Renamed driver kk. Added support for various invariants (gss + kh,

lsss, leess, sq2, s) to prepare for release of the link splitting
spectral sequence paper on the arXiv.

.gitignore

@@ -1,6 +1,6 @@
 *~
 *.o
-/gss
+/kk
 /main
 /testsurfaces
 /serial.cmd.[eo]*

Makefile

@@ -1,21 +1,22 @@
 
-BISON = /opt/local/bin/bison
+devel = 1
-FLEX = /opt/local/bin/flex
+
+BISON = bison
+FLEX = 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 -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.
+INCLUDES = -I. -I/opt/local/include 
 
-# OPTFLAGS = -g
+OPTFLAGS = -g
-OPTFLAGS = -O2 -g
+# OPTFLAGS = -O2 -g
 # OPTFLAGS = -O2 -DNDEBUG
 
-LDFLAGS = -L/opt/local/lib -L/u/cseed/llvm-3.1/lib
+LDFLAGS = -L/opt/local/lib
-# LDFLAGS = -pg -L/opt/local/lib
 
-CXXFLAGS = $(OPTFLAGS) -Wall -Wno-unused $(INCLUDES)
+CXXFLAGS = $(OPTFLAGS) -DHOME="\"`pwd`\"" -Wall -Wno-unused $(INCLUDES)
 
 LIB_OBJS = lib/refcount.o \
   lib/lib.o lib/smallbitset.o lib/bitset.o lib/setcommon.o lib/io.o lib/directed_multigraph.o
@@ -45,7 +46,7 @@ KNOTKIT_HEADERS = knotkit.h planar_diagram.h dt_code.h knot_diagram.h \
 
 LIBS = -lgmp -lz
 
-all: gss
+all: kk
 
 %.o : %.cc
 	$(CXX) -c $(CXXFLAGS) $< -o $@
@@ -53,8 +54,8 @@ all: gss
 %.o : %.cpp
 	$(CXX) -c $(CXXFLAGS) $< -o $@
 
-gss: gss.o $(COMMON_OBJS)
+kk: kk.o $(COMMON_OBJS)
-	$(CXX) $(LDFLAGS) -o gss $^ $(LIBS)
+	$(CXX) $(LDFLAGS) -o kk $^ $(LIBS)
 
 main: main.o $(COMMON_OBJS)
 	$(CXX) $(LDFLAGS) -o main $^ $(LIBS)
@@ -65,6 +66,7 @@ mpimain: mpimain.o mpi_aux.o $(COMMON_OBJS)
 testlib: testlib.o $(COMMON_OBJS)
 	$(CXX) $(LDFLAGS) -o testlib $^
 
+ifeq ($(devel),1)
 knot_parser/knot_parser.cc knot_parser/knot_parser.hh: knot_parser/knot_parser.yy
 	$(BISON) knot_parser/knot_parser.yy -o knot_parser/knot_parser.cc
 
@@ -82,6 +84,7 @@ rd_parser/rd_parser.cc rd_parser/rd_parser.hh: rd_parser/rd_parser.yy
 
 rd_parser/rd_scanner.cc: rd_parser/rd_scanner.ll
 	$(FLEX) -o rd_parser/rd_scanner.cc rd_parser/rd_scanner.ll
+endif
 
 .PHONY: parser_files
 parser_files: \
@@ -95,7 +98,7 @@ parser_files: \
 .PHONY: clean
 clean:
 	rm -f *.o lib/*.o algebra/*.o knot_parser/*.o rd_parser/*.o
-	rm -f main gss mpimain
+	rm -f main kk mpimain
 	rm -f gmon.out
 
 .PHONY: realclean
@@ -112,6 +115,6 @@ realclean: clean
 
 $(LIB_OBJS): $(LIB_HEADERS)
 $(ALGEBRA_OBJS): $(ALGEBRA_HEADERS) $(LIB_HEADERS)
-$(KNOTKIT_OBJS) main.o mpimain.o gss.o: $(KNOTKIT_HEADERS) $(ALGEBRA_HEADERS) $(LIB_HEADERS)
+$(KNOTKIT_OBJS) main.o mpimain.o kk.o: $(KNOTKIT_HEADERS) $(ALGEBRA_HEADERS) $(LIB_HEADERS)
 
 mpimain.o mpi_aux.o: mpi_aux.h

README

@@ -1 +1,156 @@
-I modified cotton's readme.
+knotkit is a C++ software package written by Cotton Seed
+(cseed@math.princeton.edu) for computing some knot and manifold
+invariants appearing in low-dimensional topology.  Other contributors
+include Josh Batson.
+
+TABLE OF CONTENTS
+
+1. INTRO
+2. BUILDING
+3. USAGE
+4. UPCOMING CHANGES
+5. FOR DEVELOPERS
+
+1. INTRO
+
+In addition to accepting knot presentations in a variety of formats
+(see usage below), knotkit contains the following tables of knot data:
+
+* The Rolfsen knot tables through 10 crossings, extracted from
+  Bar-Natan's Mathematica package, KnotTheory`,
+* The Hoste-Weeks-Thistlewaite knot tables through 16 crossings taken
+  from knotscape, and
+* and the Morwen Thistlewaite hyperbolic link tables taken from
+  SnapPy.
+
+This version of knotkit has support to compute the following
+invariants:
+
+* Khovanov homology
+See:
+M. Khovanov, A Categorification of the Jones Polynomial, Duke
+  Math. J. 101 (2000), 359--426, arXiv:math/9908171.
+D. Bar-Natan, On Khovanov's Categorification of the Jones Polynomial,
+  Algebraic and Geometric Topology 2 (2002), 337--370.
+
+* Szabo's geometric spectral sequence 
+Computing gss was the original motivation for writing knotkit.  For
+more information on gss, see:
+Z. Szabo, A geometric spectral sequence in Khovanov homology, 
+  arXiv:1010.4252, and
+C. Seed, Computations of Szabo's Geometric Spectral Sequence in Khovanov
+  Homology, arXiv:1110.0735.
+
+* The Batson-Seed link splitting spectral sequence
+See:
+J. Batson, C. Seed, A Link Splitting Spectral Sequence in Khovanov
+  Homology.
+
+* The Lipshitz-Sarkar Steenrod square on Khovanov homology
+See:
+R. Lipshitz, S. Sarkar, A Khovanov Homotopy Type, arXiv:1112.3932.
+R. Lipshitz, S. Sarkar, A Steenrod Square on Khovanov Homology,
+  arXiv:1204.5776.
+
+* Bar-Natan's analogue of Lee homology
+See:
+E. S. Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197
+  (2005), 2, 554–586, arXiv:math/0210213.
+D. Bar-Natan, Khovanov’s homology for tangles and cobordisms,
+  Geom. Topol. 9 (2005), 1443–1499, arXiv:math/0410495.
+R. Lipshitz, S. Sarkar, A refinement of Rasmussen's s-invariant,
+  arXiv:1206.3532.
+
+* The s-invariant coming from Bar-Natan's analogue of Lee homology
+In addition to the above references, see:
+J. Rasmussen, Khovanov homology and the slice genus, Invent.
+  Math. 182 2 (2010), 419--447, arXiv:math/0402131.
+R. Lipshitz, S. Sarkar, A refinement of Rasmussen's s-invariant,
+  arXiv:1206.3532.
+
+2. BUILDING
+
+To build knotkit on OS X, you will need the latest version of XCode
+(available for free in the App Store) and the GNU multiple precision
+arithmetic library (GMP).  You can get GMP here:
+
+http://gmplib.org/
+
+knotkit also builds under Linux.  In addition to GMP, you will need a
+C++ compiler which supports C++11.  I use LLVM clang, but knotkit
+should build with a recent version of GCC.
+
+knotkit doesn't have a sophisticated build system.  To build knotkit, just run:
+
+make
+
+from the knotkit source directory.  This should build the executable
+"kk".  For instructions on invoking kk, see usage below.  If you run
+into a problem, please contact me: Cotton Seed
+(cotton@math.princeton.edu).
+
+3. USAGE
+
+The usage message for kk is given below.  This can also be obtained by
+running "kk -h".
+
+A note about output.  The output for commands kh, gss, ls and lee is a
+.tex file which renders the bigraded homology group or spectral
+sequence.  The output for the command sq2 matches the output for the
+program written by Lipshitz-Sarkar and is suitable for loading into
+Sage.  The command s outputs a single line of text.
+
+usage: kk <invariant> [options...] <link>
+  compute <invariant> for knot or link <link>
+<invariant> can be one of:
+  kh: Khovanov homology
+  gss: Szabo's geometric spectral sequence
+  ls: Batson-Seed link splitting spectral sequence
+    component weights are 0, 1, ..., m
+  sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh
+    output suitable for Sage
+  leess: spectral sequence coming from Bar-Natan analogue of Lee's
+    deformation of Khovanov's complex (whew!)
+  s: Rasmussen's s-invariant coming from lee
+options:
+  -r         : compute reduced theory
+  -h         : print this message
+  -o <file>  : write output to <file>
+                (stdout is the default)
+  -f <field> : ground field (if applicable)
+                (Z2 is the default)
+  -v         : verbose: report progress as the computation proceeds
+<field> can be one of:
+  Z2, Z3, Q
+<link> can be one of:
+  - the unknot, e.g. U or unknot
+  - a torus knot, e.g. T(2,3)
+  - a Rolfsen table knot, e.g. 10_124
+  - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214
+  - a Morwen Thistlethwaite link, e.g. L9a21 or L14n7631
+  - a planar diagram, e.g.
+      PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or
+      PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]
+  - a Dowker-Thistlethwaite code, e.g.
+      DTCode[6,8,2,4],
+      DT[dadbcda] or
+      DT[{6, -8}, {-10, 12, -14, 2, -4}]
+  - a braid, e.g. BR[2, {-1, -1, -1}]
+
+4. UPCOMING CHANGES
+
+The following changes are currently planned:
+
+* support for Z/p, p arbitrary prime and F(x) field of rational functions
+* Roberts' totally twisted Khovanov homology
+* the E^3 page of the twisted spectral sequence Kh(L) => \widehat{HF}(\Sigma_L)
+* spectral sequences of PIDs: ls over F[x], gss over Z
+* maps induced by cobordisms
+
+5. FOR DEVELOPERS
+
+If you are interested in contributing to knotkit or using it for a new
+application, please contact me: Cotton Seed
+(cotton@math.princeton.edu).  I am interested in developing knotkit to
+be an open platform for performing computations arising in
+low-dimensional topology.

algebra/module.h

@@ -54,6 +54,7 @@ class module : public refcounted
   // r < i <= n
   virtual R generator_ann (unsigned i) const = 0;
 
+  basedvector<grading, 1> grading_vector () const;
   set<grading> gradings () const;
   
   bool is_free () const { return dim () == free_rank (); }
@@ -1503,6 +1504,15 @@ module<R>::free_ell_poincare_polynomial () const
   return r;
 }
 
+template<class R> basedvector<grading, 1>
+module<R>::grading_vector () const
+{
+  basedvector<grading, 1> v (dim ());
+  for (unsigned i = 1; i <= dim (); i ++)
+    v[i] = generator_grading (i);
+  return v;
+}
+
 template<class R> set<grading> 
 module<R>::gradings () const
 {

cube_impl.h

@@ -329,6 +329,13 @@ cube<R>::H_i (unsigned c)
       
       for (unsigned j = 0; j < from_s.num_monomials (); j ++)
 	{
+	  if (markedp_only)
+	    {
+	      unsigned p = from_s.edge_circle[kd.marked_edge];
+	      if (unsigned_bittest (j, p))
+		continue;
+	    }
+	  
 	  unsigned j2 = 0;
 	  for (unsigned_const_iter k = j; k; k ++)
 	    {
@@ -395,6 +402,13 @@ cube<R>::compute_dinv (unsigned c)
 	y = to_s.crossing_to_circle (kd, c);
       for (unsigned j = 0; j < from_s.num_monomials (); j ++)
 	{
+	  if (markedp_only)
+	    {
+	      unsigned p = from_s.edge_circle[kd.marked_edge];
+	      if (unsigned_bittest (j, p))
+		continue;
+	    }
+	  
 	  unsigned j2 = 0;
 	  for (unsigned_const_iter k = j; k; k ++)
 	    {

