Boundary -> BoundaryValue

experiments/flower-snarks.py

 #!/usr/bin/python
 
 DOC = """
-Calculate that the number of CDCs of Flower snark $J_k$ is $16^{(1-o(1))k}$.
+Calculate that the number of CDCs of Flower snark $J_k$ is $c16^k \pm O(15^k)$.
 
 We calculate the step matrix $M$, show that 16 is its eigenvalue by finding
 its eigenvector. The eigenvector is guessed for the ratios of coefficients
@@ -15,6 +15,18 @@ sys.path.append(os.path.dirname(__file__) + "/..")
 from graph_tools.all import *
 from sage.all import identity_matrix, QQ, DiGraph, matrix
 
+def make_P(u):
+  coords = [ r for r, c in u.dict().keys() ]
+  assert min(coords) == 1 and u[1, 0] == 1
+
+  P = matrix(QQ, u.nrows(), u.nrows(), sparse=True)
+  P[:, 0] = u
+  P[0, 1] = 1
+  for i in range(2, P.nrows()):
+    P[i, i] = 1
+    P[1, i] = -P[i, 0]
+
+  return P
 
 def deflate_eigenvector(M, u):
   coord = min(( r for r in range(u.nrows()) if u[r, 0] > 0 ), key=lambda r: u[r, 0])
@@ -87,7 +99,8 @@ if __name__ == "__main__":
     A = M * A
     nu2 = fin * A
     assert nu1 == nu2
-    print("  ν(J_%i) = %i" % (i, nu1))
+    c_approx = nu1 / 16**i
+    print("  ν(J_%i) = %i          (c = %.3f)" % (i, nu1, c_approx))
   print("  Done")
 
   print("\nCalculating the eigenvector for eigenvalue 16")
@@ -105,7 +118,7 @@ if __name__ == "__main__":
   
   print("  Checking it...")
   nex = to_dict(FlowerSnark._next_gadget(FakeGadget(6,
-    [ Boundary(b, v) for b, v in vec.items() ])).eval_gadget(CircuitDoubleCover))
+    [ BoundaryValue(b, v) for b, v in vec.items() ])).eval_gadget(CircuitDoubleCover))
 
   assert nex.keys() == vec.keys()
   for b in vec:

experiments/flowers.py

@@ -11,16 +11,14 @@ share exactly one edge, and non-consecutive neighbour faces do not
 share any edge.
 """
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
 from graph_tools.all import *
 
 @GraphSequence
 class Flower:
   sequence_start = 2
 
-  SCV = FakeGadget(3, [ Boundary(((1,), (2,), (1, 2), None), 1) ])
+  SCV = FakeGadget(3, [ BoundaryValue(((1,), (2,), (1, 2), None), 1) ])
 
   D = Gadget.join(
     [ SCV, CUBIC_VERTEX ],

graph_tools/base.py

 def _init_():
   global \
-    Boundary, \
+    BoundaryValue, \
     GraphParameterBase, SimpleParameterBase, \
     Gadget, FakeGadget, CUBIC_VERTEX, FREE_EDGE, \
     ParametrizedGraphSequence, GraphSequence
@@ -11,13 +11,13 @@ def _init_():
   from itertools import combinations, chain, product
   from functools import reduce
 
-  Boundary = namedtuple("Boundary", ['boundary', 'value', 'origins'])
-  Boundary.with_origins = lambda s, o: Boundary(s.boundary, s.value, o)
+  BoundaryValue = namedtuple("BoundaryValue", ['boundary', 'value', 'origins'])
+  BoundaryValue.with_origins = lambda s, o: BoundaryValue(s.boundary, s.value, o)
 
