Remove the unused example1.py/spline3.lyx paper that I never finished.

diff --git a/doc/example1.py b/doc/example1.py
deleted file mode 100644 (file)
index 9dbe06f..0000000
--- a/doc/example1.py
+++ /dev/null
@@ -1,100 +0,0 @@
-#!/home/mjo/bin/sage
-
-# example1.py
-#
-# In the paper, we display a lot of sage code to be entered at the
-# prompt. It's not much fun re-entering all of these formulas every
-# time you'd like to work on the paper, so a quick load('example1.py')
-# from the sage prompt will pull all of this stuff in for you.
-#
-
-x,y,z = var('x,y,z')
-
-f = 1 + x + x*y + x*y*z
-
-g = [[[ f(x=a, y=b, z=c) for a in range(0,3) ] for b in range(0,3) ] for c in range(0,3) ]
-
-def grid(x,y,z):
-    return g[z][y][x]
-
-def I(x,y,z):
-    return grid(x,y,z)
-
-def F(x,y,z):
-    return grid(x-1, y, z)
-
-def B(x,y,z):
-    return grid(x+1, y, z)
-
-def L(x,y,z):
-    return grid(x, y-1, z)
-
-def R(x,y,z):
-    return grid(x, y+1, z)
-
-def T(x,y,z): 
-    return grid(x, y, z+1)
-
-def D(x,y,z): 
-    return grid(x, y, z-1)
-
-def FL(x,y,z):
-    return grid(x-1, y-1, z)
-
-def FR(x,y,z):
-    return grid(x-1, y+1, z)
-
-def FD(x,y,z):
-    return grid(x-1, y, z-1)
-
-def FT(x,y,z):
-    return grid(x-1, y, z+1)
-
-def BL(x,y,z):
-    return grid(x+1, y-1, z)
-
-def BR(x,y,z):
-    return grid(x+1, y+1, z)
-
-def BD(x,y,z):
-    return grid(x+1, y, z-1)
-
-def BT(x,y,z):
-    return grid(x+1, y, z+1)
-
-def LD(x,y,z):
-    return grid(x, y-1, z-1)
-
-def LT(x,y,z): 
-    return grid(x, y-1, z+1)
-
-def RD(x,y,z): 
-    return grid(x, y+1, z-1)
-
-def RT(x,y,z): 
-    return grid(x, y+1, z+1)
-
-def FLD(x,y,z):
-    return grid(x-1, y-1, z-1)
-
-def FLT(x,y,z):
-    return grid(x-1, y-1, z+1)
-
-def FRD(x,y,z):
-    return grid(x-1, y+1, z-1)
-
-def FRT(x,y,z):
-    return grid(x-1, y+1, z+1)
-
-def BLD(x,y,z): 
-    return grid(x+1, y-1, z-1)
-
-def BLT(x,y,z):
-    return grid(x+1, y-1, z+1)
-
-def BRD(x,y,z):
-    return grid(x+1, y+1, z-1)
-
-def BRT(x,y,z):
-    return grid(x+1, y+1, z+1)
-

diff --git a/doc/spline3.lyx b/doc/spline3.lyx
deleted file mode 100644 (file)
index 3a9f578..0000000
--- a/doc/spline3.lyx
+++ /dev/null
@@ -1,1691 +0,0 @@
-#LyX 1.6.8 created this file. For more info see http://www.lyx.org/
-\lyxformat 345
-\begin_document
-\begin_header
-\textclass amsart
-\use_default_options false
-\begin_modules
-theorems-ams
-eqs-within-sections
-figs-within-sections
-\end_modules
-\language english
-\inputencoding auto
-\font_roman ae
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize letterpaper
-\use_geometry false
-\use_amsmath 1
-\use_esint 1
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation skip
-\defskip bigskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\author "" 
-\author "" 
-\end_header
-
-\begin_body
-
-\begin_layout Title
-Spline3
-\end_layout
-
-\begin_layout Author
-Michael Orlitzky
-\end_layout
-
-\begin_layout Example*
-First, will will define our grid 
-\begin_inset Formula $G$
-\end_inset
-
- to be over a 
-\begin_inset Formula $3\times3\times3$
-\end_inset
-
- cube having grid size 
-\begin_inset Formula $h=1$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Example*
-To test the reproduction of trilinears, we will take the function (per Sorokina
- and Zeilfelder, p.