gss.cpp

@@ -1,126 +0,0 @@
-
-#include <knotkit.h>
-
-const char *program_name;
-
-void
-usage ()
-{
-  printf ("usage: %s [-f] [-h] [-o <file>] [-v] <knot>\n", program_name);
-  printf ("  compute Szabo's geometric spectral sequence for knot <knot>\n");
-  printf ("options:\n");
-  printf ("  -f        : compute unreduced spectral sequence\n");
-  printf ("                (reduced is the default)\n");
-  printf ("  -h        : print this message\n");
-  printf ("  -o <file> : write output to <file>\n");
-  printf ("                (stdout is the default)\n");
-  printf ("  -v        : verbose: report progress as the computation proceeds\n");
-  printf ("<knot> can be one of:\n");
-  printf ("  - the unknot, e.g. U or unknot\n");
-  printf ("  - a torus knot, e.g. T(2,3)\n");
-  printf ("  - a Rolfsen table knot, e.g. 10_124\n");
-  printf ("  - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214\n");
-  printf ("  - a Morwen Thistlethwaite link, e.g. L9a21 or L14n7631\n");
-  printf ("  - a planar diagram, e.g.\n");
-  printf ("      PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or\n");
-  printf ("      PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]\n");
-  printf ("  - a Dowker-Thistlethwaite code, e.g.\n");
-  printf ("      DTCode[6,8,2,4],\n");
-  printf ("      DT[dadbcda] or\n");
-  printf ("      DT[{6, -8}, {-10, 12, -14, 2, -4}]\n");
-  printf ("  - a braid, e.g. BR[2, {-1, -1, -1}]\n");
-}
-
-int
-main (int argc, char **argv)
-{
-  program_name = argv[0];
-  
-  bool reduced = 1;
-  const char *knot = 0;
-  const char *file = 0;
-  
-  for (int i = 1; i < argc; i ++)
-    {
-      if (argv[i][0] == '-')
-	{
-	  if (strcmp (argv[i], "-f") == 0)
-	    reduced = 0;
-	  else if (strcmp (argv[i], "-h") == 0)
-	    {
-	      usage ();
-	      exit (EXIT_SUCCESS);
-	    }
-	  else if (!strcmp (argv[i], "-v"))
-	    verbose = 1;
-	  else if (!strcmp (argv[i], "-o"))
-	    {
-	      i ++;
-	      if (i == argc)
-		{
-		  fprintf (stderr, "error: missing argument to option `-o'\n");
-		  exit (EXIT_FAILURE);
-		}
-	      file = argv[i];
-	    }
-	  else
-	    {
-	      fprintf (stderr, "error: unknown argument `%s'\n", argv[1]);
-	      usage ();
-	      exit (EXIT_FAILURE);
-	    }
-	}
-      else
-	{
-	  if (knot)
-	    {
-	      fprintf (stderr, "error: too many arguments\n");
-	      usage ();
-	      exit (EXIT_FAILURE);
-	    }
-	  else
-	    knot = argv[i];
-	}
-    }
-  
-  if (!knot)
-    {
-      fprintf (stderr, "error: missing <knot> argument\n");
-      usage ();
-      exit (EXIT_FAILURE);
-    }
-  
-  FILE *outfp = 0;
-  if (file)
-    {
-      outfp = fopen (file, "w");
-      if (!outfp)
-	{
-	  stderror ("fopen: %s", file);
-	  exit (EXIT_FAILURE);
-	}
-    }
-  else
-    outfp = stdout;
-  
-  knot_diagram d = parse_knot (knot);
-  d.marked_edge = 1;
-  cube<Z2> c (d, reduced);
-  
-  fprintf (outfp, "\\documentclass{article}\n\
-\\usepackage{amsmath, tikz, hyperref}\n\
-\\DeclareMathOperator{\\rank}{rank}\n\
-\\setlength{\\parindent}{0pt}\n\
-\n\
-\\begin{document}\n\
-\\pagestyle{empty}\n\
-\\tableofcontents\n\
-\\sloppy\n");
-  
-  compute_szabo_sseq (c).texshow (outfp, d.name);
-  
-  fprintf (outfp, "\\end{document}\n");
-  
-  if (file)
-    fclose (outfp);
-}

