3 files changed, 73 insertions, 21 deletions

diff --git a/__pycache__/billiard3d.cpython-311.pyc b/__pycache__/billiard3d.cpython-311.pyc
new file mode 100644
index 0000000..5c7b5cb
--- /dev/null
+++ b/__pycache__/billiard3d.cpython-311.pyc
diff --git a/billiard3d.py b/billiard3d.py
index 904d094..806ae28 100644
--- a/billiard3d.py
+++ b/billiard3d.py
@@ -54,11 +54,7 @@ def is_double(path):
 
         return False
 
-def print_multiplicities(n, sizes, r):
-        print("")
-        print("Points with multiplicity > 1:")
-        print("")
-
+def get_multiplicities(n, sizes, r):
         d = dict()
         path = [tuple(x) for x in get_path(n, sizes, r)]
 
@@ -72,6 +68,15 @@ def print_multiplicities(n, sizes, r):
                 for p in d:
                         d[p] //= 2
 
+        return d
+
+def print_multiplicities(n, sizes, r):
+        d = get_multiplicities(n, sizes, r)
+
+        print("")
+        print("Points with multiplicity > 1:")
+        print("")
+
         for i in range(2, max(d.values())+1):
                 L = []
                 for point in d:
@@ -259,21 +264,22 @@ def user_input():
 # Main routine below
 ###############################################################################
 
-# You can choose to write your input here or to get it interactively
-#sizes, r, pic = [15, 9, 7], [2, 0, 0], "p"
-#sizes, r, pic = [2, 3, 4], [0, 0, 0], "3"
-sizes, r, pic = user_input()
+if __name__ == '__main__':
+        # You can choose to write your input here or to get it interactively
+        #sizes, r, pic = [15, 9, 7], [2, 0, 0], "p"
+        #sizes, r, pic = [2, 3, 4], [0, 0, 0], "3"
+        sizes, r, pic = user_input()
 
-print("---------------------------------")
-print_multiplicities(len(sizes), sizes, r)
-print("---------------------------------")
-print_points_on_edges(sizes, r)
-print("---------------------------------")
+        print("---------------------------------")
+        print_multiplicities(len(sizes), sizes, r)
+        print("---------------------------------")
+        print_points_on_edges(sizes, r)
+        print("---------------------------------")
 
-if pic == "p":
-        draw_3d_projections(sizes, r)
-elif pic == "3":
-        draw_3d_picture(sizes, r)
-else:
-        draw_3d_projections(sizes, r)
-        draw_3d_picture(sizes, r)
+        if pic == "p":
+                draw_3d_projections(sizes, r)
+        elif pic == "3":
+                draw_3d_picture(sizes, r)
+        else:
+                draw_3d_projections(sizes, r)
+                draw_3d_picture(sizes, r)
diff --git a/multiplicity_stats.py b/multiplicity_stats.py
new file mode 100644
index 0000000..438a2fa
--- /dev/null
+++ b/multiplicity_stats.py
@@ -0,0 +1,46 @@
+import billiard3d
+import sys
+
+def get_stats(i, j, k, mult):
+        for r1 in range(i+1):
+                for r2 in range(j+1):
+                        for r3 in range(k+1):
+                                d = billiard3d.get_multiplicities(3, [i, j, k], [r1, r2, r3])
+                                for key in d:
+                                        mult[d[key]] += 1
+
+def print_stats(N):
+        mult = [0] * 10
+        for i in range(1, N+1):
+                for j in range(i, N+1):
+                        for k in range(j, N+1):
+                                get_stats(i, j, k, mult)
+
+        print("Statistics for paths with 0 < a <= b <= c <= {0}".format(N))
+        print("Considering all paths starting from any possible point")
+        for i in range(1, 10):
+                if mult[i] != 0:
+                        print("Multiplicity {0}: {1} points".format(i, mult[i]))
+        print("There are no points of positive multiplicity different from those listed above")
+
+def print_stats_single(a, b, c):
+        mult = [0] * 10
+        get_stats(a, b, c, mult)
+
+        print("Statistics for paths with a={0}, b={1} and c={2}".format(a, b, c))
+        print("Considering all paths starting from any possible point")
+        for i in range(1, 10):
+                if mult[i] != 0:
+                        print("Multiplicity {0}: {1} points".format(i, mult[i]))
+        print("There are no points of positive multiplicity different from those listed above")
+
+if len(sys.argv) == 2:
+        N = int(sys.argv[1])
+        print_stats(N)
+elif len(sys.argv) == 4:
+        a, b, c = int(sys.argv[1]), int(sys.argv[2]), int(sys.argv[3])
+        print_stats_single(a, b, c)
+else:   
+        print("Use one of the following options:")
+        print("\tpython multiplicity_stats.py N\t\t # For all possible sizes up to N")
+        print("\tpython multiplicity_stats.py a b c\t # For all starting points for the single 3d box (a,b,c)")