From e9f41377ee2fc23e2a0f05cc9b0ff425a2513b18 Mon Sep 17 00:00:00 2001
From: Cotton Seed <cotton@alum.mit.edu>
Date: Thu, 16 Aug 2012 13:42:44 -0400
Subject: [PATCH] Compare twisted U^2 = 0 theory and untwisted theory to
 compile a list of small examples where U differentials appear.

---
 Makefile        |  8 ++---
 knot_tables.cpp |  2 +-
 main.cpp        | 82 +++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 87 insertions(+), 5 deletions(-)

diff --git a/Makefile b/Makefile
index 0aabbf9..5ac2999 100644
--- a/Makefile
+++ b/Makefile
@@ -3,14 +3,14 @@ BISON = /opt/local/bin/bison
 FLEX = /opt/local/bin/flex
 
 # CXX = g++
-CXX = OMPI_CXX=clang++ mpic++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -I/u/cseed/llvm-3.1/lib/c++/v1
-# CXX = clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11
+# CXX = OMPI_CXX=clang++ mpic++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -I/u/cseed/llvm-3.1/lib/c++/v1
+CXX = clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11
 
 INCLUDES = -I/opt/local/include -I.
 
 # OPTFLAGS = -g
-# OPTFLAGS = -O2 -g
-OPTFLAGS = -O2 -DNDEBUG
+OPTFLAGS = -O2 -g
+# OPTFLAGS = -O2 -DNDEBUG
 
 LDFLAGS = -L/opt/local/lib -L/u/cseed/llvm-3.1/lib
 # LDFLAGS = -pg -L/opt/local/lib
diff --git a/knot_tables.cpp b/knot_tables.cpp
index f63b170..3445ed7 100644
--- a/knot_tables.cpp
+++ b/knot_tables.cpp
@@ -1,7 +1,7 @@
 
 #include <knotkit.h>
 
-#define HOME "/u/cseed/src/knotkit/"
+#define HOME "/Users/cotton/src/knotkit/"
 
 bool verbose = 0;
 
diff --git a/main.cpp b/main.cpp
index 14238d3..e35381e 100644
--- a/main.cpp
+++ b/main.cpp
@@ -695,11 +695,93 @@ test_knot_sq ()
 pair<mod_map<Z2>, mod_map<Z2> > 
 compute_kh_sq (const knot_desc &desc)
 {
+  abort ();
+}
+
+template<class R> pair<ptr<const module<R> >, mod_map<R> >
+FU_complex (ptr<const module<R> > CF,
+	    mod_map<R> dF,
+	    mod_map<R> dU)
+{
+  unsigned n = CF->dim ();
+  
+  basedvector<grading, 1> hq (n * 2);
+  for (unsigned i = 1; i <= n; i ++)
+    hq[i] = hq[n + i] = CF->generator_grading (i);
+  
+  ptr<const module<R> > CFU = new explicit_module<R> (2 * n,
+							basedvector<R, 1> (),
+							hq);
+  map_builder<R> b (CFU);
+  for (unsigned i = 1; i <= n; i ++)
+    {
+      for (linear_combination_const_iter<R> j = dF[i]; j; j ++)
+	{
+	  b[i].muladd (j.val (), j.key ());
+	  b[n + i].muladd (j.val (), n + j.key ());
+	}
+      for (linear_combination_const_iter<R> j = dU[i]; j; j ++)
+	{
+	  b[i].muladd (j.val (), n + j.key ());
+	}
+    }
+  mod_map<R> dFU (b);
+  // assert (dFU.compose (dFU) == 0);
+  // dFU.check_sseq_graded ();
+  return pair<ptr<const module<R> >, mod_map<R> > (CFU, dFU);
+}
+
+void
+compute_twistedU ()
+{
+#if 0
+  for (unsigned i = 1; i <= 11; i ++)
+    for (unsigned j = 1; j <= htw_knots (i, 0); j ++)
+      {
+	knot_diagram kd (htw_knot (i, 0, j));
+      ...}
+#endif
+  for (unsigned i = 1; i <= 10; i ++)
+    for (unsigned j = 1; j <= mt_links (i, 0); j ++)
+      {
+	knot_diagram kd (mt_link (i, 0, j));
+	
+	kd.marked_edge = 1;
+	show (kd); newline ();
+	
+	typedef spanning_tree_complex<Z2>::R R;
+	
+	spanning_tree_complex<Z2> c (kd);
+	ptr<const module<R> > C = c.C;
+	
+	mod_map<R> d2 = c.twisted_d2 ();
+	assert (d2.compose (d2) == 0);
+	
+	mod_map<R> d2U = c.twisted_d2Un (1);
+	assert (d2.compose (d2U) == d2U.compose (d2));
+	
+	chain_complex_simplifier<R> s (C, d2, 2);
+	assert (s.new_d == 0);
+	printf ("|s.new_C| = %d\n", s.new_C->dim ());
+	
+	pair<ptr<const module<R> >, mod_map<R> > p = FU_complex (C, d2, d2U);
+	ptr<const module<R> > CFU = p.first;
+	mod_map<R> dFU = p.second;
+	
+	chain_complex_simplifier<R> s2 (CFU, dFU, 2);
+	assert (s2.new_d == 0);
+	printf ("|s2.new_C| = %d\n", s2.new_C->dim ());
+	
+	if (s2.new_C->dim () < 2 * s.new_C->dim ())
+	  printf (" > EXAMPLE\n");
+      }
 }
 
 int
 main ()
 {
+  compute_twistedU ();
+  
 #if 1
   knot_desc desc;
   desc.t = knot_desc::HTW;