kk.cpp

@@ -0,0 +1,660 @@
+
+#include <knotkit.h>
+
+const char *program_name;
+
+void
+usage ()
+{
+  printf ("usage: %s <invariant> [options...] <link>\n", program_name);
+  printf ("  compute <invariant> for knot or link <link>\n");
+  printf ("<invariant> can be one of:\n");
+  printf ("  kh: Khovanov homology\n");
+  printf ("  gss: Szabo's geometric spectral sequence\n");
+  printf ("  ls: Batson-Seed link splitting spectral sequence\n");
+  printf ("    component weights are 0, 1, ..., m\n");
+  printf ("  sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh\n");
+  printf ("    output suitable for Sage\n");
+  printf ("  leess: spectral sequence coming from Bar-Natan analogue of Lee's\n");
+  printf ("    deformation of Khovanov's complex (whew!)\n");
+  printf ("  s: Rasmussen's s-invariant coming from lee\n");
+  printf ("options:\n");
+  printf ("  -r         : compute reduced theory\n");
+  printf ("  -h         : print this message\n");
+  printf ("  -o <file>  : write output to <file>\n");
+  printf ("                (stdout is the default)\n");
+  printf ("  -f <field> : ground field (if applicable)\n");
+  printf ("                (Z2 is the default)\n");
+  printf ("  -v         : verbose: report progress as the computation proceeds\n");
+  printf ("<field> can be one of:\n");
+  printf ("  Z2, Z3, Q\n");
+  printf ("<link> can be one of:\n");
+  printf ("  - the unknot, e.g. U or unknot\n");
+  printf ("  - a torus knot, e.g. T(2,3)\n");
+  printf ("  - a Rolfsen table knot, e.g. 10_124\n");
+  printf ("  - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214\n");
+  printf ("  - a Morwen Thistlethwaite link, e.g. L9a21 or L14n7631\n");
+  printf ("  - a planar diagram, e.g.\n");
+  printf ("      PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or\n");
+  printf ("      PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]\n");
+  printf ("  - a Dowker-Thistlethwaite code, e.g.\n");
+  printf ("      DTCode[6,8,2,4],\n");
+  printf ("      DT[dadbcda] or\n");
+  printf ("      DT[{6, -8}, {-10, 12, -14, 2, -4}]\n");
+  printf ("  - a braid, e.g. BR[2, {-1, -1, -1}]\n");
+}
+
+FILE *outfp = stdout;
+
+void tex_header ()
+{
+  fprintf (outfp, "\\documentclass{article}\n\
+\\usepackage{amsmath, tikz, hyperref}\n\
+\\DeclareMathOperator{\\rank}{rank}\n\
+\\setlength{\\parindent}{0pt}\n\
+\n\
+\\begin{document}\n\
+\\pagestyle{empty}\n\
+\\sloppy\n");
+}
+
+void tex_footer ()
+{
+  fprintf (outfp, "\\end{document}\n");
+}
+
+const char *knot = 0;
+const char *invariant = 0;
+const char *field = "Z2";
+
+knot_diagram kd;
+
+bool reduced = 0;
+
+class hg_grading_mapper
+{
+  unsigned m;
+  
+public:
+  hg_grading_mapper (unsigned m_) : m(m_) { }
+  
+  grading operator () (grading hq) const
+  {
+    int t = hq.q - (int)m;
+    if (reduced)
+      t --;
+    
+    assert (is_even (t));
+    return grading (hq.h, t / 2);
+  }
+  
+  grading map_delta (grading d_hq) const
+  {
+    assert (is_even (d_hq.q));
+    return grading (d_hq.h, d_hq.q / 2);
+  }
+  
+  void x_label (FILE *fp, int h) const
+  {
+    fprintf (fp, "%d", h);
+  }
+  void y_label (FILE *fp, int g) const
+  {
+    unsigned q = 2*g + (int)m;
+    if (reduced)
+      q ++;
+    
+    fprintf (fp, "%d", q);
+  }
+};
+
+template<class R> mod_map<R>
+compute_link_splitting_d (knot_diagram &kd,
+			  cube<R> &c,
+			  basedvector<R, 1> comp_weight)
+{
+  unsigned n = kd.num_components ();
+  
+  unionfind<1> u (kd.num_edges ());
+  for (unsigned i = 1; i <= kd.n_crossings; i ++)
+    {
+      u.join (kd.ept_edge (kd.crossings[i][1]),
+	      kd.ept_edge (kd.crossings[i][3]));
+      u.join (kd.ept_edge (kd.crossings[i][2]),
+	      kd.ept_edge (kd.crossings[i][4]));
+    }
+	
+  map<unsigned, unsigned> root_comp;
+  unsigned t = 0;
+  for (unsigned i = 1; i <= kd.num_edges (); i ++)
+    {
+      if (u.find (i) == i)
+	{
+	  ++ t;
+	  root_comp.push (i, t);
+	}
+    }
+  assert (t == n);
+  
+  assert (comp_weight.size () == n);
+  
+  map<unsigned, R> crossing_over_sign;
+	
+  // crossings
+  set<unsigned> pending;
+  set<unsigned> finished;
+	
+  crossing_over_sign.push (1, R (1));
+  pending.push (1);
+  
+  while (pending.card () > 0)
+    {
+      unsigned x = pending.pop ();
+      finished.push (x);
+      
+      R s = crossing_over_sign(x);
+      
+      for (unsigned j = 1; j <= 4; j ++)
+	{
+	  unsigned p = kd.crossings[x][j];
+	  R t = kd.is_over_ept (p) ? s : -s;  // sign of (x, p)
+	  
+	  unsigned q = kd.edge_other_ept (p);
+	  unsigned x2 = kd.ept_crossing[q];
+	  
+	  R u = kd.is_over_ept (q) ? -t : t;
+	  
+	  if (crossing_over_sign % x2)
+	    assert (crossing_over_sign(x2) == u);
+	  else
+	    crossing_over_sign.push (x2, u);
+	  
+	  if (! (finished % x2))
+	    pending += x2;
+	}
+    }
+  assert (finished.card () == kd.n_crossings);
+  
+  mod_map<R> untwisted_d = c.compute_d (1, 0, 0, 0, 0);
+  assert (untwisted_d.compose (untwisted_d) == 0);
+  
+  mod_map<R> d = untwisted_d;
+  for (unsigned x = 1; x <= kd.n_crossings; x ++)
+    {
+      unsigned p1 = kd.crossings[x][1],
+	p2 = kd.crossings[x][2];
+      assert (kd.is_over_ept (p2));
+      
+      unsigned r1 = u.find (kd.ept_edge (p1)),
+	r2 = u.find (kd.ept_edge (p2));
+      
+      unsigned c1 = root_comp(r1),
+	c2 = root_comp(r2);
+      
+      if (c1 != c2)
+	{
+	  R s = crossing_over_sign(x);
+		
+	  R w_under = comp_weight[c1];
+	  R w_over = comp_weight[c2];
+		
+	  d = d + c.compute_dinv (x)*(s*(w_over - w_under));
+	}
+    }
+  
+  assert (d.compose (d) == 0);
+  return d;
+}
+
+void
+compute_gss ()
+{
+  cube<Z2> c (kd, reduced);
+  ptr<const module<Z2> > C = c.khC;
+  mod_map<Z2> d = c.compute_d (0, 0, 0, 0, 0);
+  
+  unsigned m = kd.num_components ();
+  hg_grading_mapper mapper (m);
+  
+  sseq_bounds b (C, mapper);
+  basedvector<sseq_page, 1> pages;
+  
+  unsigned k = 1;
+  for (;;)
+    {
+      chain_complex_simplifier<Z2> s (C, d,
+				      maybe<int> (k), maybe<int> (2*k - 2));
+      C = s.new_C;
+      d = s.new_d;
+      k ++;
+      
+      grading dk_gr (k, 2*k - 2);
+      pages.append (sseq_page (b, k, dk_gr, d.graded_piece (dk_gr), mapper));
+      if (d == 0)
+	break;
+    }
+  
+  sseq ss (b, pages);
+  
+  tex_header ();
+  fprintf (outfp, "$E_k = %s^{Sz}_k(\\verb~%s~; \\verb~%s~)$:\\\\\n",
+	       (reduced
+		? "\\widetilde{E}"
+		: "E"),
+	   knot, field);
+  ss.texshow (outfp, mapper);
+  tex_footer ();
+}
+
+template<class R> void
+compute_invariant ()
+{
+  if (!strcmp (invariant, "kh"))
+    {
+      cube<R> c (kd, reduced);
+      ptr<const module<R> > C = c.khC;
+      mod_map<R> d = c.compute_d (1, 0, 0, 0, 0);
+      
+      unsigned m = kd.num_components ();
+      hg_grading_mapper mapper (m);
+      
+      chain_complex_simplifier<R> s (C, d,
+				     maybe<int> (1), maybe<int> (0));
+      C = s.new_C;
+      d = s.new_d;
+      
+      sseq_bounds b (C, mapper);
+      sseq_page pg (b, 2, grading (0, 0), mod_map<R> (C), mapper);
+      
+      tex_header ();
+      
+      fprintf (outfp, "Kh = $%s(\\verb~%s~; \\verb~%s~)$:\\\\\n",
+	       (reduced
+		? "\\widetilde{Kh}"
+		: "Kh"),
+	       knot,
+	       field);
+      fprintf (outfp, "$\\rank Kh = %d$\\\\\n", C->dim ());
+      
+      char buf[1000];
+      sprintf (buf, "$Kh$");
+      pg.texshow (outfp, b, buf, mapper);
+      
+      tex_footer ();
+    }
+  else if (!strcmp (invariant, "lsss"))
+    {
+      cube<R> c (kd, reduced);
+      ptr<const module<R> > C = c.khC;
+      
+      unsigned m = kd.num_components ();
+      basedvector<R, 1> comp_weight (m);
+      for (unsigned i = 1; i <= m; i ++)
+	comp_weight[i] = R ((int)(i - 1));
+      
+      mod_map<R> d = compute_link_splitting_d (kd, c, comp_weight);
+      
+      hg_grading_mapper mapper (m);
+      
+      sseq_bounds b (C, mapper);
+      basedvector<sseq_page, 1> pages;
+      
+      int k = 0;
+      for (;;)
+	{
+	  chain_complex_simplifier<R> s (C, d,
+					 maybe<int> (1 - 2*k), maybe<int> (-2*k));
+	  C = s.new_C;
+	  d = s.new_d;
+	  k ++;
+	  
+	  grading dk_gr (1 - 2*k, -2*k);
+	  pages.append (sseq_page (b, k, dk_gr, d.graded_piece (dk_gr), mapper));
+	  if (d == 0)
+	    break;
+	}
+      
+      sseq ss (b, pages);
+      
+      tex_header ();
+      fprintf (outfp, "$E_k = %s^{BS}_k(\\verb~%s~; \\verb~%s~)$:\\\\\n",
+	       (reduced
+		? "\\widetilde{E}"
+		: "E"),
+	       knot,
+	       field);
+      ss.texshow (outfp, mapper);
+      tex_footer ();
+    }
+  else if (!strcmp (invariant, "leess"))
+    {
+      cube<R> c (kd, reduced);
+      ptr<const module<R> > C = c.khC;
+      
+      mod_map<R> d = c.compute_d (1, 0, 0, 0, 0);
+      for (unsigned i = 1; i <= kd.n_crossings; i ++)
+	d = d + c.H_i (i);
+      assert (d.compose (d) == 0);
+      
+      unsigned m = kd.num_components ();
+      hg_grading_mapper mapper (m);
+      
+      sseq_bounds b (C, mapper);
+      basedvector<sseq_page, 1> pages;
+      
+      int k = 0;
+      for (;;)
+	{
+	  chain_complex_simplifier<R> s (C, d,
+					 maybe<int> (1), maybe<int> (2*k));
+	  C = s.new_C;
+	  d = s.new_d;
+	  k ++;
+	  
+	  grading dk_gr (1, 2*k);
+	  pages.append (sseq_page (b, k, dk_gr, d.graded_piece (dk_gr), mapper));
+	  if (d == 0)
+	    break;
+	}
+      
+      sseq ss (b, pages);
+      
+      tex_header ();
+      fprintf (outfp, "$E_k = %s^{BN}_k(\\verb~%s~; \\verb~%s~)$:\\\\\n",
+	       (reduced
+		? "\\widetilde{E}"
+		: "E"),
+	       knot, field);
+      ss.texshow (outfp, mapper);
+      tex_footer ();
+    }
+  else if (!strcmp (invariant, "s"))
+    {
+      unsigned m = kd.num_components ();
+      if (m != 1)
+	{
+	  fprintf (stderr, "error: s-invariant only defined for knots\n");
+	  exit (EXIT_FAILURE);
+	}
+      
+      cube<R> c (kd, 0);
+      ptr<const module<R> > C = c.khC;
+      
+      mod_map<R> d = c.compute_d (1, 0, 0, 0, 0);
+      for (unsigned i = 1; i <= kd.n_crossings; i ++)
+	d = d + c.H_i (i);
+      assert (d.compose (d) == 0);
+      
+      int k = 0;
+      for (;;)
+	{
+	  chain_complex_simplifier<R> s (C, d,
+					 maybe<int> (1), maybe<int> (2*k));
+	  C = s.new_C;
+	  d = s.new_d;
+	  k ++;
+	  
+	  if (d == 0)
+	    break;
+	}
+      
+      assert (C->dim () == 2);
+      grading gr1 = C->generator_grading (1),
+	gr2 = C->generator_grading (2);
+      
+      int qmin = gr1.q,
+	qmax = gr2.q;
+      if (qmax < qmin)
+	std::swap (qmin, qmax);
+      
+      assert (qmax == qmin + 2);
+      
+      fprintf (outfp, "s(%s; %s) = %d\n", knot, field, qmin + 1);
+    }
+  else 
+    {
+      fprintf (stderr, "error: unknown invariant %s\n", invariant);
+      exit (EXIT_FAILURE);
+    }
+}
+
+void
+sage_show (FILE *fp,
+	   map<grading, basedvector<unsigned, 1> > hq_gens,
+	   ptr<const module<Z2> > H)
+{
+  fprintf (fp, "hom={");
+  bool first = 1;
+  for (map<grading, basedvector<unsigned, 1> >::const_iter i = hq_gens; i; i ++)
+    {
+      if (first)
+	first = 0;
+      else
+	fprintf (fp, ", ");
+      fprintf (fp, "(%d, %d): %d", i.key ().h, i.key ().q, i.val ().size ());
+    }      
+  fprintf (fp, "}\n");
+}
+
+void
+sage_show (FILE *fp,
+	   map<grading, basedvector<unsigned, 1> > hq_gens,
+	   std::string name,
+	   grading delta,
+	   mod_map<Z2> f)
+{
+  fprintf (fp, "%s={", name.c_str ());
+  
+  bool first = 1;
+  for (map<grading, basedvector<unsigned, 1> >::const_iter i = hq_gens; i; i ++)
+    {
+      grading from_hq = i.key ();
+      basedvector<unsigned, 1> from_gens = i.val ();
+      
+      grading to_hq = from_hq + delta;
+      if (hq_gens % to_hq)
+	{
+	  basedvector<unsigned, 1> to_gens = hq_gens(to_hq);
+	  
+	  if (first)
+	    first = 0;
+	  else
+	    fprintf (fp, ", ");
+	  fprintf (fp, "(%d, %d): [", from_hq.h, from_hq.q);
+	  bool first2 = 1;
+	  for (unsigned j = 1; j <= from_gens.size (); j ++)
+	    {
+	      unsigned gj = from_gens[j];
+	      
+	      if (first2)
+		first2 = 0;
+	      else
+		fprintf (fp, ", ");
+	      fprintf (fp, "(");
+	      for (unsigned k = 1; k <= to_gens.size (); k ++)
+		{
+		  unsigned gk = to_gens[k];
+		  
+		  if (k > 1)
+		    fprintf (fp, ", ");
+		  if (f[gj](gk) == 1)
+		    fprintf (fp, "1");
+		  else
+		    {
+		      assert (f[gj](gk) == 0);
+		      fprintf (fp, "0");
+		    }
+		}
+	      fprintf (fp, ")");
+	    }
+	  fprintf (fp, "]");
+	}
+    }
+  fprintf (fp, "}\n");
+}
+
+void
+sage_show_khsq (FILE *fp,
+		ptr<const module<Z2> > H,
+		mod_map<Z2> sq1,
+		mod_map<Z2> sq2)
+{
+  unsigned n = H->dim ();
+  
+  map<grading, basedvector<unsigned, 1> > hq_gens;
+  for (unsigned i = 1; i <= H->dim (); i ++)
+    hq_gens[H->generator_grading (i)].append (i);
+  
+  unsigned t = 0;
+  for (map<grading, basedvector<unsigned, 1> >::const_iter i = hq_gens; i; i ++)
+    t += i.val ().size ();
+  assert (t == n);
+  
+  sage_show (fp, hq_gens, H);
+  sage_show (fp, hq_gens, "sq1", grading (1, 0), sq1);
+  sage_show (fp, hq_gens, "sq2", grading (2, 0), sq2);
+}
+
+void
+compute_sq2 ()
+{
+  cube<Z2> c (kd);
+  mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
+  
+  chain_complex_simplifier<Z2> s (c.khC, d, maybe<int> (1), maybe<int> (0));
+  assert (s.new_d == 0);
+  
+  steenrod_square sq (c, d, s);
+  mod_map<Z2> sq1 = sq.sq1 ();
+  mod_map<Z2> sq2 = sq.sq2 ();
+  
+  ptr<const module<Z2> > H = sq1.domain ();
+  
+  sage_show_khsq (outfp, H, sq1, sq2);
+}
+
+int
+main (int argc, char **argv)
+{
+  program_name = argv[0];
+  
+  const char *file = 0;
+  
+  for (int i = 1; i < argc; i ++)
+    {
+      if (argv[i][0] == '-')
+	{
+	  if (strcmp (argv[i], "-r") == 0)
+	    reduced = 1;
+	  else if (strcmp (argv[i], "-h") == 0)
+	    {
+	      usage ();
+	      exit (EXIT_SUCCESS);
+	    }
+	  else if (!strcmp (argv[i], "-v"))
+	    verbose = 1;
+	  else if (!strcmp (argv[i], "-f"))
+	    {
+	      i ++;
+	      if (i == argc)
+		{
+		  fprintf (stderr, "error: missing argument to option `-f'\n");
+		  exit (EXIT_FAILURE);
+		}
+	      field = argv[i];
+	    }
+	  else if (!strcmp (argv[i], "-o"))
+	    {
+	      i ++;
+	      if (i == argc)
+		{
+		  fprintf (stderr, "error: missing argument to option `-o'\n");
+		  exit (EXIT_FAILURE);
+		}
+	      file = argv[i];
+	    }
+	  else
+	    {
+	      fprintf (stderr, "error: unknown argument `%s'\n", argv[1]);
+	      fprintf (stderr, "  use -h for usage\n");
+	      exit (EXIT_FAILURE);
+	    }
+	}
+      else
+	{
+	  if (knot)
+	    {
+	      fprintf (stderr, "error: too many arguments\n");
+	      fprintf (stderr, "  use -h for usage\n");
+	      exit (EXIT_FAILURE);
+	    }
+	  else if (invariant)
+	    knot = argv[i];
+	  else
+	    {
+	      assert (invariant == 0);
+	      invariant = argv[i];
+	    }
+	}
+    }
+  
+  if (!knot)
+    {
+      fprintf (stderr, "error: too few arguments, <invariant> or <knot> missing\n");
+      fprintf (stderr, "  use -h for usage\n");
+      exit (EXIT_FAILURE);
+    }
+  
+  if (file)
+    {
+      outfp = fopen (file, "w");
+      if (!outfp)
+	{
+	  stderror ("fopen: %s", file);
+	  exit (EXIT_FAILURE);
+	}
+    }
+  else
+    outfp = stdout;
+  
+  kd = parse_knot (knot);
+  kd.marked_edge = 1;
+  
+  if (!strcmp (invariant, "sq2"))
+    {
+      if (strcmp (field, "Z2"))
+	{
+	  fprintf (stderr, "warning: sq2 only defined over Z2, ignoring -f %s\n", field);
+	  field = "Z2";
+	}
+      
+      compute_sq2 ();
+    }
+  else if (!strcmp (invariant, "gss"))
+    {
+      if (strcmp (field, "Z2"))
+	{
+	  fprintf (stderr, "warning: gss only defined over Z2, ignoring -f %s\n", field);
+	  field = "Z2";
+	}
+      
+      compute_gss ();
+    }
+  else
+    {
+      if (!strcmp (field, "Z2"))
+	compute_invariant<Z2> ();
+      else if (!strcmp (field, "Z3"))
+	compute_invariant<Zp<3> > ();
+      else if (!strcmp (field, "Q"))
+	compute_invariant<Q> ();
+      else
+	{
+	  fprintf (stderr, "error: unknown field %s\n", field);
+	  exit (EXIT_FAILURE);
+	}
+    }
+  
+  if (file)
+    fclose (outfp);
+}

knot_diagram.cpp

@@ -626,7 +626,7 @@ knot_diagram::total_linking_number () const
 	assert (is_even (lk));
 	lk /= 2;
 	
-	total_lk += std::abs (lk);
+	total_lk += abs (lk);
       }
   
   return total_lk;

knot_parser/knot_parser.cc

@@ -1,9 +1,8 @@
-/* A Bison parser, made by GNU Bison 2.4.3.  */
+/* A Bison parser, made by GNU Bison 2.6.5.  */
 
 /* Skeleton implementation for Bison LALR(1) parsers in C++
    
-      Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free
+      Copyright (C) 2002-2012 Free Software Foundation, Inc.
-   Software Foundation, Inc.
    