- 88),
-\end_layout
-
-\begin_layout Example*
-\begin_inset Formula \[
-f\left(x,y,z\right)=1+x+xy+xyz\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-and compute its value at the 27 points, 
-\begin_inset Formula $\left(0,0,0\right),\left(0,0,1\right),\dots\left(2,2,2\right)$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Example*
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Plain Layout
-
-sage: x,y,z = var('x,y,z')
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f = 1 + x + x*y + x*y*z
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=0, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=0, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-2
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=0, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-3
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=1, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=1, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-3
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=1, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-5
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=2, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=2, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-4
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=2, z=0)
-\end_layout
-
-\begin_layout Plain Layout
-
-7
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=0, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=0, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-2
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=0, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-3
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=1, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=1, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-4
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=1, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-7
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=2, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=2, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-6
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=2, z=1)
-\end_layout
-
-\begin_layout Plain Layout
-
-11
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=0, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=0, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-2
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=0, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-3
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=1, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=1, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-5
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=1, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-9 
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=0, y=2, z=2) 
-\end_layout
-
-\begin_layout Plain Layout
-
-1
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=1, y=2, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-8 
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: f(x=2, y=2, z=2)
-\end_layout
-
-\begin_layout Plain Layout
-
-15
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-We are most interested in the 
-\begin_inset Quotes eld
-\end_inset
-
-interior
-\begin_inset Quotes erd
-\end_inset
-
- cube centered at 
-\begin_inset Formula $\left(1,1,1\right)$
-\end_inset
-
- with datum 
-\begin_inset Formula $4$
-\end_inset
-
-.
- We can enter the data above into a list,
-\end_layout
-
-\begin_layout Example*
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Plain Layout
-
-sage: g = [[[ f(x=a, y=b, z=c) for a in range(0,3) ] for b in range(0,3)
- ] for c in range(0,3) ]
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: g
-\end_layout
-
-\begin_layout Plain Layout
-
-[[[1, 2, 3], [1, 3, 5], [1, 4, 7]],
-\end_layout
-
-\begin_layout Plain Layout
-
- [[1, 2, 3], [1, 4, 7], [1, 6, 11]],
-\end_layout
-
-\begin_layout Plain Layout
-
- [[1, 2, 3], [1, 5, 9], [1, 8, 15]]]
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-although the list will be indexed by 
-\begin_inset Formula $\left(z,y,x\right)$
-\end_inset
-
- so we define a function to access it by 
-\begin_inset Formula $\left(x,y,z\right)$
-\end_inset
-
-,
-\end_layout
-
-\begin_layout Example*
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Plain Layout
-
-sage: def grid(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return g[z][y][x]
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-and define directional functions according to Sorokina and Zeilfelder, p.
- 81.
-\end_layout
-
-\begin_layout Example*
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Plain Layout
-
-sage: def I(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x,y,z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def F(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def B(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def L(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y-1, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def R(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y+1, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def T(x,y,z): 
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def D(x,y,z): 
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FL(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y-1, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FR(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y+1, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FD(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FT(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BL(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y-1, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BR(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y+1, z)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BD(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BT(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def LD(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y-1, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def LT(x,y,z): 
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y-1, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def RD(x,y,z): 
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y+1, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def RT(x,y,z): 
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x, y+1, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FLD(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y-1, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FLT(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y-1, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FRD(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y+1, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def FRT(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x-1, y+1, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BLD(x,y,z): 
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y-1, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BLT(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y-1, z+1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BRD(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y+1, z-1)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: def BRT(x,y,z):
-\end_layout
-
-\begin_layout Plain Layout
-
-....:     return grid(x+1, y+1, z+1)
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-Next, we define the coefficients for the cube centered on 
-\begin_inset Formula $\left(1,1,1\right)$
-\end_inset
-
- based on these directional functions.