   OriginJoinEdge = namedtuple("OriginJoinEdge", ['boundary', 'e1', 'e2', 'info'])
   OriginJoinBoundaries = namedtuple("OriginJoinBoundaries", ['boundaries', 'info'])
   # hack compatible with Python < 3.7
-  Boundary.__new__.__defaults__ = (None, None, None)
+  BoundaryValue.__new__.__defaults__ = (None, None, None)
 
 
   class GraphParameterBase:
@@ -49,14 +49,14 @@ def _init_():
       for e1, e2 in joins: it = join(it, e1, e2)
 
       def project_and_canonize(b):
-        return Boundary(self.project_and_canonize(outs, b.boundary), b.value, b.origins)
+        return BoundaryValue(self.project_and_canonize(outs, b.boundary), b.value, b.origins)
 
       it = ( project_and_canonize(b) for b in it )
 
       ret = dict()
       for b in it:
         if b.boundary in ret:
-          ret[b.boundary] = Boundary(b.boundary,
+          ret[b.boundary] = BoundaryValue(b.boundary,
             self.merge_values(ret[b.boundary].value, b.value),
             ret[b.boundary].origins + b.origins if track_origins else None
           )
@@ -72,7 +72,7 @@ def _init_():
 
   class SimpleParameterBase(GraphParameterBase):
     def join_boundaries(self, x, _):
-      yield Boundary(
+      yield BoundaryValue(
         tuple(chain.from_iterable( b.boundary for b in x )),
         reduce(lambda acc, b: acc*b.value, x, 1)
       )
@@ -256,7 +256,7 @@ def _init_():
         boundaries = new_boundaries
         gadget = FakeGadget(
           start_gadget.size(),
-          [ Boundary(k, 1) for k in boundaries ]
+          [ BoundaryValue(k, 1) for k in boundaries ]
         )
         out = self._next_gadget(gadget).eval_gadget(parameter, no_cache=True)
         new_boundaries = set( b.boundary for b in out )
@@ -272,7 +272,7 @@ def _init_():
         (rename[b.boundary], rename[col]): b.value
         for col in sorted_boundaries
         for b in self._next_gadget(FakeGadget(start_gadget.size(),
-          [ Boundary(col, 1) ])).eval_gadget(parameter, no_cache=True)
+          [ BoundaryValue(col, 1) ])).eval_gadget(parameter, no_cache=True)
       })
 
       iv = matrix(QQ, size, 1, {
@@ -282,7 +282,7 @@ def _init_():
 
       fin = matrix(QQ, 1, size, {
         (0, rename[col]): self._make_graph(FakeGadget(start_gadget.size(),
-          [ Boundary(col, 1) ])).eval(parameter, no_cache=True)
+          [ BoundaryValue(col, 1) ])).eval(parameter, no_cache=True)
         for col in sorted_boundaries
       })
 

graph_tools/misc.py

@@ -3,7 +3,7 @@ def _init_():
     edge_model_join, edge_model_join_matrix, parameter_matrix, \
     enumerate_diamond_matchings
 
-  from .base import Gadget, CUBIC_VERTEX, Boundary, FakeGadget
+  from .base import Gadget, CUBIC_VERTEX, BoundaryValue, FakeGadget
   from .parameters import CircuitDoubleCover
   from .sequences import Necklace
 
@@ -177,7 +177,7 @@ def _init_():
 
 
   def edge_model_join_matrix(P, k):
-    BG = [ FakeGadget(k, [ Boundary(b, 1) ]) for b in P.enumerate_boundaries(k) ]
+    BG = [ FakeGadget(k, [ BoundaryValue(b, 1) ]) for b in P.enumerate_boundaries(k) ]
     return parameter_matrix(P, BG)
 
 

graph_tools/parameters.py

@@ -13,7 +13,7 @@ def _init_():
     UnionFind
 
   from .base import \
-    Boundary, \
+    BoundaryValue as BV, \
     SimpleParameterBase, GraphParameterBase
 