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
@@ -34,37 +33,41 @@
 
 /* First part of user declarations.  */
 
-
+/* Line 278 of lalr1.cc  */
-/* Line 311 of lalr1.cc  */
+#line 38 "knot_parser/knot_parser.cc"
-#line 40 "knot_parser/knot_parser.cc"
 
 
 #include "knot_parser.hh"
 
 /* User implementation prologue.  */
 
-
+/* Line 284 of lalr1.cc  */
-/* Line 317 of lalr1.cc  */
+#line 46 "knot_parser/knot_parser.cc"
-#line 49 "knot_parser/knot_parser.cc"
 /* Unqualified %code blocks.  */
-
+/* Line 285 of lalr1.cc  */
-/* Line 318 of lalr1.cc  */
 #line 15 "knot_parser/knot_parser.yy"
 
 #define YY_DECL \
   yy::knot_parser::token_type knot_yylex (yy::knot_parser::semantic_type *yylval)
 YY_DECL;
 
-
+/* Line 285 of lalr1.cc  */
-/* Line 318 of lalr1.cc  */
 #line 29 "knot_parser/knot_parser.yy"
 
 #define yylex knot_yylex
 
 
+/* Line 285 of lalr1.cc  */
+#line 62 "knot_parser/knot_parser.cc"
 
-/* Line 318 of lalr1.cc  */
+
-#line 68 "knot_parser/knot_parser.cc"
+# ifndef YY_NULL
+#  if defined __cplusplus && 201103L <= __cplusplus
+#   define YY_NULL nullptr
+#  else
+#   define YY_NULL 0
+#  endif
+# endif
 
 #ifndef YY_
 # if defined YYENABLE_NLS && YYENABLE_NLS
@@ -78,6 +81,27 @@ YY_DECL;
 # endif
 #endif
 
+#define YYRHSLOC(Rhs, K) ((Rhs)[K])
+/* YYLLOC_DEFAULT -- Set CURRENT to span from RHS[1] to RHS[N].
+   If N is 0, then set CURRENT to the empty location which ends
+   the previous symbol: RHS[0] (always defined).  */
+
+# ifndef YYLLOC_DEFAULT
+#  define YYLLOC_DEFAULT(Current, Rhs, N)                               \
+    do                                                                  \
+      if (N)                                                            \
+        {                                                               \
+          (Current).begin  = YYRHSLOC (Rhs, 1).begin;                   \
+          (Current).end    = YYRHSLOC (Rhs, N).end;                     \
+        }                                                               \
+      else                                                              \
+        {                                                               \
+          (Current).begin = (Current).end = YYRHSLOC (Rhs, 0).end;      \
+        }                                                               \
+    while (/*CONSTCOND*/ false)
+# endif
+
+
 /* Suppress unused-variable warnings by "using" E.  */
 #define YYUSE(e) ((void) (e))
 
@@ -128,49 +152,8 @@ do {					\
 
 
 namespace yy {
-
+/* Line 352 of lalr1.cc  */
-/* Line 380 of lalr1.cc  */
+#line 157 "knot_parser/knot_parser.cc"
-#line 134 "knot_parser/knot_parser.cc"
-#if YYERROR_VERBOSE
-
-  /* Return YYSTR after stripping away unnecessary quotes and
-     backslashes, so that it's suitable for yyerror.  The heuristic is
-     that double-quoting is unnecessary unless the string contains an
-     apostrophe, a comma, or backslash (other than backslash-backslash).
-     YYSTR is taken from yytname.  */
-  std::string
-  knot_parser::yytnamerr_ (const char *yystr)
-  {
-    if (*yystr == '"')
-      {
-        std::string yyr = "";
-        char const *yyp = yystr;
-
-        for (;;)
-          switch (*++yyp)
-            {
-            case '\'':
-            case ',':
-              goto do_not_strip_quotes;
-
-            case '\\':
-              if (*++yyp != '\\')
-                goto do_not_strip_quotes;
-              /* Fall through.  */
-            default:
-              yyr += *yyp;
-              break;
-
-            case '"':
-              return yyr;
-            }
-      do_not_strip_quotes: ;
-      }
-
-    return yystr;
-  }
-
-#endif
 
   /// Build a parser object.
   knot_parser::knot_parser (knot_diagram &parsed_knot_yyarg)
@@ -198,6 +181,9 @@ namespace yy {
   {
     YYUSE (yylocationp);
     YYUSE (yyvaluep);
+    std::ostream& yyo = debug_stream ();
+    std::ostream& yyoutput = yyo;
+    YYUSE (yyoutput);
     switch (yytype)
       {
          default:
@@ -271,6 +257,18 @@ namespace yy {
   }
 #endif
 
+  inline bool
+  knot_parser::yy_pact_value_is_default_ (int yyvalue)
+  {
+    return yyvalue == yypact_ninf_;
+  }
+
+  inline bool
+  knot_parser::yy_table_value_is_error_ (int yyvalue)
+  {
+    return yyvalue == yytable_ninf_;
+  }
+
   int
   knot_parser::parse ()
   {
@@ -278,17 +276,18 @@ namespace yy {
     int yychar = yyempty_;
     int yytoken = 0;
 
-    /* State.  */
+    // State.
     int yyn;
     int yylen = 0;
     int yystate = 0;
 
-    /* Error handling.  */
+    // Error handling.
     int yynerrs_ = 0;
     int yyerrstatus_ = 0;
 
     /// Semantic value of the lookahead.
-    semantic_type yylval;
+    static semantic_type yyval_default;
+    semantic_type yylval = yyval_default;
     /// Location of the lookahead.
     location_type yylloc;
     /// The locations where the error started and ended.
@@ -330,7 +329,7 @@ namespace yy {
 
     /* Try to take a decision without lookahead.  */
     yyn = yypact_[yystate];
-    if (yyn == yypact_ninf_)
+    if (yy_pact_value_is_default_ (yyn))
       goto yydefault;
 
     /* Read a lookahead token.  */
@@ -340,7 +339,6 @@ namespace yy {
 	yychar = yylex (&yylval);
       }
 
-
     /* Convert token to internal form.  */
     if (yychar <= yyeof_)
       {
@@ -363,8 +361,8 @@ namespace yy {
     yyn = yytable_[yyn];
     if (yyn <= 0)
       {
-	if (yyn == 0 || yyn == yytable_ninf_)
+	if (yy_table_value_is_error_ (yyn))
-	goto yyerrlab;
+	  goto yyerrlab;
 	yyn = -yyn;
 	goto yyreduce;
       }
@@ -419,8 +417,7 @@ namespace yy {
     switch (yyn)
       {
 	  case 10:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 67 "knot_parser/knot_parser.yy"
     { 
 	unsigned n = (yysemantic_stack_[(3) - (1)].integer),
@@ -439,8 +436,7 @@ namespace yy {
     break;
 
   case 11:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 85 "knot_parser/knot_parser.yy"
     {
 	unsigned n = (yysemantic_stack_[(3) - (1)].integer),
@@ -460,8 +456,7 @@ namespace yy {
     break;
 
   case 12:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 104 "knot_parser/knot_parser.yy"
     {
 	unsigned n = (yysemantic_stack_[(4) - (2)].integer),
@@ -481,22 +476,19 @@ namespace yy {
     break;
 
   case 13:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 123 "knot_parser/knot_parser.yy"
     { parsed_knot = knot_diagram (planar_diagram ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
     break;
 
   case 14:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 125 "knot_parser/knot_parser.yy"
     { parsed_knot = knot_diagram (planar_diagram ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
     break;
 
   case 15:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 130 "knot_parser/knot_parser.yy"
     {
 	basedvector<basedvector<int, 1>, 1> even_labels (1);
@@ -506,36 +498,31 @@ namespace yy {
     break;
 
   case 16:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 136 "knot_parser/knot_parser.yy"
     { parsed_knot = knot_diagram (dt_code ("<parsed>", *(yysemantic_stack_[(4) - (3)].int_vec2))); }
     break;
 
   case 17:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 138 "knot_parser/knot_parser.yy"
     { parsed_knot = knot_diagram (dt_code ("<parsed>", (yysemantic_stack_[(4) - (3)].string))); }
     break;
 
   case 18:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 143 "knot_parser/knot_parser.yy"
     { parsed_knot = knot_diagram (torus_knot ((yysemantic_stack_[(6) - (3)].integer), (yysemantic_stack_[(6) - (5)].integer))); }
     break;
 
   case 19:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 148 "knot_parser/knot_parser.yy"
     { parsed_knot = knot_diagram (braid ((yysemantic_stack_[(6) - (3)].integer), *(yysemantic_stack_[(6) - (5)].int_vec))); }
     break;
 
   case 20:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 153 "knot_parser/knot_parser.yy"
     {
 	unsigned unknot_ar[1][4] = {
@@ -546,8 +533,7 @@ namespace yy {
     break;
 
   case 23:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 168 "knot_parser/knot_parser.yy"
     {
 	basedvector<basedvector<int, 1>, 1> *v
@@ -558,8 +544,7 @@ namespace yy {
     break;
 
   case 24:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 175 "knot_parser/knot_parser.yy"
     { 
 	basedvector<basedvector<int, 1>, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec2);
@@ -569,22 +554,19 @@ namespace yy {
     break;
 
   case 25:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 184 "knot_parser/knot_parser.yy"
     { (yyval.int_vec) = (yysemantic_stack_[(3) - (2)].int_vec); }
     break;
 
   case 26:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 186 "knot_parser/knot_parser.yy"
     { (yyval.int_vec) = (yysemantic_stack_[(3) - (2)].int_vec); }
     break;
 
   case 27:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 191 "knot_parser/knot_parser.yy"
     {
 	basedvector<int, 1> *v =
@@ -595,8 +577,7 @@ namespace yy {
     break;
 
   case 28:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 198 "knot_parser/knot_parser.yy"
     {
 	basedvector<int, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec);
@@ -606,8 +587,7 @@ namespace yy {
     break;
 
   case 29:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 207 "knot_parser/knot_parser.yy"
     {
 	basedvector<basedvector<int, 1>, 1> *v
@@ -618,8 +598,7 @@ namespace yy {
     break;
 
   case 30:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 214 "knot_parser/knot_parser.yy"
     { 
 	basedvector<basedvector<int, 1>, 1> *v = (yysemantic_stack_[(3) - (1)].int_vec2);
@@ -629,8 +608,7 @@ namespace yy {
     break;
 
   case 31:
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
 #line 223 "knot_parser/knot_parser.yy"
     {
 	basedvector<int, 1> *v
@@ -644,12 +622,22 @@ namespace yy {
     break;
 
 
-
+/* Line 661 of lalr1.cc  */
-/* Line 678 of lalr1.cc  */
+#line 627 "knot_parser/knot_parser.cc"
-#line 650 "knot_parser/knot_parser.cc"
 	default:
           break;
       }
+    /* User semantic actions sometimes alter yychar, and that requires
+       that yytoken be updated with the new translation.  We take the
+       approach of translating immediately before every use of yytoken.
+       One alternative is translating here after every semantic action,
+       but that translation would be missed if the semantic action
+       invokes YYABORT, YYACCEPT, or YYERROR immediately after altering
+       yychar.  In the case of YYABORT or YYACCEPT, an incorrect
+       destructor might then be invoked immediately.  In the case of
+       YYERROR, subsequent parser actions might lead to an incorrect
+       destructor call or verbose syntax error message before the
+       lookahead is translated.  */
     YY_SYMBOL_PRINT ("-> $$ =", yyr1_[yyn], &yyval, &yyloc);
 
     yypop_ (yylen);
@@ -673,11 +661,17 @@ namespace yy {
   | yyerrlab -- here on detecting error |
   `------------------------------------*/
   yyerrlab:
+    /* Make sure we have latest lookahead translation.  See comments at
+       user semantic actions for why this is necessary.  */
+    yytoken = yytranslate_ (yychar);
+
     /* If not already recovering from an error, report this error.  */
     if (!yyerrstatus_)
       {
 	++yynerrs_;
-	error (yylloc, yysyntax_error_ (yystate));
+	if (yychar == yyempty_)
+	  yytoken = yyempty_;
+	error (yylloc, yysyntax_error_ (yystate, yytoken));
       }
 
     yyerror_range[1] = yylloc;
@@ -732,7 +726,7 @@ namespace yy {
     for (;;)
       {
 	yyn = yypact_[yystate];
-	if (yyn != yypact_ninf_)
+	if (!yy_pact_value_is_default_ (yyn))
 	{
 	  yyn += yyterror_;
 	  if (0 <= yyn && yyn <= yylast_ && yycheck_[yyn] == yyterror_)
@@ -782,7 +776,13 @@ namespace yy {
 
   yyreturn:
     if (yychar != yyempty_)
-      yydestruct_ ("Cleanup: discarding lookahead", yytoken, &yylval, &yylloc);
+      {
+        /* Make sure we have latest lookahead translation.  See comments
+           at user semantic actions for why this is necessary.  */
+        yytoken = yytranslate_ (yychar);
+        yydestruct_ ("Cleanup: discarding lookahead", yytoken, &yylval,
+                     &yylloc);
+      }
 
     /* Do not reclaim the symbols of the rule which action triggered
        this YYABORT or YYACCEPT.  */
@@ -801,51 +801,9 @@ namespace yy {
 
   // Generate an error message.
   std::string
-  knot_parser::yysyntax_error_ (int yystate)
+  knot_parser::yysyntax_error_ (int, int)
   {
-    std::string res;
+    return YY_("syntax error");
-    YYUSE (yystate);
-#if YYERROR_VERBOSE
-    int yyn = yypact_[yystate];
-    if (yypact_ninf_ < yyn && yyn <= yylast_)
-      {
-	/* Start YYX at -YYN if negative to avoid negative indexes in
-	   YYCHECK.  */
-	int yyxbegin = yyn < 0 ? -yyn : 0;
-
-	/* Stay within bounds of both yycheck and yytname.  */
-	int yychecklim = yylast_ - yyn + 1;
-	int yyxend = yychecklim < yyntokens_ ? yychecklim : yyntokens_;
-	int count = 0;
-	for (int x = yyxbegin; x < yyxend; ++x)
-	  if (yycheck_[x + yyn] == x && x != yyterror_)
-	    ++count;
-
-	// FIXME: This method of building the message is not compatible
-	// with internationalization.  It should work like yacc.c does it.
-	// That is, first build a string that looks like this:
-	// "syntax error, unexpected %s or %s or %s"
-	// Then, invoke YY_ on this string.
-	// Finally, use the string as a format to output
-	// yytname_[tok], etc.
-	// Until this gets fixed, this message appears in English only.
-	res = "syntax error, unexpected ";
-	res += yytnamerr_ (yytname_[tok]);
-	if (count < 5)
-	  {
-	    count = 0;
-	    for (int x = yyxbegin; x < yyxend; ++x)
-	      if (yycheck_[x + yyn] == x && x != yyterror_)
-		{
-		  res += (!count++) ? ", expecting " : " or ";
-		  res += yytnamerr_ (yytname_[x]);
-		}
-	  }
-      }
-    else
-#endif
-      res = YY_("syntax error");
-    return res;
   }
 
