#!/usr/bin/python 
# outputs Macaulay 2 Code for the ideal I_{mn}
# as defined in Evans/Sturmfels/Uhler 08

import sys

print "-- Macaulay 2 Code for the Commuting Birth and Death Ideal:"

# Catching arguments:
try:
    m = int(sys.argv[1])
    n = int(sys.argv[2])
    r = int(sys.argv[3])
except IndexError:
    print '-- Please give 3 integer arguments'
    m = 1;
    n = 1;
    r = 1;

print ('-- m = %i ,n = %i , r=%i ' % (m,n,r))

# Generating the variable list:
varlist = []
for i in range(m+1):
    for j in range (n+1):
        for k in range (r+1):
            if i<m: varlist.append(''.join(["R",str(i),str(j),str(k)]))
            if i>0: varlist.append(''.join(["L",str(i),str(j),str(k)]))
            if j>0: varlist.append(''.join(["D",str(i),str(j),str(k)]))
            if j<n: varlist.append(''.join(["U",str(i),str(j),str(k)]))
            if k<r: varlist.append(''.join(["F",str(i),str(j),str(k)]))
            if k>0: varlist.append(''.join(["B",str(i),str(j),str(k)]))

# varlist = varlist.sort()

s = "S = QQ["
s += ",".join(varlist)
s += "];"
print s

# Generating the equations LR is i, UD is j, FB is k
eqlist = []
for i in range(m):
    for j in range (n):
        for k in range (r):
            # UD-RL Pairs, k fixed.
            eqlist.append(''.join(["U",str(i),str(j),str(k),"*R",str(i),str(j+1),str(k),"-",\
                                   "R",str(i),str(j),str(k),"*U",str(i+1),str(j),str(k)]))
            eqlist.append(''.join(["R",str(i),str(j+1),str(k),"*D",str(i+1),str(j+1),str(k),"-",\
                                   "D",str(i),str(j+1),str(k),"*R",str(i),str(j),str(k)]))
            eqlist.append(''.join(["D",str(i+1),str(j+1),str(k),"*L",str(i+1),str(j),str(k),"-",\
                                   "L",str(i+1),str(j+1),str(k),"*D",str(i),str(j+1),str(k)]))
            eqlist.append(''.join(["L",str(i+1),str(j),str(k),"*U",str(i),str(j),str(k),"-",\
                                   "U",str(i+1),str(j),str(k),"*L",str(i+1),str(j+1),str(k)]))
            eqlist.append(''.join(["U",str(i),str(j),str(k+1),"*R",str(i),str(j+1),str(k+1),"-",\
                                   "R",str(i),str(j),str(k+1),"*U",str(i+1),str(j),str(k+1)]))
            eqlist.append(''.join(["R",str(i),str(j+1),str(k+1),"*D",str(i+1),str(j+1),str(k+1),"-",\
                                   "D",str(i),str(j+1),str(k+1),"*R",str(i),str(j),str(k+1)]))
            eqlist.append(''.join(["D",str(i+1),str(j+1),str(k+1),"*L",str(i+1),str(j),str(k+1),"-",\
                                   "L",str(i+1),str(j+1),str(k+1),"*D",str(i),str(j+1),str(k+1)]))
            eqlist.append(''.join(["L",str(i+1),str(j),str(k+1),"*U",str(i),str(j),str(k+1),"-",\
                                   "U",str(i+1),str(j),str(k+1),"*L",str(i+1),str(j+1),str(k+1)]))
            # UD-FB Pairs, i fixed
            eqlist.append(''.join(["U",str(i),str(j),str(k),"*F",str(i),str(j+1),str(k),"-",\
                                   "F",str(i),str(j),str(k),"*U",str(i),str(j),str(k+1)]))
            eqlist.append(''.join(["F",str(i),str(j+1),str(k),"*D",str(i),str(j+1),str(k+1),"-",\
                                   "D",str(i),str(j+1),str(k),"*F",str(i),str(j),str(k)]))
            eqlist.append(''.join(["D",str(i),str(j+1),str(k+1),"*B",str(i),str(j),str(k+1),"-",\
                                   "B",str(i),str(j+1),str(k+1),"*D",str(i),str(j+1),str(k)]))
            eqlist.append(''.join(["B",str(i),str(j),str(k+1),"*U",str(i),str(j),str(k),"-",\
                                   "U",str(i),str(j),str(k+1),"*B",str(i),str(j+1),str(k+1)]))
            eqlist.append(''.join(["U",str(i+1),str(j),str(k),"*F",str(i+1),str(j+1),str(k),"-",\
                                 "F",str(i+1),str(j),str(k),"*U",str(i+1),str(j),str(k+1)]))
            eqlist.append(''.join(["F",str(i+1),str(j+1),str(k),"*D",str(i+1),str(j+1),str(k+1),"-",\
                                 "D",str(i+1),str(j+1),str(k),"*F",str(i+1),str(j),str(k)]))
            eqlist.append(''.join(["D",str(i+1),str(j+1),str(k+1),"*B",str(i+1),str(j),str(k+1),"-",\
                                 "B",str(i+1),str(j+1),str(k+1),"*D",str(i+1),str(j+1),str(k)]))
            eqlist.append(''.join(["B",str(i+1),str(j),str(k+1),"*U",str(i+1),str(j),str(k),"-",\
                                   "U",str(i+1),str(j),str(k+1),"*B",str(i+1),str(j+1),str(k+1)]))
            # FB-RL-Pairs, j fixed
            eqlist.append(''.join(["F",str(i),str(j),str(k),"*R",str(i),str(j),str(k+1),"-",\
                                   "R",str(i),str(j),str(k),"*F",str(i+1),str(j),str(k)]))
            eqlist.append(''.join(["R",str(i),str(j),str(k+1),"*B",str(i+1),str(j),str(k+1),"-",\
                                   "B",str(i),str(j),str(k+1),"*R",str(i),str(j),str(k)]))
            eqlist.append(''.join(["B",str(i+1),str(j),str(k+1),"*L",str(i+1),str(j),str(k),"-",\
                                   "L",str(i+1),str(j),str(k+1),"*B",str(i),str(j),str(k+1)]))
            eqlist.append(''.join(["L",str(i+1),str(j),str(k),"*F",str(i),str(j),str(k),"-",\
                                   "F",str(i+1),str(j),str(k),"*L",str(i+1),str(j),str(k+1)]))
            eqlist.append(''.join(["F",str(i),str(j+1),str(k),"*R",str(i),str(j+1),str(k+1),"-",\
                                   "R",str(i),str(j+1),str(k),"*F",str(i+1),str(j+1),str(k)]))
            eqlist.append(''.join(["R",str(i),str(j+1),str(k+1),"*B",str(i+1),str(j+1),str(k+1),"-",\
                                   "B",str(i),str(j+1),str(k+1),"*R",str(i),str(j+1),str(k)]))
            eqlist.append(''.join(["B",str(i+1),str(j+1),str(k+1),"*L",str(i+1),str(j+1),str(k),"-",\
                                   "L",str(i+1),str(j+1),str(k+1),"*B",str(i),str(j+1),str(k+1)]))
            eqlist.append(''.join(["L",str(i+1),str(j+1),str(k),"*F",str(i),str(j+1),str(k),"-",\
                                   "F",str(i+1),str(j+1),str(k),"*L",str(i+1),str(j+1),str(k+1)]))

s = 'I = ideal ('
s += ",".join(eqlist)
s += ");"

print s