analyze-cut

analyze-cycle.py

+from flower_snarks import *
+from sage.all import *
+from collections import namedtuple
+from itertools import *
+
+
+def calc(s):
+  b = list(CircuitDoubleCover.enumerate_boundaries(s))
+  m = dict()
+
+  _bmap = { x: i for i, x in enumerate(b) }
+  def eval_(g):
+    ret = set()
+    for b_ in ( _bmap[x.boundary] for x in g.eval(CircuitDoubleCover) if x.value > 0 ):
+      if b_ not in m:
+        x = set()
+        cg = FakeGadget(s, [ Boundary(b[b_], 1) ])
+        for r, rb in enumerate(b):
+          rg = FakeGadget(s, [ Boundary(rb, 1) ])
+          v = Gadget.join(
+            [ cg, rg ],
+            [ ((1, i), (2, i)) for i in range(1, s+1) ],
+            []
+          ).eval(CircuitDoubleCover)
+          if v > 0: x.add(r)
+        m[b_] = x
+
+      ret.update(m[b_])
+
+    return ret
+
+  ret = namedtuple("calc_ret", ["boundaries", "eval", "map"])
+  ret.boundaries = b
+  ret.eval = eval_
+  ret.map = lambda x: _bmap[x]
+
+  return ret
+def C_k(k):  
+  return Gadget.join(
+    [CUBIC_VERTEX]*k,
+    [ ((i+1, 2), (((i+1) % k) + 1, 1)) for i in range(k) ],
+    [ (i+1, 3) for i in range(k) ]
+  )
+
+def G_k(k):
+  return Gadget.join(
+    [CUBIC_VERTEX]*k,
+    [ ((i+1, 2), (((i+1) % (k-1)) + 1, 1)) for i in range(k-1) ] + [ ((1,3), (k,1)) ],
+    [ (i+2, 3) for i in range(k-2) ] + [ (k, 2), (k, 3) ]
+  )
+
+k = 6
+c = calc(k)
+e = c.eval(C_k(k))
+f = c.eval(G_k(k))
+
+print(len(e))
+print(len(f))
+print(len(set(f).intersection(set(e))))
+