 
@@ -865,9 +823,9 @@ namespace yy {
       54,    58,    59,   -36
   };
 
-  /* YYDEFACT[S] -- default rule to reduce with in state S when YYTABLE
+  /* YYDEFACT[S] -- default reduction number in state S.  Performed when
-     doesn't specify something else to do.  Zero means the default is an
+     YYTABLE doesn't specify something else to do.  Zero means the
-     error.  */
+     default is an error.  */
   const unsigned char
   knot_parser::yydefact_[] =
   {
@@ -899,7 +857,7 @@ namespace yy {
 
   /* YYTABLE[YYPACT[STATE-NUM]].  What to do in state STATE-NUM.  If
      positive, shift that token.  If negative, reduce the rule which
-     number is the opposite.  If zero, do what YYDEFACT says.  */
+     number is the opposite.  If YYTABLE_NINF_, syntax error.  */
   const signed char knot_parser::yytable_ninf_ = -1;
   const unsigned char
   knot_parser::yytable_[] =
@@ -975,7 +933,7 @@ namespace yy {
        3,    10
   };
 
-#if YYDEBUG || YYERROR_VERBOSE || YYTOKEN_TABLE
+#if YYDEBUG
   /* YYTNAME[SYMBOL-NUM] -- String name of the symbol SYMBOL-NUM.
      First, the terminals, then, starting at \a yyntokens_, nonterminals.  */
   const char*
@@ -986,11 +944,10 @@ namespace yy {
   "']'", "'('", "','", "')'", "'{'", "'}'", "$accept", "knot",
   "rolfsen_knot", "htw_knot", "mt_link", "planar_diagram", "dt",
   "torus_link", "braid", "unknot", "alt_spec", "int_vec2", "int_vec",
-  "int_vec_1", "crossing_vec", "crossing", 0
+  "int_vec_1", "crossing_vec", "crossing", YY_NULL
   };
-#endif
 
-#if YYDEBUG
+
   /* YYRHS -- A `-1'-separated list of the rules' RHS.  */
   const knot_parser::rhs_number_type
   knot_parser::yyrhs_[] =
@@ -1115,12 +1072,9 @@ namespace yy {
 
 
 } // yy
-
+/* Line 1106 of lalr1.cc  */
-/* Line 1054 of lalr1.cc  */
+#line 1077 "knot_parser/knot_parser.cc"
-#line 1121 "knot_parser/knot_parser.cc"
+/* Line 1107 of lalr1.cc  */
-
-
-/* Line 1056 of lalr1.cc  */
 #line 233 "knot_parser/knot_parser.yy"
 
 
@@ -1145,4 +1099,3 @@ parse_knot (const char *s)
   
   return d;
 }
-

knot_parser/knot_parser.hh

@@ -1,9 +1,8 @@
-/* A Bison parser, made by GNU Bison 2.4.3.  */
+/* A Bison parser, made by GNU Bison 2.6.5.  */
 
 /* Skeleton interface for Bison LALR(1) parsers in C++
    
-      Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free
+      Copyright (C) 2002-2012 Free Software Foundation, Inc.
-   Software Foundation, Inc.
    
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
@@ -31,41 +30,30 @@
    This special exception was added by the Free Software Foundation in
    version 2.2 of Bison.  */
 
+/**
+ ** \file knot_parser/knot_parser.hh
+ ** Define the yy::parser class.
+ */
+
 /* C++ LALR(1) parser skeleton written by Akim Demaille.  */
 
-#ifndef PARSER_HEADER_H
+#ifndef YY_YY_KNOT_PARSER_KNOT_PARSER_HH_INCLUDED
-# define PARSER_HEADER_H
+# define YY_YY_KNOT_PARSER_KNOT_PARSER_HH_INCLUDED
 
 /* "%code requires" blocks.  */
-
+/* Line 36 of lalr1.cc  */
-/* Line 35 of lalr1.cc  */
 #line 11 "knot_parser/knot_parser.yy"
 
 #include <knotkit.h>
 
 
-
+/* Line 36 of lalr1.cc  */
-/* Line 35 of lalr1.cc  */
+#line 52 "knot_parser/knot_parser.hh"
-#line 50 "knot_parser/knot_parser.hh"
 
 
 #include <string>
 #include <iostream>
 #include "stack.hh"
-
-
-namespace yy {
-
-/* Line 35 of lalr1.cc  */
-#line 61 "knot_parser/knot_parser.hh"
-  class position;
-  class location;
-
-} // yy
-
-/* Line 35 of lalr1.cc  */
-#line 68 "knot_parser/knot_parser.hh"
-
 #include "location.hh"
 
 /* Enabling traces.  */
@@ -73,43 +61,10 @@ namespace yy {
 # define YYDEBUG 0
 #endif
 
-/* Enabling verbose error messages.  */
-#ifdef YYERROR_VERBOSE
-# undef YYERROR_VERBOSE
-# define YYERROR_VERBOSE 1
-#else
-# define YYERROR_VERBOSE 0
-#endif
-
-/* Enabling the token table.  */
-#ifndef YYTOKEN_TABLE
-# define YYTOKEN_TABLE 0
-#endif
-
-/* YYLLOC_DEFAULT -- Set CURRENT to span from RHS[1] to RHS[N].
-   If N is 0, then set CURRENT to the empty location which ends
-   the previous symbol: RHS[0] (always defined).  */
-
-#ifndef YYLLOC_DEFAULT
-# define YYLLOC_DEFAULT(Current, Rhs, N)		\
-do {							\
-  if (N)						\
-    {							\
-      (Current).begin = (Rhs)[1].begin;			\
-      (Current).end   = (Rhs)[N].end;			\
-    }							\
-  else							\
-    {							\
-      (Current).begin = (Current).end = (Rhs)[0].end;	\
-    }							\
-} while (false)
-#endif
-
 
 namespace yy {
-
+/* Line 36 of lalr1.cc  */
-/* Line 35 of lalr1.cc  */
+#line 68 "knot_parser/knot_parser.hh"
-#line 113 "knot_parser/knot_parser.hh"
 
   /// A Bison parser.
   class knot_parser
@@ -119,8 +74,7 @@ namespace yy {
 #ifndef YYSTYPE
     union semantic_type
     {
-
+/* Line 36 of lalr1.cc  */
-/* Line 35 of lalr1.cc  */
 #line 21 "knot_parser/knot_parser.yy"
 
   int integer;
@@ -130,9 +84,8 @@ namespace yy {
   const char *string;
 
 
-
+/* Line 36 of lalr1.cc  */
-/* Line 35 of lalr1.cc  */
+#line 89 "knot_parser/knot_parser.hh"
-#line 136 "knot_parser/knot_parser.hh"
     };
 #else
     typedef YYSTYPE semantic_type;
@@ -194,7 +147,7 @@ namespace yy {
     /// Generate an error message.
     /// \param state   the state where the error occurred.
     /// \param tok     the lookahead token.
-    virtual std::string yysyntax_error_ (int yystate);
+    virtual std::string yysyntax_error_ (int yystate, int tok);
 
 #if YYDEBUG
     /// \brief Report a symbol value on the debug stream.
@@ -230,6 +183,14 @@ namespace yy {
     /// The location stack.
     location_stack_type yylocation_stack_;
 
+    /// Whether the given \c yypact_ value indicates a defaulted state.
+    /// \param yyvalue   the value to check
+    static bool yy_pact_value_is_default_ (int yyvalue);
+
+    /// Whether the given \c yytable_ value indicates a syntax error.
+    /// \param yyvalue   the value to check
+    static bool yy_table_value_is_error_ (int yyvalue);
+
     /// Internal symbol numbers.
     typedef unsigned char token_number_type;
     /* Tables.  */
@@ -237,7 +198,7 @@ namespace yy {
     static const signed char yypact_[];
     static const signed char yypact_ninf_;
 
-    /// For a state, default rule to reduce.
+    /// For a state, default reduction number.
     /// Unless\a  yytable_ specifies something else to do.
     /// Zero means the default is an error.
     static const unsigned char yydefact_[];
@@ -263,17 +224,10 @@ namespace yy {
     /// For a rule, its RHS length.
     static const unsigned char yyr2_[]; 
 
-#if YYDEBUG || YYERROR_VERBOSE || YYTOKEN_TABLE
+#if YYDEBUG
     /// For a symbol, its name in clear.
     static const char* const yytname_[];
-#endif
 
-#if YYERROR_VERBOSE
-    /// Convert the symbol name \a n to a form suitable for a diagnostic.
-    virtual std::string yytnamerr_ (const char *n);
-#endif
-
-#if YYDEBUG
     /// A type to store symbol numbers and -1.
     typedef signed char rhs_number_type;
     /// A `-1'-separated list of the rules' RHS.
@@ -328,10 +282,9 @@ namespace yy {
   };
 
 } // yy
-
+/* Line 36 of lalr1.cc  */
-/* Line 35 of lalr1.cc  */
+#line 287 "knot_parser/knot_parser.hh"
-#line 334 "knot_parser/knot_parser.hh"
 
 
 
-#endif /* ! defined PARSER_HEADER_H */
+#endif /* !YY_YY_KNOT_PARSER_KNOT_PARSER_HH_INCLUDED  */

knot_parser/location.hh

@@ -1,9 +1,8 @@
-/* A Bison parser, made by GNU Bison 2.4.3.  */
+/* A Bison parser, made by GNU Bison 2.6.5.  */
 
 /* Locations for Bison parsers in C++
    
-      Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2009, 2010 Free Software
+      Copyright (C) 2002-2007, 2009-2012 Free Software Foundation, Inc.
-   Foundation, Inc.
    
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
@@ -32,39 +31,55 @@
    version 2.2 of Bison.  */
 
 /**
- ** \file location.hh
+ ** \file knot_parser/location.hh
  ** Define the yy::location class.
  */
 
-#ifndef BISON_LOCATION_HH
+#ifndef YY_YY_KNOT_PARSER_LOCATION_HH_INCLUDED
-# define BISON_LOCATION_HH
+# define YY_YY_KNOT_PARSER_LOCATION_HH_INCLUDED
 
-# include <iostream>
-# include <string>
 # include "position.hh"
 
 
 namespace yy {
-
+/* Line 164 of location.cc  */
-/* Line 163 of location.cc  */
+#line 47 "knot_parser/location.hh"
-#line 51 "knot_parser/location.hh"
 
   /// Abstract a location.
   class location
   {
   public:
 
-    /// Construct a location.
+    /// Construct a location from \a b to \a e.
-    location ()
+    location (const position& b, const position& e)
-      : begin (), end ()
+      : begin (b)
+      , end (e)
+    {
+    }
+
+    /// Construct a 0-width location in \a p.
+    explicit location (const position& p = position ())
+      : begin (p)
+      , end (p)
+    {
+    }
+
+    /// Construct a 0-width location in \a f, \a l, \a c.
+    explicit location (std::string* f,
+                       unsigned int l = 1u,
+                       unsigned int c = 1u)
+      : begin (f, l, c)
+      , end (f, l, c)
     {
     }
 
 
     /// Initialization.
-    inline void initialize (std::string* fn)
+    void initialize (std::string* f = YY_NULL,
+                     unsigned int l = 1u,
+                     unsigned int c = 1u)
     {
-      begin.initialize (fn);
+      begin.initialize (f, l, c);
       end = begin;
     }
 
@@ -72,19 +87,19 @@ namespace yy {
      ** \{ */
   public:
     /// Reset initial location to final location.
-    inline void step ()
+    void step ()
     {
       begin = end;
     }
 
     /// Extend the current location to the COUNT next columns.
-    inline void columns (unsigned int count = 1)
+    void columns (unsigned int count = 1)
     {
       end += count;
     }
 
     /// Extend the current location to the COUNT next lines.
-    inline void lines (unsigned int count = 1)
+    void lines (unsigned int count = 1)
     {
       end.lines (count);
     }
@@ -158,8 +173,7 @@ namespace yy {
 
 
 } // yy
+/* Line 292 of location.cc  */
+#line 178 "knot_parser/location.hh"
 
-/* Line 272 of location.cc  */
+#endif /* !YY_YY_KNOT_PARSER_LOCATION_HH_INCLUDED  */
-#line 164 "knot_parser/location.hh"
-
-#endif // not BISON_LOCATION_HH

knot_parser/position.hh

@@ -1,9 +1,8 @@
-/* A Bison parser, made by GNU Bison 2.4.3.  */
+/* A Bison parser, made by GNU Bison 2.6.5.  */
 
 /* Positions for Bison parsers in C++
    
-      Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2009, 2010 Free Software
+      Copyright (C) 2002-2007, 2009-2012 Free Software Foundation, Inc.
-   Foundation, Inc.
    