   from fractions import Fraction
@@ -27,9 +27,9 @@ def _init_():
     def __init__(self, group, nowherezero):
       self.group = group
       self.nowherezero = nowherezero
-      self.FREE_EDGE = [ Boundary((i, i), 1) for i in group if not nowherezero or i != 0 ]
+      self.FREE_EDGE = [ BV((i, i), 1) for i in group if not nowherezero or i != 0 ]
       self.CUBIC_VERTEX = [
-        Boundary((i, j, l), 1) for i in group for j in group
+        BV((i, j, l), 1) for i in group for j in group
         for l in group if i + j + l == 0 and
         (not nowherezero or i != 0 and j != 0 and l != 0)
       ]
@@ -41,9 +41,9 @@ def _init_():
   class CycleDoubleCover(SimpleParameterBase):
     def __init__(self, k):
       self.k = k
-      self.FREE_EDGE = [ Boundary(((i, j), (i, j)), 1) for i in range(k) for j in range(i+1, k) ]
+      self.FREE_EDGE = [ BV(((i, j), (i, j)), 1) for i in range(k) for j in range(i+1, k) ]
       self.CUBIC_VERTEX = [
-        Boundary((tuple(sorted((i, j))), tuple(sorted((i, l))), tuple(sorted((j, l)))), 1)
+        BV((tuple(sorted((i, j))), tuple(sorted((i, l))), tuple(sorted((j, l)))), 1)
         for i in range(k) for j in range(k) for l in range(k)
         if i != j and j != l and i != l
       ]
@@ -81,9 +81,9 @@ def _init_():
 
     def __init__(self, k):
       self.k = k
-      self.FREE_EDGE = [ Boundary((i, i), 1) for i in range(k) ]
+      self.FREE_EDGE = [ BV((i, i), 1) for i in range(k) ]
       self.CUBIC_VERTEX = [
-        Boundary((i, j, l), 1) for i in range(k) for j in range(k)
+        BV((i, j, l), 1) for i in range(k) for j in range(k)
         for l in range(k) if i != j and j != l and i != l
       ]
 
@@ -95,7 +95,7 @@ def _init_():
   class VertexColoring(SimpleParameterBase):
     def __init__(self, k):
       self.k = k
-      self.CUBIC_VERTEX = [ Boundary((i, i, i), 1) for i in range(k) ]
+      self.CUBIC_VERTEX = [ BV((i, i, i), 1) for i in range(k) ]
 
     def is_compatible(self, boundary, e_a, e_b):
       return boundary[e_a] != boundary[e_b]
@@ -106,7 +106,7 @@ def _init_():
     from sage.all import Graph
 
     CUBIC_VERTEX = [
-      Boundary((0, 0, 0), Graph([[0], []], multiedges=True, loops=True, immutable=True))
+      BV((0, 0, 0), Graph([[0], []], multiedges=True, loops=True, immutable=True))
     ]
 
     def join_boundaries(self, x, _):
@@ -119,7 +119,7 @@ def _init_():
         for i, b in enumerate(x)
       )
 
-      yield Boundary(
+      yield BV(
         tuple(chain.from_iterable(
           [ v + offsets[i] for v in b.boundary ] for i, b in enumerate(x)
         )),
@@ -129,7 +129,7 @@ def _init_():
     def join_edges(self, b, e1, e2):
       g = b.value.copy(immutable=False)
       g.add_edge(b.boundary[e1], b.boundary[e2])
-      yield Boundary(b.boundary, g.copy(immutable=True))
+      yield BV(b.boundary, g.copy(immutable=True))
 
     def project_and_canonize(self, sel, b):
       return select(sel, b)
@@ -149,11 +149,11 @@ def _init_():
     Same as `gadget.eval(UnderlayingGraph).num_verts()` but
     also works for gadgets containing FREE_EDGE.
     """
-    CUBIC_VERTEX = [ Boundary(None, 1) ]
-    FREE_EDGE = [ Boundary(None, 0) ]
+    CUBIC_VERTEX = [ BV(None, 1) ]
+    FREE_EDGE = [ BV(None, 0) ]
 
     def join_boundaries(self, x, _):
-      yield Boundary(None, sum( b.value for b in x ))
+      yield BV(None, sum( b.value for b in x ))
 
     def join_edges(self, b, _, __): yield b
     def project_and_canonize(self, _, b): return b
@@ -162,11 +162,11 @@ def _init_():
 