-\end_layout
-
-\begin_layout Example*
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Plain Layout
-
-sage: c0030 = (1/8)*( I(1,1,1) + F(1,1,1) + L(1,1,1) + T(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-                      LT(1,1,1) + FL(1,1,1) + FT(1,1,1) + FLT(1,1,1) )
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0003 = (1/8)*( I(1,1,1) + F(1,1,1) + R(1,1,1) + T(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-                RT(1,1,1) + FR(1,1,1) + FT(1,1,1) + FRT(1,1,1) )
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0021 = (5/24)*(I(1,1,1) + F(1,1,1) + T(1,1,1) + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/24)*(L(1,1,1) + FL(1,1,1) + LT(1,1,1) + FLT(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0012 = (5/24)*(I(1,1,1) + F(1,1,1) + T(1,1,1) + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/24)*(R(1,1,1) + FR(1,1,1) + RT(1,1,1) + FRT(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0120 = (5/24)*(I(1,1,1) + F(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/8)*(L(1,1,1) + T(1,1,1) + FL(1,1,1) + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/24)*(LT(1,1,1) + FLT(1,1,1)) 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0102 = (5/24)*(I(1,1,1) + F(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/8)*(R(1,1,1) + T(1,1,1) + FR(1,1,1) + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/24)*(RT(1,1,1) + FRT(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0111 = (13/48)*(I(1,1,1) + F(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (7/48)*(T(1,1,1) + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/32)*(L(1,1,1) + R(1,1,1) + FL(1,1,1) + FR(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(LT(1,1,1) + RT(1,1,1) + FLT(1,1,1) + FRT(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0210 = (13/48)*(I(1,1,1) + F(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (17/192)*(L(1,1,1) + T(1,1,1) + FL(1,1,1) + FT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(LT(1,1,1) + FLT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/64)*(R(1,1,1) + D(1,1,1) + FR(1,1,1) + FD(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/192)*(RT(1,1,1) + LD(1,1,1) + FRT(1,1,1) + FLD(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0201 = (13/48)*(I(1,1,1) + F(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (17/192)*(R(1,1,1) + T(1,1,1) + FR(1,1,1) + FT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(RT(1,1,1) + FRT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/64)*(L(1,1,1) + D(1,1,1) + FL(1,1,1) + FD(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/192)*(RD(1,1,1) + LT(1,1,1) + FLT(1,1,1) + FRD(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0300 = (13/48)*(I(1,1,1) + F(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/96)*(L(1,1,1) + R(1,1,1) + T(1,1,1) + D(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-                      FL(1,1,1) + FR(1,1,1) + FT(1,1,1) + FD(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/192)*(RT(1,1,1) + RD(1,1,1) + LT(1,1,1) + LD(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-                       FRT(1,1,1) + FRD(1,1,1) + FLT(1,1,1) + FLD(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1020 = (1/4)*I(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/6)*(F(1,1,1) + L(1,1,1) + T(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/12)*(LT(1,1,1) + FL(1,1,1) + FT(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1002 = (1/4)*I(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/6)*(F(1,1,1) + R(1,1,1) + T(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/12)*(RT(1,1,1) + FR(1,1,1) + FT(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1011 = (1/3)*I(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/24)*(F(1,1,1) + T(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/12)*FT(1,1,1) + (1/24)*(L(1,1,1) + R(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/48)*(LT(1,1,1) + RT(1,1,1) + FL(1,1,1) + FR(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1110 = (1/3)*I(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/24)*F(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/8)*(L(1,1,1) + T(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/96)*(FL(1,1,1) + FT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/48)*(D(1,1,1) + R(1,1,1) + LT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(FD(1,1,1) + LD(1,1,1) + RT(1,1,1) + FR(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1101 = (1/3)*I(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/24)*F(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/8)*(R(1,1,1) + T(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/96)*(FR(1,1,1) + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/48)*(D(1,1,1) + L(1,1,1) + RT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(FD(1,1,1) + LT(1,1,1) + RD(1,1,1) + FL(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1200 = (1/3)*I(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (5/24)*F(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (7/96)*(L(1,1,1) + R(1,1,1) + T(1,1,1) + D(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/32)*(FL(1,1,1) + FR(1,1,1) + FT(1,1,1) + FD(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(RT(1,1,1) + RD(1,1,1) + LT(1,1,1) + LD(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c2010 = (3/8)*I(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (7/48)*(F(1,1,1) + T(1,1,1) + L(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/48)*(R(1,1,1) + D(1,1,1) + B(1,1,1) + LT(1,1,1) + FL(1,1,1)