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
@@ -32,60 +31,71 @@
    version 2.2 of Bison.  */
 
 /**
- ** \file position.hh
+ ** \file knot_parser/position.hh
  ** Define the yy::position class.
  */
 
-#ifndef BISON_POSITION_HH
+#ifndef YY_YY_KNOT_PARSER_POSITION_HH_INCLUDED
-# define BISON_POSITION_HH
+# define YY_YY_KNOT_PARSER_POSITION_HH_INCLUDED
 
+# include <algorithm> // std::max
 # include <iostream>
 # include <string>
-# include <algorithm>
+
+# ifndef YY_NULL
+#  if defined __cplusplus && 201103L <= __cplusplus
+#   define YY_NULL nullptr
+#  else
+#   define YY_NULL 0
+#  endif
+# endif
 
 
 namespace yy {
-
 /* Line 38 of location.cc  */
-#line 51 "knot_parser/position.hh"
+#line 57 "knot_parser/position.hh"
   /// Abstract a position.
   class position
   {
   public:
 
     /// Construct a position.
-    position ()
+    explicit position (std::string* f = YY_NULL,
-      : filename (0), line (1), column (1)
+                       unsigned int l = 1u,
+                       unsigned int c = 1u)
+      : filename (f)
+      , line (l)
+      , column (c)
     {
     }
 
 
     /// Initialization.
-    inline void initialize (std::string* fn)
+    void initialize (std::string* fn = YY_NULL,
+                     unsigned int l = 1u,
+                     unsigned int c = 1u)
     {
       filename = fn;
-      line = 1;
+      line = l;
-      column = 1;
+      column = c;
     }
 
     /** \name Line and Column related manipulators
      ** \{ */
-  public:
     /// (line related) Advance to the COUNT next lines.
-    inline void lines (int count = 1)
+    void lines (int count = 1)
     {
-      column = 1;
+      column = 1u;
       line += count;
     }
 
     /// (column related) Advance to the COUNT next columns.
-    inline void columns (int count = 1)
+    void columns (int count = 1)
     {
       column = std::max (1u, column + count);
     }
     /** \} */
 
-  public:
     /// File name to which this position refers.
     std::string* filename;
     /// Current line number.
@@ -95,7 +105,7 @@ namespace yy {
   };
 
   /// Add and assign a position.
-  inline const position&
+  inline position&
   operator+= (position& res, const int width)
   {
     res.columns (width);
@@ -111,7 +121,7 @@ namespace yy {
   }
 
   /// Add and assign a position.
-  inline const position&
+  inline position&
   operator-= (position& res, const int width)
   {
     return res += -width;
@@ -156,7 +166,6 @@ namespace yy {
 
 
 } // yy
-
+/* Line 149 of location.cc  */
-/* Line 145 of location.cc  */
+#line 171 "knot_parser/position.hh"
-#line 162 "knot_parser/position.hh"
+#endif /* !YY_YY_KNOT_PARSER_POSITION_HH_INCLUDED  */
-#endif // not BISON_POSITION_HH

knot_parser/stack.hh

@@ -1,9 +1,8 @@
-/* A Bison parser, made by GNU Bison 2.4.3.  */
+/* A Bison parser, made by GNU Bison 2.6.5.  */
 
 /* Stack handling for Bison parsers in C++
    
-      Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free
+      Copyright (C) 2002-2012 Free Software Foundation, Inc.
-   Software Foundation, Inc.
    
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
@@ -31,21 +30,24 @@
    This special exception was added by the Free Software Foundation in
    version 2.2 of Bison.  */
 
-#ifndef BISON_STACK_HH
+/**
-# define BISON_STACK_HH
+ ** \file knot_parser/stack.hh
+ ** Define the yy::stack class.
+ */
 
-#include <deque>
+#ifndef YY_YY_KNOT_PARSER_STACK_HH_INCLUDED
+# define YY_YY_KNOT_PARSER_STACK_HH_INCLUDED
+
+# include <deque>
 
 
 namespace yy {
-
+/* Line 37 of stack.hh  */
-/* Line 1067 of lalr1.cc  */
+#line 47 "knot_parser/stack.hh"
-#line 44 "knot_parser/stack.hh"
   template <class T, class S = std::deque<T> >
   class stack
   {
   public:
-
     // Hide our reversed order.
     typedef typename S::reverse_iterator iterator;
     typedef typename S::const_reverse_iterator const_iterator;
@@ -84,7 +86,7 @@ namespace yy {
     pop (unsigned int n = 1)
     {
       for (; n; --n)
-	seq_.pop_front ();
+        seq_.pop_front ();
     }
 
     inline
@@ -98,7 +100,6 @@ namespace yy {
     inline const_iterator end () const { return seq_.rend (); }
 
   private:
-
     S seq_;
   };
 
@@ -107,10 +108,9 @@ namespace yy {
   class slice
   {
   public:
-
+    slice (const S& stack, unsigned int range)
-    slice (const S& stack,
+      : stack_ (stack)
-	   unsigned int range) : stack_ (stack),
+      , range_ (range)
-				 range_ (range)
     {
     }
 
@@ -122,15 +122,12 @@ namespace yy {
     }
 
   private:
-
     const S& stack_;
     unsigned int range_;
   };
 
 } // yy
+/* Line 119 of stack.hh  */
+#line 132 "knot_parser/stack.hh"
 
-/* Line 1153 of lalr1.cc  */
+#endif /* !YY_YY_KNOT_PARSER_STACK_HH_INCLUDED  */
-#line 134 "knot_parser/stack.hh"
-
-#endif // not BISON_STACK_HH[]dnl
-

knot_tables.cpp

@@ -1,8 +1,6 @@
 
 #include <knotkit.h>
 
-#define HOME "/Users/cotton/src/knotkit/"
-
 bool verbose = 0;
 
 static const struct {
@@ -402,7 +400,7 @@ htw_knot (unsigned n, bool alternating, unsigned k)
 	before += htw_alternating[i];
       off = 8 * (before + k - 1);
       
-      file = HOME "alternating";
+      file = HOME "/alternating";
     }
   else
     {
@@ -411,7 +409,7 @@ htw_knot (unsigned n, bool alternating, unsigned k)
 	before += htw_nonalternating[i];
       off = 10 * (before + k - 1);
       
-      file = HOME "nonalternating";
+      file = HOME "/nonalternating";
     }
   FILE *fp = fopen (file, "r");
   if (fp == 0)
@@ -514,7 +512,7 @@ mt_link (unsigned n, bool alternating, unsigned k)
   
   char buf[1000];
   
-  sprintf (buf, HOME "mtlinks/hyperbolic_data_%02d%c", n, alternating ? 'a' : 'n');
+  sprintf (buf, HOME "/mtlinks/hyperbolic_data_%02d%c", n, alternating ? 'a' : 'n');
   FILE *fp = fopen (buf, "r");
   if (fp == 0)
     {
@@ -717,7 +715,7 @@ mutant_knot_groups (unsigned n)
   assert (11 <= n && n <= 15);
   
   char buf[1000];
-  sprintf (buf, HOME "mutant_knot_groups/dat%d", n);
+  sprintf (buf, HOME "/mutant_knot_groups/dat%d", n);
   
   FILE *fp = fopen (buf, "r");
   if (fp == 0)

main.cpp

@@ -1282,7 +1282,9 @@ compute_forgetfulss (knot_diagram &kd,
 	break;
     }
 
-  return sseq (bounds, pages);
+  abort ();
+  // ???
+  return sseq (bounds, grading (0, 0), grading (0, 0), pages);
 }
 
 void

rd_parser/rd_scanner.cc

@@ -66,6 +66,7 @@ typedef int16_t flex_int16_t;
 typedef uint16_t flex_uint16_t;
 typedef int32_t flex_int32_t;
 typedef uint32_t flex_uint32_t;
+typedef uint64_t flex_uint64_t;
 #else
 typedef signed char flex_int8_t;
 typedef short int flex_int16_t;
@@ -172,7 +173,12 @@ typedef unsigned int flex_uint32_t;
 typedef struct yy_buffer_state *YY_BUFFER_STATE;
 #endif
 
-extern int rd_yyleng;
+#ifndef YY_TYPEDEF_YY_SIZE_T
+#define YY_TYPEDEF_YY_SIZE_T
+typedef size_t yy_size_t;
+#endif
+
+extern yy_size_t rd_yyleng;
 
 extern FILE *rd_yyin, *rd_yyout;
 
@@ -198,11 +204,6 @@ extern FILE *rd_yyin, *rd_yyout;
 
 #define unput(c) yyunput( c, (yytext_ptr)  )
 
-#ifndef YY_TYPEDEF_YY_SIZE_T
-#define YY_TYPEDEF_YY_SIZE_T
-typedef size_t yy_size_t;
-#endif
-
 #ifndef YY_STRUCT_YY_BUFFER_STATE
 #define YY_STRUCT_YY_BUFFER_STATE
 struct yy_buffer_state
@@ -220,7 +221,7 @@ struct yy_buffer_state
 	/* Number of characters read into yy_ch_buf, not including EOB
 	 * characters.
 	 */
-	int yy_n_chars;
+	yy_size_t yy_n_chars;
 
 	/* Whether we "own" the buffer - i.e., we know we created it,
 	 * and can realloc() it to grow it, and should free() it to
@@ -290,8 +291,8 @@ static YY_BUFFER_STATE * yy_buffer_stack = 0; /**< Stack as an array. */
 
 /* yy_hold_char holds the character lost when rd_yytext is formed. */
 static char yy_hold_char;
-static int yy_n_chars;		/* number of characters read into yy_ch_buf */
+static yy_size_t yy_n_chars;		/* number of characters read into yy_ch_buf */
-int rd_yyleng;
+yy_size_t rd_yyleng;
 
 /* Points to current character in buffer. */
 static char *yy_c_buf_p = (char *) 0;
@@ -319,7 +320,7 @@ static void rd_yy_init_buffer (YY_BUFFER_STATE b,FILE *file  );
 
 YY_BUFFER_STATE rd_yy_scan_buffer (char *base,yy_size_t size  );
 YY_BUFFER_STATE rd_yy_scan_string (yyconst char *yy_str  );
-YY_BUFFER_STATE rd_yy_scan_bytes (yyconst char *bytes,int len  );
+YY_BUFFER_STATE rd_yy_scan_bytes (yyconst char *bytes,yy_size_t len  );
 
 void *rd_yyalloc (yy_size_t  );
 void *rd_yyrealloc (void *,yy_size_t  );
@@ -377,7 +378,7 @@ static void yy_fatal_error (yyconst char msg[]  );
  */
 #define YY_DO_BEFORE_ACTION \
 	(yytext_ptr) = yy_bp; \
-	rd_yyleng = (size_t) (yy_cp - yy_bp); \
+	rd_yyleng = (yy_size_t) (yy_cp - yy_bp); \
 	(yy_hold_char) = *yy_cp; \
 	*yy_cp = '\0'; \
 	(yy_c_buf_p) = yy_cp;
@@ -483,7 +484,7 @@ char *rd_yytext;
 
 typedef yy::rd_parser::token token;
 typedef yy::rd_parser::token_type token_type;
-#line 487 "rd_parser/rd_scanner.cc"
+#line 488 "rd_parser/rd_scanner.cc"
 
 #define INITIAL 0
 
@@ -522,7 +523,7 @@ FILE *rd_yyget_out (void );
 
 void rd_yyset_out  (FILE * out_str  );
 
-int rd_yyget_leng (void );
+yy_size_t rd_yyget_leng (void );
 
 char *rd_yyget_text (void );
 
@@ -581,7 +582,7 @@ static int input (void );
 	if ( YY_CURRENT_BUFFER_LVALUE->yy_is_interactive ) \
 		{ \
 		int c = '*'; \
-		int n; \
+		yy_size_t n; \
 		for ( n = 0; n < max_size && \
 			     (c = getc( rd_yyin )) != EOF && c != '\n'; ++n ) \
 			buf[n] = (char) c; \
@@ -666,7 +667,7 @@ YY_DECL
 #line 16 "rd_parser/rd_scanner.ll"
 
 
-#line 670 "rd_parser/rd_scanner.cc"
+#line 671 "rd_parser/rd_scanner.cc"
 
 	if ( !(yy_init) )
 		{
@@ -794,7 +795,7 @@ YY_RULE_SETUP
 #line 49 "rd_parser/rd_scanner.ll"
 ECHO;
 	YY_BREAK
-#line 798 "rd_parser/rd_scanner.cc"
+#line 799 "rd_parser/rd_scanner.cc"
 case YY_STATE_EOF(INITIAL):
 	yyterminate();
 
@@ -981,7 +982,7 @@ static int yy_get_next_buffer (void)
 
 	else
 		{
-			int num_to_read =
+			yy_size_t num_to_read =
 			YY_CURRENT_BUFFER_LVALUE->yy_buf_size - number_to_move - 1;
 
 		while ( num_to_read <= 0 )
@@ -995,7 +996,7 @@ static int yy_get_next_buffer (void)
 
 			if ( b->yy_is_our_buffer )
 				{
-				int new_size = b->yy_buf_size * 2;
+				yy_size_t new_size = b->yy_buf_size * 2;
 
 				if ( new_size <= 0 )
 					b->yy_buf_size += b->yy_buf_size / 8;
@@ -1026,7 +1027,7 @@ static int yy_get_next_buffer (void)
 
