misc: add vertex-model related functions and diamond matchings

graph_tools/misc.py

 def _init_():
-  global sun, count_cdc_naive, graph_to_gadget
+  global sun, count_cdc_naive, graph_to_gadget, \
+    edge_model_join, edge_model_join_matrix, parameter_matrix, \
+    enumerate_diamond_matchings
 
-  from .base import Gadget, CUBIC_VERTEX
+  from .base import Gadget, CUBIC_VERTEX, Boundary, FakeGadget
   from .parameters import CircuitDoubleCover
+  from .sequences import Necklace
 
 
   def sun(k):
@@ -113,5 +116,45 @@ def _init_():
     return b
 
 
+  def edge_model_join(g1 : Gadget, g2 : Gadget):
+    assert g1.size() == g2.size()
+    joins = [ ((1, i+1), (2, i+1)) for i in range(g1.size()) ]
+    return Gadget.join([ g1, g2 ], joins, [])
+
+
+  def parameter_matrix(P, gadgets):
+    from sage.all import matrix, QQ
+
+    m = matrix(QQ, len(gadgets), len(gadgets))
+
+    for r, gr in enumerate(gadgets):
+      for c, gc in enumerate(gadgets):
+        m[r, c] = edge_model_join(gr, gc).eval(P)
+
+    return m
+
+
+  def edge_model_join_matrix(P, k):
+    BG = [ FakeGadget(k, [ Boundary(b, 1) ]) for b in P.enumerate_boundaries(k) ]
+    return parameter_matrix(P, BG)
+
+
+  def enumerate_diamond_matchings(k):
+    assert k % 2 == 0 and k >= 2
+
+    b = Necklace.gadget(1)
+
+    if k == 2:
+      yield b
+      return
+
+    for m in enumerate_diamond_matchings(k - 2):
+      for i in range(k - 1):
+        o = [ (1, i+1) for i in range(k - 2) ]
+        o.insert(i, (2, 1))
+        o.append((2, 2))
+        yield Gadget.join([ m, b ], [], o)
+
+
 _init_()