#!/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)