 		/* Read in more data. */
 		YY_INPUT( (&YY_CURRENT_BUFFER_LVALUE->yy_ch_buf[number_to_move]),
-			(yy_n_chars), (size_t) num_to_read );
+			(yy_n_chars), num_to_read );
 
 		YY_CURRENT_BUFFER_LVALUE->yy_n_chars = (yy_n_chars);
 		}
@@ -1148,7 +1149,7 @@ static int yy_get_next_buffer (void)
 
 		else
 			{ /* need more input */
-			int offset = (yy_c_buf_p) - (yytext_ptr);
+			yy_size_t offset = (yy_c_buf_p) - (yytext_ptr);
 			++(yy_c_buf_p);
 
 			switch ( yy_get_next_buffer(  ) )
@@ -1172,7 +1173,7 @@ static int yy_get_next_buffer (void)
 				case EOB_ACT_END_OF_FILE:
 					{
 					if ( rd_yywrap( ) )
-						return EOF;
+						return 0;
 
 					if ( ! (yy_did_buffer_switch_on_eof) )
 						YY_NEW_FILE;
@@ -1424,7 +1425,7 @@ void rd_yypop_buffer_state (void)
  */
 static void rd_yyensure_buffer_stack (void)
 {
-	int num_to_alloc;
+	yy_size_t num_to_alloc;
     
 	if (!(yy_buffer_stack)) {
 
@@ -1521,12 +1522,11 @@ YY_BUFFER_STATE rd_yy_scan_string (yyconst char * yystr )
  * 
  * @return the newly allocated buffer state object.
  */
-YY_BUFFER_STATE rd_yy_scan_bytes  (yyconst char * yybytes, int  _yybytes_len )
+YY_BUFFER_STATE rd_yy_scan_bytes  (yyconst char * yybytes, yy_size_t  _yybytes_len )
 {
 	YY_BUFFER_STATE b;
 	char *buf;
-	yy_size_t n;
+	yy_size_t n, i;
-	int i;
     
 	/* Get memory for full buffer, including space for trailing EOB's. */
 	n = _yybytes_len + 2;
@@ -1608,7 +1608,7 @@ FILE *rd_yyget_out  (void)
 /** Get the length of the current token.
  * 
  */
-int rd_yyget_leng  (void)
+yy_size_t rd_yyget_leng  (void)
 {
         return rd_yyleng;
 }

simplify_chain_complex.h

@@ -63,8 +63,7 @@ class chain_complex_simplifier
  public:
   chain_complex_simplifier (ptr<const module<R> > C_,
 			    const mod_map<R> &d_,
-			    int dq);
+			    maybe<int> dh, maybe<int> dq);
-  
 };
 
 template<class R> void
@@ -145,7 +144,7 @@ chain_complex_simplifier<R>::cancel (unsigned i, R b, unsigned j)
 template<class R>
 chain_complex_simplifier<R>::chain_complex_simplifier (ptr<const module<R> > C_,
 						       const mod_map<R> &d_,
-						       int dq)
+						       maybe<int> dh, maybe<int> dq)
   : C(C_), n(C_->dim ()), d(d_),
     new_d_columns(n),
     preim(n),
@@ -173,8 +172,10 @@ chain_complex_simplifier<R>::chain_complex_simplifier (ptr<const module<R> > C_,
 	{
 	  grading jgr = C->generator_grading (j.key ());
 	  if (j.val ().is_unit ()
-	      && jgr.q - igr.q == dq
+	      && (dh.is_none ()
-	      )
+		  || (jgr.h - igr.h == dh.some ()))
+	      && (dq.is_none ()
+		  || (jgr.q - igr.q == dq.some ())))
 	    {
 	      cancel (i, j.val (), j.key ());
 	      break;

sseq.cpp

@@ -2,7 +2,8 @@
 #include <knotkit.h>
 
 sseq_page::sseq_page (const sseq_bounds &b)
-  : rank(b.width ()),
+  : k(0),
+    rank(b.width ()),
     im_rank(b.width ())
 {
   for (unsigned i = 0; i < b.width (); i ++)
@@ -140,87 +141,6 @@ sseq_page::delta_poincare_polynomial (const sseq_bounds &b) const
   return r;
 }
 
-void
-sseq_page::texshow (FILE *fp, const sseq_bounds &b, unsigned dh, bool last)
-{
-  fprintf (fp, "\
-\\begin{tikzpicture}[scale=.66]\n\
-  \\draw[->] (0,0) -- (%d.5,0) node[right] {$t$};\n\
-  \\draw[->] (0,0) -- (0,%d.5) node[above] {$q$};\n\
-  \\draw[step=1] (0,0) grid (%d,%d);\n",
-	   b.width (), (b.height () + 1) / 2, b.width (), (b.height () + 1) / 2);
-
-  fprintf (fp, "  \\draw (%.3f,-0.8) node[below] {$",
-	   ((double)b.width () + 0.5) / 2);
-  if (last)
-    fprintf (fp, "E_\\infty = ");
-  fprintf (fp, "E_{%d}$};\n",
-	   dh);
-  
-  /* label axes */
-  for (int x = b.minh; x <= b.maxh; x ++)
-    {
-      fprintf (fp, "\
-  \\draw (%d.5,-.2) node[below] {$%d$};\n",
-	       x - b.minh, x);
-    }
-  for (int y = b.minq; y <= b.maxq; y += 2)
-    {
-      fprintf (fp, "\
-  \\draw (-.2,%d.5) node[left] {$%d$};\n",
-	       (y - b.minq) / 2, y);
-    }
-  
-  for (unsigned i = 0; i < b.width (); i ++)
-    for (unsigned j = 0; j < b.height (); j ++)
-      {
-	int r = rank[i][j];
-	if (r == 1)
-	  {
-	    assert (is_even (j));
-	    fprintf (fp, "\
-  \\fill (%d.5, %d.5) circle (.15);\n",
-		     i, j / 2);
-	  }
-	else if (r > 1)
-	  {
-	    assert (is_even (j));
-	    fprintf (fp, "\
-  \\draw (%d.5, %d.5) node {$%d$};\n",
-		    i, j / 2, r);
-	  }
-      }
-  
-  for (unsigned i = 0; i < b.width (); i ++)
-    for (unsigned j = 0; j < b.height (); j ++)
-      {
-	unsigned r = im_rank[i][j];
-	if (r == 0)
-	  continue;
-	
-	unsigned dx = dh,
-	  dy = dh - 1;  // in "boxes"
-	assert (dx >= 2); // eliminated d_1
-	
-	double h = sqrt ((double)(dx * dx + dy * dy));
-	double xadj = (double)dx / h * 0.3;
-	double yadj = (double)dy / h * 0.3;
-	
-	assert (is_even (j));
-	fprintf (fp, "  \\draw[->] (%.3f, %.3f) -- ",
-		(double)i + 0.5 + xadj, (double)(j / 2) + 0.5 + yadj);
-	if (r > 1)
-	  fprintf (fp, "node[color=red!75!black] {$%d$} ", r);
-	fprintf (fp, "(%.3f, %.3f);\n",
-		(double)(i + dx) + 0.5 - xadj, (double)(j / 2 + dy) + 0.5 - yadj);
-      }
-  
-  fprintf (fp, "\
-\\end{tikzpicture}\n");
-  
-  fflush (fp);
-}
-
 sseq
 sseq::operator + (const sseq &ss2) const
 {
@@ -280,36 +200,6 @@ sseq::shift (int dh, int dq) const
 	       pages);
 }
 
-bool
-sseq::equal_as_spaces (const sseq &ss) const
-{
-  if (bounds != ss.bounds
-      || pages.size () != ss.pages.size ())
-    return 0;
-  
-  for (unsigned i = 1; i <= pages.size (); i ++)
-    {
-      if (!pages[i].equal_as_spaces (ss.pages[i]))
-	return 0;
-    }
-  
-  return 1;
-}
-
-void
-sseq::texshow (FILE *fp, std::string name)
-{
-  fprintf (fp, "\\section{Knot $%s$}\n", name.c_str ());
-  
-  unsigned n = pages.size ();
-  for (unsigned i = 1; i <= n; i ++)
-    fprintf (fp, "$\\rank E_%d = %d$ \\\\\n",
-	    i + 1, pages[i].total_rank ());
-  
-  for (unsigned i = 1; i <= n; i ++)
-    pages[i].texshow (fp, bounds, i + 1, i == n);
-}
-
 void
 sseq_builder::cancel (unsigned d)
 {

sseq.h

@@ -7,6 +7,27 @@ class sseq_bounds
   
  public:
   sseq_bounds () { }
+  
+  template<class R, class M> sseq_bounds (ptr<const module<R> > C, M m)
+  {
+    grading hq1 = m(C->generator_grading (1));
+    minh = maxh = hq1.h;
+    minq = maxq = hq1.q;
+    
+    for (unsigned i = 2; i <= C->dim (); i ++)
+      {
+	grading hq = m(C->generator_grading (i));
+	if (hq.h < minh)
+	  minh = hq.h;
+	if (hq.h > maxh)
+	  maxh = hq.h;
+	if (hq.q < minq)
+	  minq = hq.q;
+	if (hq.q > maxq)
+	  maxq = hq.q;
+      }
+  }
+  
   sseq_bounds (int minh_, int maxh_, int minq_, int maxq_)
     : minh(minh_), maxh(maxh_), minq(minq_), maxq(maxq_)
   { }
@@ -41,21 +62,33 @@ class sseq_page
 {
  public:
   /* bounds come from sseq */
+  unsigned k;
+  grading dk_gr;
   vector<vector<unsigned> > rank,
     im_rank;
   
  public:
   sseq_page () { }
   sseq_page (const sseq_bounds &b);
+  template<class R, class M> sseq_page (const sseq_bounds &b,
+					unsigned k_,
+					grading dk_gr_,
+					mod_map<R> d,
+					M m);
   sseq_page (const sseq_page &pg)
-    : rank(pg.rank), im_rank(pg.im_rank)
+    : k(pg.k), dk_gr(pg.dk_gr), rank(pg.rank), im_rank(pg.im_rank)
   { }
   ~sseq_page () { }
   
-  bool operator == (const sseq_page &pg) const { return rank == pg.rank && im_rank == pg.im_rank; }
+  bool operator == (const sseq_page &pg) const
-  bool operator != (const sseq_page &pg) const { return !operator == (pg); }
+  {
+    return k == pg.k
+    && dk_gr == pg.dk_gr
+    && rank == pg.rank
+    && im_rank == pg.im_rank;
+  }
 
-  bool equal_as_spaces (const sseq_page &pg) const { return rank == pg.rank; }
+  bool operator != (const sseq_page &pg) const { return !operator == (pg); }
   
   unsigned total_rank () const;
   multivariate_laurentpoly<Z> poincare_polynomial (const sseq_bounds &b) const;
@@ -67,7 +100,7 @@ class sseq_page
 		     const sseq_bounds &b1, const sseq_page &pg1,
 		     const sseq_bounds &b2, const sseq_page &pg2);
   
-  void texshow (FILE *fp, const sseq_bounds &b, unsigned dh, bool last);
+  template<class M> void texshow (FILE *fp, const sseq_bounds &b, const char *label, M m);
 };
 
 class sseq
@@ -78,8 +111,10 @@ class sseq
   
  public:
   sseq () { }
-  sseq (const sseq_bounds &b, const basedvector<sseq_page, 1> &pages_)
+  sseq (const sseq_bounds &b,
-    : bounds(b), pages(pages_)
+	const basedvector<sseq_page, 1> &pages_)
+    : bounds(b),
+      pages(pages_)
   { }
   sseq (const sseq_bounds &b)
     : bounds(b)
@@ -87,7 +122,12 @@ class sseq
   sseq (const sseq &ss) : bounds(ss.bounds), pages(ss.pages) { }
   ~sseq () { }
   
-  sseq &operator = (const sseq &ss) { bounds = ss.bounds; pages = ss.pages; return *this; }
+  sseq &operator = (const sseq &ss)
+  {
+    bounds = ss.bounds;
+    pages = ss.pages;
+    return *this;
+  }
   
   sseq operator + (const sseq &ss2) const;  // direct sum
   sseq otimes (const sseq &ss2) const; // tensor product
@@ -100,284 +140,157 @@ class sseq
   bool operator == (const sseq &ss) const { return bounds == ss.bounds && pages == ss.pages; }
   bool operator != (const sseq &ss) const { return !operator == (ss); }
   
-  
+  template<class M> void texshow (FILE *fp, M m);
-  bool equal_as_spaces (const sseq &ss) const;
-  
-  void texshow (FILE *fp, std::string name);
 };
 
-#if 0
+template<class R, class M> 
-template<class R> class simplified_complex_generators
+sseq_page::sseq_page (const sseq_bounds &b,
+		      unsigned k_,
+		      grading dk_gr_,
+		      mod_map<R> dk,
+		      M m)
+  : k(k_),
+    dk_gr(dk_gr_),
+    rank(b.width ()),
+    im_rank(b.width ())
 {
-  unsigned new_n;
+  dk.check_grading (dk_gr);
-  ptr<const module<R> > C;
-  basedvector<unsigned, 1> new_C_to_C_generator;
   
