Added io support for module, linear_combination, mod_map and grading.

Added intersection and sum for free_submodule.  Modified mpimain to
dump cohomology, sq1 and sq2 as objects (instead of poincare series).

algebra/Z2.h

@@ -15,6 +15,7 @@ class Z2
   Z2 (bool v_) : v(v_) { }
   Z2 (const Z2 &x) : v(x.v) { }
   Z2 (copy, const Z2 &x) : v(x.v) { }
+  Z2 (reader &r) { v = r.read_bool (); }
   ~Z2 () { }
   
   Z2 &operator = (const Z2 &x) { v = x.v; return *this; }
@@ -64,6 +65,7 @@ class Z2
   }
   
   static void show_ring () { printf ("Z2"); }
+  void write_self (writer &w) const { w.write_bool (v); }
   void show_self () const { printf ("%d", (int)v); }
   void display_self () const { printf ("%d\n", (int)v); }
 };

algebra/grading.h

@@ -8,6 +8,12 @@ class grading
   grading () : h(0), q(0) { }
   grading (int h_, int q_) : h(h_), q(q_) { }
   grading (const grading &gr) : h(gr.h), q(gr.q) { }
+  grading (reader &r)
+  {
+    h = r.read_int ();
+    q = r.read_int ();
+  }
+  
   ~grading () { }
   
   grading &operator = (const grading &gr) { h = gr.h; q = gr.q; return *this; }
@@ -46,6 +52,12 @@ class grading
   
   grading mirror_grading (unsigned nplus, unsigned nminus, bool torsion) const;
 
+  void write_self (writer &w) const
+  {
+    w.write_int (h);
+    w.write_int (q);
+  }
+    
   void show_self () const;
   void display_self () const;
 };

algebra/linear_combination.h

@@ -39,6 +39,13 @@ class linear_combination
     for (typename map<unsigned, R>::const_iter i = lc.v; i; i ++)
       v.push (i.key (), R (COPY, i.val ()));
   }
+  
+  linear_combination (reader &r)
+  {
+    m = r.read_mod<R> ();
+    v = map<unsigned, R> (r);
+  }
+  
   ~linear_combination () { }
   
   linear_combination &operator = (const linear_combination &lc)
@@ -165,6 +172,12 @@ class linear_combination
   }
 #endif
 
+  void write_self (writer &w) const
+  {
+    write (w, *m);
+    write (w, v);
+  }
+  
   void show_self () const;
   void display_self () const { show_self (); newline (); }
 };
@@ -337,6 +350,12 @@ class linear_combination<Z2>
   linear_combination (ptr<const Z2mod> m_) : m(m_) { }
   linear_combination (const linear_combination &lc) : m(lc.m), v(lc.v) { }
   linear_combination (copy, const linear_combination &lc) : m(lc.m), v(COPY, lc.v) { }
+  linear_combination (reader &r)
+  {
+    m = r.read_mod<Z2> ();
+    v = set<unsigned> (r);
+  }
+  
   ~linear_combination () { }
   
   linear_combination &operator = (const linear_combination &lc)
@@ -446,6 +465,12 @@ class linear_combination<Z2>
   void check () const;
 #endif
   
+  void write_self (writer &w) const
+  {
+    write (w, *m);
+    write (w, v);
+  }
+  
   void show_self () const;
   void display_self () const { show_self (); newline (); }
 };

algebra/module.h

@@ -14,10 +14,15 @@ template<class R>
 class module : public refcounted
 {
  private:
+  friend class reader;
+  friend class writer;
+  
   unsigned id;
   
   static unsigned id_counter;
   
+  static basedvector<ptr<const module<R> >, 1> id_module;
+  
   static map<basedvector<unsigned, 1>,
     ptr<const direct_sum<R> > > direct_sum_idx;
   static map<basedvector<unsigned, 1>,
@@ -28,8 +33,11 @@ class module : public refcounted
  public:
   module ()
   {
-    id = id_counter;
     id_counter ++;
+    id = id_counter;
+    
+    id_module.append (this);
+    assert (id_module.size () == id_counter);
   }
   module (const module &) = delete;
   virtual ~module () { }
@@ -49,6 +57,8 @@ class module : public refcounted
   // r < i <= n
   virtual R generator_ann (unsigned i) const = 0;
   
+  set<grading> gradings () const;
+  
   bool is_free () const { return dim () == free_rank (); }
   
   bool is_zero (R c, unsigned i) const
@@ -143,11 +153,16 @@ class module : public refcounted
     factors.append (this);
   }
   