- + FT(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(RT(1,1,1) + BT(1,1,1) + FR(1,1,1) + FD(1,1,1) + LD(1,1,1)
- + BL(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c2001 = (3/8)*I(1,1,1) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (7/48)*(F(1,1,1) + T(1,1,1) + R(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/48)*(L(1,1,1) + D(1,1,1) + B(1,1,1) + RT(1,1,1) + FR(1,1,1)
- + FT(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(LT(1,1,1) + BT(1,1,1) + FL(1,1,1) + FD(1,1,1) + RD(1,1,1)
- + BR(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c2100 = (3/8)*I(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/12)*(T(1,1,1) + R(1,1,1) + L(1,1,1) + D(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/64)*(FT(1,1,1) + FR(1,1,1) + FL(1,1,1) + FD(1,1,1)) +
-\end_layout
-
-\begin_layout Plain Layout
-
-              (7/48)*F(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/48)*B(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(RT(1,1,1) + LD(1,1,1) + LT(1,1,1) + RD(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/192)*(BT(1,1,1) + BR(1,1,1) + BL(1,1,1) + BD(1,1,1))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c3000 = (3/8)*I(1,1,1) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/12)*(T(1,1,1) + F(1,1,1) + L(1,1,1) + R(1,1,1) + D(1,1,1)
- + B(1,1,1)) + 
-\end_layout
-
-\begin_layout Plain Layout
-
-              (1/96)*(LT(1,1,1) + FL(1,1,1) + FT(1,1,1) + RT(1,1,1) + BT(1,1,1)
- + FR(1,1,1)  +
-\end_layout
-
-\begin_layout Plain Layout
-
-                      FD(1,1,1) + LD(1,1,1) + BD(1,1,1) + BR(1,1,1) + RD(1,1,1)
- + BL(1,1,1))
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-We can see what the constant values are now:
-\end_layout
-
-\begin_layout Example*
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Plain Layout
-
-sage: c0030
-\end_layout
-
-\begin_layout Plain Layout
-
-17/8
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0003
-\end_layout
-
-\begin_layout Plain Layout
-
-27/8
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0021
-\end_layout
-
-\begin_layout Plain Layout
-
-61/24
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0012
-\end_layout
-
-\begin_layout Plain Layout
-
-71/24
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0120
-\end_layout
-
-\begin_layout Plain Layout
-
-55/24
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0102
-\end_layout
-
-\begin_layout Plain Layout
-
-73/24
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0111
-\end_layout
-
-\begin_layout Plain Layout
-
-8/3
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0210 
-\end_layout
-
-\begin_layout Plain Layout
-
-29/12
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0201
-\end_layout
-
-\begin_layout Plain Layout
-
-11/4
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c0300
-\end_layout
-
-\begin_layout Plain Layout
-
-5/2
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1020
-\end_layout
-
-\begin_layout Plain Layout
-
-8/3
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1002
-\end_layout
-
-\begin_layout Plain Layout
-
-23/6
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1011
-\end_layout
-
-\begin_layout Plain Layout
-
-13/4
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1110
-\end_layout
-
-\begin_layout Plain Layout
-
-23/8
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1101
-\end_layout
-
-\begin_layout Plain Layout
-
-27/8
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c1200
-\end_layout
-
-\begin_layout Plain Layout
-
-3
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c2010
-\end_layout
-
-\begin_layout Plain Layout
-
-10/3
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c2001
-\end_layout
-
-\begin_layout Plain Layout
-
-4
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c2100
-\end_layout
-
-\begin_layout Plain Layout
-
-7/2
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-sage: c3000
-\end_layout
-
-\begin_layout Plain Layout
-
-4
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Example*
-Now that we have the coefficients, we'll choose a particular tetrahedron
- and compute the polynomial over it.
- If we look at the 
-\begin_inset Quotes eld
-\end_inset
-
-top
-\begin_inset Quotes erd
-\end_inset
-
- face of the cube (in the positive 
-\begin_inset Formula $z$
-\end_inset
-
- direction), there are only four tetrahedra to choose from.
- We'll be consider the 
-\begin_inset Quotes eld
-\end_inset
-
-right
-\begin_inset Quotes erd
-\end_inset
-
- tetrahedron; that is, the one with vertices,
-\end_layout
-
-\begin_layout Example*
-\begin_inset Formula \begin{eqnarray*}
-v_{0}=\left(0.5,1.5,1.5\right) &  & \mbox{at the front-right of the cube}\\
-v_{1}=\left(1.5,1.5,1.5\right) &  & \mbox{at the back-right of the cube}\\
-v_{2}=\left(1,1,1.5\right) &  & \mbox{at the center of the top face of the cube}\\
-v_{3}=\left(1,1,1\right) &  & \mbox{at the center of the cube}\end{eqnarray*}
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document