-public:
+  grading m_dk_gr = m.map_delta(dk_gr);
-  simplified_complex_generators (const simplified_complex_generators &g)
-    : new_n(g.new_n),
-      C(g.C),
-      new_C_to_C_generator(g.new_C_to_C_generator)
-  { }
-  simplified_complex_generators (unsigned new_n_,
-				 ptr<const module<R> > C_,
-				 basedvector<unsigned, 1> new_C_to_C_generator_)
-    : new_n(new_n_),
-      C(C_),
-      new_C_to_C_generator(new_C_to_C_generator_)
-  { }
-  ~simplified_complex_generators () { }
   
-  simplified_complex_generators &operator = (const simplified_complex_generators &) = delete;
+  for (unsigned i = 0; i < b.width (); i ++)
-  
-  unsigned dim () const { return new_n; }
-  unsigned free_rank () const { return new_n; }
-  grading generator_grading (unsigned i) const { return C->generator_grading (new_C_to_C_generator[i]); }
-  void show_generator (unsigned i) const { C->show_generator (new_C_to_C_generator[i]); }
-  R generator_ann (unsigned i) const { abort (); }
-};
-
-template<class R> 
-class chain_complex_simplifier
-{
- public:
-  typedef typename R::linear_combination linear_combination;
-  typedef typename R::linear_combination_const_iter linear_combination_const_iter;
-  
- public:
-  ptr<const module<R> > C;
-  unsigned n; // |C|
-  const mod_map<R> &d;
-  
-  ptr<const module<R> > new_C;
-  mod_map<R> new_d;
-  
-  // chain homotopy equivalences
-  // pi : C -> new_C, iota : new_C -> C
-  mod_map<R> pi, iota;
-  
- private:
-  basedvector<linear_combination, 1> new_d0;
-  basedvector<set<unsigned>, 1> preim;
-  
-  bool build_pi_iota;
-  mod_map<R> pi0, iota0;
-  set<unsigned> canceled;
-  
-  void cancel (unsigned i, R b, unsigned j);
-  
- public:
-  chain_complex_simplifier (ptr<const module<R> > C_,
-			    const mod_map<R> &d_,
-			    int dh,
-			    bool build_pi_iota_ = 0);
-  
-};
-
-template<class R> void
-chain_complex_simplifier<R>::cancel (unsigned i, R b, unsigned j)
-{
-  assert (i != j);
-  assert (b.is_unit ());
-  
-  R binv = b.recip ();
-  
-  canceled.push (i);
-  canceled.push (j);
-  
-  new_d0[i].yank (j);
-  preim[j].yank (i);
-  
-  for (linear_combination_const_iter k = new_d0[i]; k; k ++)
-    preim[k.key ()].yank (i);
-  for (set_const_iter<unsigned> k = preim[i]; k; k ++)
-    new_d0[k.val ()].yank (i);
-  for (linear_combination_const_iter k = new_d0[j]; k; k ++)
-    preim[k.key ()].yank (j);
-
-  if (build_pi_iota)
     {
-      mod_map<R> local_pi0 (C, 1),
+      vector<unsigned> r (b.height ()),
-	local_iota0 (C, 1);
+	im_r (b.height ());
+      for (unsigned j = 0; j < b.height (); j ++)
+	r[j] = im_r[j] = 0;
       
-      local_pi0[i].clear ();
+      rank[i] = r;
-      local_pi0[j].clear ();
+      im_rank[i] = im_r;
-      
-      local_iota0[i].clear ();
-      local_iota0[j].clear ();
-      
-      for (linear_combination_const_iter ll = new_d0[i]; ll; ll ++)
-	{
-	  R c = ll.val ();
-	  local_pi0[j].mulsub (binv * c, ll.key ());
-	}
-      
-      for (set_const_iter<unsigned> kk = preim[j]; kk; kk ++)
-	{
-	  unsigned k = kk.val ();
-	  R a = new_d0[k](j);
-	  assert (a != 0);
-	  
-	  local_iota0[k].mulsub (a * binv, i);
-	}
-      
-      pi0 = local_pi0.compose (pi0);
-      iota0 = iota0.compose (local_iota0);
     }
   
-  for (set_const_iter<unsigned> kk = preim[j]; kk; kk ++)
+  ptr<const module<R> > C = dk.domain ();
+  for (unsigned i = 1; i <= C->dim (); i ++)
     {
-      unsigned k = kk.val ();
+      grading gr = m(C->generator_grading (i));
-      R a = new_d0[k](j);
+      rank[(unsigned)(gr.h - b.minh)][(unsigned)(gr.q - b.minq)] ++;
-      assert (a != 0);
-      
-      R abinv = a * binv;
-      
-      for (linear_combination_const_iter ll = new_d0[i]; ll; ll ++)
-	{
-	  unsigned ell = ll.key ();
-	  R c = ll.val ();
-	  
-	  assert (! (canceled % k));
-	  assert (! (canceled % ell));
-	  assert (k != i);
-	  assert (k != j);
-	  assert (ell != i);
-	  assert (ell != j);
-	  assert (ell != k);
-	  
-	  new_d0[k].mulsub (abinv * c, ell);
-	  if (new_d0[k] % ell)
-	    preim[ell] += k;
-	  else
-	    preim[ell] -= k;
-	}
     }
   
-  for (set_const_iter<unsigned> k = preim[j]; k; k ++)
+  ptr<const free_submodule<R> > im = dk.image ();
-    new_d0[k.val ()].yank (j);
+  for (unsigned i = 1; i <= im->dim (); i ++)
-  
-  new_d0[i].clear ();
-  preim[i].clear ();
-  new_d0[j].clear ();
-  preim[j].clear ();
-  
-#if 0  // expensive
-  if (build_pi_iota)
     {
-      assert (pi0.compose (d) == new_d0.compose (pi0));
+      grading gr = m(im->generator_grading (i));
-      assert (iota0.compose (new_d0) == d.compose (iota0));
+      im_rank[(unsigned)(gr.h - m_dk_gr.h - b.minh)][(unsigned)(gr.q - m_dk_gr.q - b.minq)] ++;
     }
-#endif
 }
 
-template<class R>
+
-chain_complex_simplifier<R>::chain_complex_simplifier (ptr<const module<R> > C_,
+template<class M> void
-						       const mod_map<R> &d_,
+sseq_page::texshow (FILE *fp, const sseq_bounds &b, const char *label, M m)
-						       int dh,
-						       bool build_pi_iota_)
-  : C(C_), n(C_->dim ()), d(d_),
-    new_d0(COPY2, d_.explicit_columns ()),
-    preim(C_->dim ()),
-    build_pi_iota(build_pi_iota_)
 {
+  grading m_dk_gr = m.map_delta(dk_gr);
+  
+  unsigned dh = m_dk_gr.h,
+    dq = m_dk_gr.q;
+  
+  fprintf (fp, "\
+\\begin{tikzpicture}[scale=.66]\n\
+  \\draw[->] (0,0) -- (%d.5,0) node[right] {$t$};\n\
+  \\draw[->] (0,0) -- (0,%d.5) node[above] {$q$};\n\
+  \\draw[step=1] (0,0) grid (%d,%d);\n",
+	   b.width (), b.height (), b.width (), b.height ());
+  
+  fprintf (fp, "  \\draw (%.3f,-0.8) node[below] {%s};\n",
+	   ((double)b.width () + 0.5) / 2, label);
+  
+  /* label axes */
+  for (int x = b.minh; x <= b.maxh; x ++)
+    {
+      fprintf (fp, "\
+  \\draw (%d.5,-.2) node[below] {$",
+	       x - b.minh);
+      m.x_label (fp, x);
+      fprintf (fp, "$};\n");
+    }
+  for (int y = b.minq; y <= b.maxq; y ++)
+    {
+      fprintf (fp, "\
+  \\draw (-.2,%d.5) node[left] {$",
+	       y - b.minq);
+      m.y_label (fp, y);
+      fprintf (fp, "$};\n");
+    }
+  
+  for (unsigned i = 0; i < b.width (); i ++)
+    for (unsigned j = 0; j < b.height (); j ++)
+      {
+	int r = rank[i][j];
+	if (r == 1)
+	  {
+	    fprintf (fp, "\
+  \\fill (%d.5, %d.5) circle (.15);\n",
+		     i, j);
+	  }
+	else if (r > 1)
+	  {
+	    fprintf (fp, "\
+  \\draw (%d.5, %d.5) node {$%d$};\n",
+		    i, j, r);
+	  }
+      }
+  
+  for (unsigned i = 0; i < b.width (); i ++)
+    for (unsigned j = 0; j < b.height (); j ++)
+      {
+	unsigned r = im_rank[i][j];
+	if (r == 0)
+	  continue;
+	
+	int dx = dh,
+	  dy = dq;  // in "boxes"
+	
+	double h = sqrt ((double)(dx * dx + dy * dy));
+	double xadj = (double)dx / h * 0.3;
+	double yadj = (double)dy / h * 0.3;
+	
+	fprintf (fp, "  \\draw[->] (%.3f, %.3f) -- ",
+		(double)i + 0.5 + xadj, (double)j + 0.5 + yadj);
+	if (r > 1)
+	  fprintf (fp, "node[color=red!75!black] {$%d$} ", r);
+	fprintf (fp, "(%.3f, %.3f);\n",
+		 (double)((int)i + dx) + 0.5 - xadj, (double)((int)j + dy) + 0.5 - yadj);
+      }
+  
+  fprintf (fp, "\
+\\end{tikzpicture}\n");
+  
+  fflush (fp);
+}
+
+template<class M> void
+sseq::texshow (FILE *fp, M m)
+{
+  unsigned n = pages.size ();
   for (unsigned i = 1; i <= n; i ++)
     {
-      for (linear_combination_const_iter j = d[i]; j; j ++)
+      if (i == n)
-	preim[j.key ()].push (i);
+	fprintf (fp, "$\\rank E_\\infty = \\rank E_%d = %d$ \\\\\n",
+		 pages[i].k, pages[i].total_rank ());
+      else
+	fprintf (fp, "$\\rank E_%d = %d$ \\\\\n",
+		 pages[i].k, pages[i].total_rank ());
     }
   
-  if (build_pi_iota)
+  for (unsigned i = 1; i <= n; i ++)
     {
-      pi0 = mod_map<R> (C, 1);
+      char buf[1000];
-      iota0 = mod_map<R> (C, 1);
+      if (i == n)
-      
+	sprintf (buf, "$E_\\infty = E_{%d}$", pages[i].k);
-#if 0 // expensive
+      else
-      assert (pi0.compose (d) == new_d0.compose (pi0));
+	sprintf (buf, "$E_{%d}$", pages[i].k);
-      assert (iota0.compose (new_d0) == d.compose (iota0));
+      pages[i].texshow (fp, bounds, buf, m);
-#endif
-    }
-  
- Lretry:
-  for (unsigned i = n; i >= 1; i --)
-    {
-      if (canceled % i)
-	continue;
-      
-      grading igr = C->generator_grading (i);
-      for (linear_combination_const_iter j = new_d0[i]; j; j ++)
-	{
-	  grading jgr = C->generator_grading (j.key ());
-	  assert (jgr.h >= igr.h);
-	  if (j.val ().is_unit ()
-	      && jgr.h - igr.h == dh)
-	    {
-	      cancel (i, j.val (), j.key ());
-	      goto Lretry;
-	    }
-	}
-    }
-  
-  unsigned new_n = n - canceled.card ();
-  basedvector<unsigned, 1> new_C_to_C_generator (new_n),
-    C_to_new_C_generator (n);
-  for (unsigned i = 1, j = 1; i <= n; i ++)
-    {
-      if (canceled % i)
-	{
-	  C_to_new_C_generator[i] = 0;
-	  continue;
-	}
-      
-      C_to_new_C_generator[i] = j;
-      new_C_to_C_generator[j] = i;
-      j ++;
-    }
-  
-  new_C = (new base_module<R, simplified_complex_generators<R> >
-	   (simplified_complex_generators<R> (new_n, C, new_C_to_C_generator)));
-  new_d = mod_map<R> (new_C);
-  
-  for (unsigned i = 1; i <= new_n; i ++)
-    {
-      unsigned i0 = new_C_to_C_generator[i];
-	  
-      for (linear_combination_const_iter j0 = new_d0[i0]; j0; j0 ++)
-	{
-	  unsigned j = C_to_new_C_generator[j0.key ()];
-	  assert (j != 0);
-	  
-	  new_d[i].muladd (j0.val (), j);
-	}
-    }
-  
-  if (build_pi_iota)
-    {
-      pi = mod_map<R> (C, new_C);
-      iota = mod_map<R> (new_C, C);
-      
-      for (unsigned i0 = 1; i0 <= n; i0 ++)
-	{
-	  for (linear_combination_const_iter j0 = pi0[i0]; j0; j0 ++)
-	    {
-	      unsigned j = C_to_new_C_generator[j0.key ()];
-	      pi[i0].muladd (j0.val (), j);
-	    }
-	}
-      
-      for (unsigned i = 1; i <= new_n; i ++)
-	{
-	  unsigned i0 = new_C_to_C_generator[i];
-	  iota[i] = iota0[i0];
-	}
-      
-#if 0  // expensive
-      assert (pi.compose (d) == new_d.compose (pi));
-      assert (d.compose (iota) == iota.compose (new_d));
-#endif
     }
 }
-#endif
 
 class sseq_builder
 {