   @Singleton
   class HamiltonianCycle(GraphParameterBase):
-    FREE_EDGE = [ Boundary((1, 1), 1), Boundary((None, None), 1) ]
+    FREE_EDGE = [ BV((1, 1), 1), BV((None, None), 1) ]
     CUBIC_VERTEX = [
-      Boundary((1, 1, None), 1),
-      Boundary((1, None, 1), 1),
-      Boundary((None, 1, 1), 1)
+      BV((1, 1, None), 1),
+      BV((1, None, 1), 1),
+      BV((None, 1, 1), 1)
     ]
 
     def join_boundaries(self, x, _):
@@ -185,7 +185,7 @@ def _init_():
         [ shift(x, offsets[i]) for x in b.boundary ] for i, b in enumerate(x)
       ]))
 
-      yield Boundary(ret_b, prod( b.value for b in x ))
+      yield BV(ret_b, prod( b.value for b in x ))
 
     def join_edges(self, b, e1, e2):
       # print("%s %s %s" % (b, e1, e2))
@@ -198,7 +198,7 @@ def _init_():
       if c1 != c2:
         if c1 > c2: c1, c2 = c2, c1
         boundary = tuple( v if v != c2 else c1 for v in b.boundary )
-        yield Boundary(boundary, b.value)
+        yield BV(boundary, b.value)
       elif max_(b.boundary) == 1:
         yield b
 
@@ -223,8 +223,8 @@ def _init_():
 
   @Singleton
   class CircuitDoubleCover(GraphParameterBase):
-    FREE_EDGE = [ Boundary(((1,2), (1,2), None), Fraction(1, 2)) ]
-    CUBIC_VERTEX = [ Boundary(((1,2), (2,3), (1,3), None), 1) ]
+    FREE_EDGE = [ BV(((1,2), (1,2), None), Fraction(1, 2)) ]
+    CUBIC_VERTEX = [ BV(((1,2), (2,3), (1,3), None), 1) ]
 
     def __init__(self):
       super().__init__()
@@ -242,19 +242,19 @@ def _init_():
       ]))
       ret_b = tuple(chain(*tmp[0], (None,), *tmp[1]))
 
-      yield Boundary(ret_b, prod( b.value for b in x ))
+      yield BV(ret_b, prod( b.value for b in x ))
 
     def join_edges(self, b, e1, e2):
       """
-      >>> from .base import Boundary as B
+      >>> from .base import BoundaryValue as BV
       >>> def test(*args): return list(CircuitDoubleCover.join_edges(*args))
-      >>> test(B(((1,2), (2,3), (1,3), None), 1), 1, 2)
+      >>> test(BV(((1,2), (2,3), (1,3), None), 1), 1, 2)
       []
-      >>> assert test(B(((1,2), (2,3), (1,4), (3,4), None), 1), 1, 2) == \
-            [B(((3, 2), (2, 3), (3, 2), (3, 2), None), 1)]
-      >>> test(B(((1,2), (2,3), (1,4), (3,4), None, (1,3)), 1), 1, 2)
+      >>> assert test(BV(((1,2), (2,3), (1,4), (3,4), None), 1), 1, 2) == \
+            [BV(((3, 2), (2, 3), (3, 2), (3, 2), None), 1)]
+      >>> test(BV(((1,2), (2,3), (1,4), (3,4), None, (1,3)), 1), 1, 2)
       []
-      >>> len(test(B(((1,2), (2,3), (4,5), (1,3), (4,5), None), 1), 1, 2))
+      >>> len(test(BV(((1,2), (2,3), (4,5), (1,3), (4,5), None), 1), 1, 2))
       2
       """
       assert len(b.boundary[e1]) == len(b.boundary[e2])
@@ -269,7 +269,7 @@ def _init_():
             if len(t) == 2 and t[0] == t[1]: break
             ret_b.append(t)
         else:
-          yield Boundary(tuple(ret_b), b.value)
+          yield BV(tuple(ret_b), b.value)
 
       if len(b.boundary[e1]) == 1:
         uf = UnionFind(len(b.boundary))

graph_tools/sequences.py

@@ -5,7 +5,6 @@ def _init_():
     GeneralizedPetersen, Petersen
 
   from .base import \
-    Boundary, \
     Gadget, FakeGadget, CUBIC_VERTEX, FREE_EDGE, \
     GraphSequence, ParametrizedGraphSequence