3 files changed, 172 insertions, 0 deletions
diff --git a/common.py b/common.py
new file mode 100755
index 0000000..411867b
--- /dev/null
+++ b/common.py
@@ -0,0 +1,73 @@
+#!/usr/bin/env python3
+from itertools import combinations
+
+def increment(dictionary, key):
+    dictionary[key] = dictionary.get(key, 0) + 1
+
+def print_dict(dictionary):
+    keys = sorted(list(dictionary.keys()))
+    for key in keys:
+        print(key, dictionary[key])
+
+def distribution(counts, capset, num):
+    combs = tuple(combinations(range(counts["dim"]), num))
+    num_i = len(combs)
+    num_j = 3**num
+    dists = [[0 for j in range(num_j)]
+                for i in range(num_i)]
+    for card in capset:
+        for i, indices in enumerate(combs):
+            substr = "".join(card[indices[n]] for n in range(num))
+            j = int(substr, 3)
+            dists[i][j] += 1
+    metadist = {}
+    for i in range(num_i):
+        dists[i] = "".join(map(str, sorted(dists[i])))
+        name = "dist" + str(num) + ":" + dists[i]
+        increment(counts, name)
+        increment(metadist, name)
+    if counts["premeta" + str(num)]:
+        z = tuple(zip(*counts["premeta" + str(num)].items()))
+    else:
+        z = ([],[])
+    if metadist in z[1]:
+        key = z[0][z[1].index(metadist)]
+    else:
+        key = len(z[0])
+        counts["premeta" + str(num)][key] = metadist
+    name = "premeta" + str(num) + ":" + str(key)
+    increment(counts, name)
+
+def metadistribution(counts, num):
+    dists = tuple(sorted(key for key in counts.keys()
+                             if key.startswith("dist" + str(num))))
+    for key in counts["premeta" + str(num)]:
+        count = counts["premeta" + str(num) + ":" + str(key)]
+        metadist = counts["premeta" + str(num)][key]
+        newstr = "".join(str(metadist.get(dist, 0)) for dist in dists)
+        counts["meta" + str(num) + ":" + newstr] = count
+    for key in counts.copy():
+        if key.startswith("premeta" + str(num)):
+            del counts[key]
+
+def main():
+    capsets = []
+    capset_file = open("capset.out", "r")
+    for line in capset_file:
+        capsets.append(line[1:-2].split(" "))
+    capset_file.close()
+
+    counts = {"count" : 0,
+              "dim"   : len(capsets[0][0])}
+    nums = range(1, counts["dim"])
+    for num in nums:
+        counts["premeta" + str(num)] = {}
+    for capset in capsets:
+        counts["count"] += 1
+        for num in nums:
+            distribution(counts, capset, num)
+    for num in nums:
+        metadistribution(counts, num)
+    print_dict(counts)
+
+if __name__ == "__main__": main()
diff --git a/connected.py b/connected.py
new file mode 100755
index 0000000..ee3ae70
--- /dev/null
+++ b/connected.py
@@ -0,0 +1,46 @@
+#!/usr/bin/env python3
+from sys import argv
+if len(argv) == 1: NUM = 1
+if len(argv) == 2: NUM = int(argv[1])
+
+def is_connected(capset0, capset1):
+    count = 0
+    for card in capset0:
+        if card in capset1:
+            continue
+        count += 1
+    return count <= NUM
+
+def next_connected(disconnected):
+    newly_connected = [disconnected.pop()]
+    connected = []
+    while newly_connected:
+        check_capsets = iter(newly_connected[:])
+        connected.extend(newly_connected)
+        newly_connected = []
+        for con_capset in check_capsets:
+            for index, dis_capset in reversed(list(enumerate(disconnected[:]))):
+                if is_connected(con_capset, dis_capset):
+                    newly_connected.append(disconnected.pop(index))
+    return connected
+
+def main():
+    capsets = []
+    capset_file = open("capset.out", "r")
+    for line in capset_file:
+        capsets.append(tuple(line[1:-2].split(" ")))
+    capset_file.close()
+
+    connecteds = []
+    while capsets:
+        connecteds.append(next_connected(capsets))
+    #for connected in connecteds:
+    #    print("\nThe following are connected:")
+    #    for capset in connected:
+    #        print(capset)
+    print("\nThere are", len(connecteds), "partitions.")
+    lengths = list(map(len, connecteds))
+    for length in sorted(set(lengths)):
+        print("There are", lengths.count(length), "with length", length)
+
+if __name__ == "__main__": main()
diff --git a/reverse.py b/reverse.py
new file mode 100755
index 0000000..304baa1
--- /dev/null
+++ b/reverse.py
@@ -0,0 +1,53 @@
+#!/usr/bin/env python3
+from sys import argv
+
+def int2card(num, dim=4):
+    if num != int(num):
+        raise Exception("Number must be an integer.")
+    if num < 0:
+        raise Exception("Number must be nonnegative.")
+    if num >= 3**dim:
+        raise Exception("Number must be less than {}.".format(3**dim))
+    strlist = []
+    for i in range(dim):
+        strlist.append(str(num%3))
+        num //= 3
+    return ''.join(reversed(strlist))
+
+def main():
+    """Reverses the card identities in a capset.out file.
+
+    222 becomes 000, etc.
+    By default, reads in capset.out and writes to capset.new
+    You may give other input/output files as optional arguments.
+    It will NOT reverse in-place: you must give a different output file.
+    """
+    inname = "capset.out"
+    outname = "capset.new"
+    if len(argv) == 2:
+        inname = argv[1]
+    if len(argv) == 3:
+        inname = argv[1]
+        outname = argv[2]
+        if inname == outname:
+            raise Exception("Input and output files must differ!")
+    infile = open(inname, "r")
+    outfile = open(outname, "w")
+
+    firstline = infile.readline()
+    infile.seek(0)
+    capset = firstline[1:-2].split(" ")
+    dim = len(capset[0])
+
+    for line in infile:
+        capset = line[1:-2].split(" ")
+        newcards = []
+        for card in capset:
+            newcard = 3**dim - 1 - int(card, 3)
+            newcards.append(int2card(newcard, dim))
+        outfile.write("[" + " ".join(newcards) + "]\n")
+
+    infile.close()
+    outfile.close()
+
+if __name__ == "__main__": main()