b in basis)
         sage: f = sin(x)
         sage: legendre_basis = [ legendre_p(k, x, a, b) for k in xrange(4) ]
         sage: proj = project(legendre_basis, f)
@@ -92,7 +89,7 @@ def legendre_p(n, x, a = -1, b = 1):
     We should agree with Maxima for all `n`::
 
         sage: eq = lambda k: bool(legendre_p(k,x) == legendre_P(k,x))
-        sage: all([eq(k) for k in xrange(20) ]) # long time
+        sage: all( eq(k) for k in xrange(20) ) # long time
         True
 
     We can evaluate the result of the zeroth polynomial::
@@ -196,6 +193,6 @@ def legendre_p(n, x, a = -1, b = 1):
 
     # From Abramowitz & Stegun, (22.3.2) with alpha = beta = 0.
     # Also massaged to support finite field elements.
-    P = sum([ c(m)*g(m) for m in xrange(n+1) ])/(2**n)
+    P = sum( c(m)*g(m) for m in xrange(n+1) )/(2**n)
 
     return P