From 31f171adf74a9633cb7888971787430164fc353a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Radek=20Hu=C5=A1ek?= <husek@iuuk.mff.cuni.cz>
Date: Tue, 1 Feb 2022 18:05:42 +0100
Subject: [PATCH] improve experiments' docs
---
experiments/cdc_4_boundaries.py | 17 +++++++----------
experiments/cdc_5_boundaries.py | 19 ++++++++++---------
experiments/flower-snarks.py | 17 +++++++----------
experiments/flowers.py | 16 ++++++++--------
experiments/ladders.py | 9 +++------
experiments/reduce-cycle.py | 6 ++----
experiments/small-snarks.py | 9 +++------
7 files changed, 40 insertions(+), 53 deletions(-)
diff --git a/experiments/cdc_4_boundaries.py b/experiments/cdc_4_boundaries.py
index 3fbcff8..3a76890 100755
--- a/experiments/cdc_4_boundaries.py
+++ b/experiments/cdc_4_boundaries.py
@@ -1,22 +1,19 @@
#!/usr/bin/python
"""
-Calculate a lower bound on the number of 4-boundaries
-of a linear representation of the number of circuit double
-covers.
+ Calculate a the number of 4-boundaries of a linear
+ representation of the number of circuit double covers.
-It uses cyclic ladder gadgets with sizes 2 up to 7 with
-permutations of all half-edges except the first one.
-This gives matrix of size 36 with rank 21.
+ It uses cyclic ladder gadgets with sizes 2 up to 7 with
+ permutations of all half-edges except the first one.
+ This gives matrix of size 36 with rank 21 which matches
+ the upper bound which is the rank of the join matrix.
"""
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
from itertools import permutations
from graph_tools.all import *
-
LadderGadget = lambda k: CyclicLadder().gadget(k)
ladders = list(map(LadderGadget, range(2, 8)))
gadgets = [ l.permute((1,) + p)
diff --git a/experiments/cdc_5_boundaries.py b/experiments/cdc_5_boundaries.py
index ccc0ddd..44946cc 100755
--- a/experiments/cdc_5_boundaries.py
+++ b/experiments/cdc_5_boundaries.py
@@ -1,18 +1,19 @@
#!/usr/bin/python
"""
-Calculate a lower bound on the number of 4-boundaries
-of a linear representation of the number of circuit double
-covers.
+ Calculate a lower bound on the number of 5-boundaries
+ of a linear representation of the number of circuit double
+ covers.
-It uses cyclic ladder gadgets with sizes 2 up to 7 with
-permutations of all half-edges except the first one.
-This gives matrix of size 36 with rank 21.
-"""
+ It uses cyclic ladder gadgets with sizes 2 up to 7 with
+ permutations of all half-edges except the first one.
+ This gives matrix of size 576 with rank 161. The upper
+ bound is 202 -- the rank of the join matrix.
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
+ WARNING: This experiment takes a long time to complete.
+"""
+import _experiment
from itertools import permutations
from graph_tools.all import *
diff --git a/experiments/flower-snarks.py b/experiments/flower-snarks.py
index f71438d..f282955 100755
--- a/experiments/flower-snarks.py
+++ b/experiments/flower-snarks.py
@@ -1,17 +1,15 @@
#!/usr/bin/python
-DOC = """
-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
-of $M^10 x$ and $M^9 x$ where $x$ is the initial vector. This eigenvector
-shares one non-zero coordinate with the final vector.
"""
+ Calculate that the number of CDCs of Flower snark $J_k$ is $c16^k \pm O(15^k)$.
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
+ 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
+ of $M^10 x$ and $M^9 x$ where $x$ is the initial vector. This eigenvector
+ shares one non-zero coordinate with the final vector.
+"""
+import _experiment
from graph_tools.all import *
from sage.all import identity_matrix, QQ, DiGraph, matrix
@@ -77,7 +75,6 @@ def matrix_to_rev_graph(M):
if __name__ == "__main__":
- print(DOC)
print("Stabilizing...")
S = FlowerSnark.stabilize(CircuitDoubleCover, jordan=False)
print("Done")
diff --git a/experiments/flowers.py b/experiments/flowers.py
index 393a824..16271fd 100755
--- a/experiments/flowers.py
+++ b/experiments/flowers.py
@@ -1,14 +1,14 @@
#!/usr/bin/python
"""
-Derive a formula for the number of circuit double covers of a flower.
-
-Let $G$ be embedding of a graph into some surface. We say that a face
-$f$ of size $k$ together with its neighbour faces are a {\em $k$-flower
-with center $f$} given that $k \geq 3$, $f$ shares exactly one edge
-with each of its neighbour faces, consecutive neighbour faces also
-share exactly one edge, and non-consecutive neighbour faces do not
-share any edge.
+ Derive a formula for the number of circuit double covers of a flower.
+
+ Let $G$ be embedding of a graph into some surface. We say that a face
+ $f$ of size $k$ together with its neighbour faces are a {\em $k$-flower
+ with center $f$} given that $k \geq 3$, $f$ shares exactly one edge
+ with each of its neighbour faces, consecutive neighbour faces also
+ share exactly one edge, and non-consecutive neighbour faces do not
+ share any edge.
"""
import _experiment
diff --git a/experiments/ladders.py b/experiments/ladders.py
index b84f6c1..e14ac96 100755
--- a/experiments/ladders.py
+++ b/experiments/ladders.py
@@ -1,20 +1,17 @@
#!/usr/bin/python
"""
-Derive a formula for the number of circuit double covers
-of cyclic ladders and crossed cyclic ladders.
+ Derive a formula for the number of circuit double covers
+ of cyclic ladders and crossed cyclic ladders.
"""
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
from graph_tools.all import *
L = CyclicLadder().stabilize(CircuitDoubleCover, jordan=True)
CL = CyclicLadder(True).stabilize(CircuitDoubleCover, jordan=True)
if __name__ == "__main__":
- print(__doc__)
print("Cyclic ladders:\n Formula: %s\n Under the condition %s\n" %
(L["formula"], L["formula_if"]))
print("Crossed cyclic ladders:\n Formula: %s\n Under the condition %s" %
diff --git a/experiments/reduce-cycle.py b/experiments/reduce-cycle.py
index 097b443..d7726ec 100755
--- a/experiments/reduce-cycle.py
+++ b/experiments/reduce-cycle.py
@@ -2,14 +2,12 @@
"""
Application of Theorem 6.12 to triangles, 4-cycles (Theorem 6.13)
-and 5.cycles (Theorem 6.14). Note that the results are numeric
+and 5-cycles (Theorem 6.14). Note that the results are numeric
calculation so it is necessary to review the system of equations
by hand. (It is printed by the command-line parameter -v.)
"""
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
from graph_tools.base import *
from graph_tools.parameters import CircuitDoubleCover, VertexCount
from graph_tools.misc import sun
diff --git a/experiments/small-snarks.py b/experiments/small-snarks.py
index ff84ada..e6885df 100755
--- a/experiments/small-snarks.py
+++ b/experiments/small-snarks.py
@@ -1,13 +1,11 @@
#!/usr/bin/python
"""
-Calculate the number of circuit double covers for the Petersen
-graph a Blanusa snarks.
+ Calculate the number of circuit double covers for the Petersen
+ graph and Blanusa snarks.
"""
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
from graph_tools.all import *
from sage.all import graphs
@@ -18,7 +16,6 @@ L = {
}
if __name__ == "__main__":
- print(__doc__)
for n, g in L.items():
print("%s: %i" % (n, graph_to_gadget(g).eval(CircuitDoubleCover)))
--
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