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flat_deficiency.sage

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+# compute the average deficiency for flats of small matroids
+
+from sage.all import *
+from sage.matroids.all import *
+from sage.graphs.all import *
+import gurobipy as gp
+from gurobipy import GRB
+
+import json
+
+def check(M):
+    data={}
+    # collect the largest hyperplane and optimal F*
+    strength=1000000
+    for r in range(0,M.rank()):
+        #enumerate all flats
+        rank_deficiency=M.rank()-r
+        max_size=0
+        for F in M.flats(r):
+            max_size=max(len(F),max_size)
+        avg_deficiency=(M.size()-max_size)/rank_deficiency
+        strength=min(strength,avg_deficiency)
+        data["avg "+str(rank_deficiency)+"-cocycle"]=str(avg_deficiency)
+    data["strength"]=str(strength)
+    return data
+counter=0
+
+with open("flat_deficiency.jsonl", "a") as f:   # .jsonl = JSON Lines
+    for N in range(10):
+        for M in matroids.AllMatroids(N):
+            counter += 1
+            record = { "id": str(counter), "value": check(M) }
+            f.write(json.dumps(record) + "\n")
+            f.flush()     # ensure write hits disk