+  ptr<const free_submodule<R> > graded_piece (grading hq) const;
+  
+  void write_self (writer &w) const { w.write_mod<R> (this); }
   void show_self () const;
   void display_self () const;
 };
 
-template<class R> unsigned module<R>::id_counter = 1;
+template<class R> unsigned module<R>::id_counter = 0;
+
+template<class R> basedvector<ptr<const module<R> >, 1> module<R>::id_module;
 
 template<class R> map<basedvector<unsigned, 1>,
   ptr<const direct_sum<R> > > module<R>::direct_sum_idx;
@@ -542,6 +557,9 @@ class free_submodule : public module<R>
   
   linear_combination<R> restrict (linear_combination<R> v0) const;
   ptr<const free_submodule<R> > restrict_submodule (ptr<const free_submodule<R> > m) const;
+  
+  ptr<const free_submodule<R> > intersection (ptr<const free_submodule<R> > m) const;
+  ptr<const free_submodule<R> > plus (ptr<const free_submodule<R> > m) const;
 };
 
 template<class R> 
@@ -854,6 +872,15 @@ class mod_map
   mod_map (const map_builder<R> &b)
     : impl(new explicit_map_impl<R> (b.from, b.to, b.columns))
   { }
+  
+  mod_map (reader &r)
+  {
+    ptr<const module<R> > from = r.read_mod<R> ();
+    ptr<const module<R> > to = r.read_mod<R> ();
+    basedvector<linear_combination<R>, 1> columns (r);
+    impl = new explicit_map_impl<R> (from, to, columns);
+  }
+  
   ~mod_map () { }
   
   mod_map &operator = (const mod_map &m) { impl = m.impl; return *this; }
@@ -945,6 +972,14 @@ class mod_map
   // ???
   basedvector<linear_combination<R>, 1> explicit_columns () const;
   
+  void write_self (writer &w) const
+  {
+    // write explicitly
+    write (w, *impl->from);
+    write (w, *impl->to);
+    write (w, explicit_columns ());
+  }
+  
   void show_self () const;
   void display_self () const;
 };
@@ -1445,6 +1480,35 @@ module<R>::free_delta_poincare_polynomial () const
   return r;
 }
 
+template<class R> set<grading> 
+module<R>::gradings () const
+{
+  set<grading> gs;
+  for (unsigned i = 1; i <= dim (); i ++)
+    gs += generator_grading (i);
+  return gs;
+}
+
+template<class R> ptr<const free_submodule<R> > 
+module<R>::graded_piece (grading hq) const
+{
+  basedvector<linear_combination<R>, 1> s;
+  for (unsigned i = 1; i <= dim (); i ++)
+    {
+      grading ihq = generator_grading (i);
+      if (ihq.h == hq.h
+	  && ihq.q == hq.q)
+	{
+	  linear_combination<R> v (this);
+	  v.muladd (1, i);
+	  s.append (v);
+	}
+    }
+  
+  mod_span<R> span (this, s);
+  return submodule (span);
+}
+
 template<class R> void
 module<R>::show_self () const
 {
@@ -1536,7 +1600,7 @@ mod_map<R>::restrict_from (ptr<const free_submodule<R> > new_from) const
   basedvector<linear_combination<R>, 1> v (new_from->dim ());
   for (unsigned i = 1; i <= new_from->dim (); i ++)
     v[i] = map (new_from->inject_generator (i));
-  return new explicit_map_impl<R> (new_from, impl->to, v);
+  return mod_map (IMPL, new explicit_map_impl<R> (new_from, impl->to, v));
 }
 
 template<class R> mod_map<R> 
@@ -1560,7 +1624,7 @@ mod_map<R>::restrict (ptr<const free_submodule<R> > new_from,
   basedvector<linear_combination<R>, 1> v (new_from->dim ());
   for (unsigned i = 1; i <= new_from->dim (); i ++)
     v[i] = new_to->restrict (map (new_from->inject_generator (i)));
-  return new explicit_map_impl<R> (new_from, new_to, v);
+  return mod_map (IMPL, new explicit_map_impl<R> (new_from, new_to, v));
 }
 
 template<class R> linear_combination<R>
@@ -1606,6 +1670,93 @@ free_submodule<R>::restrict_submodule (ptr<const free_submodule<R> > m) const
   return this->submodule (span2);
 }
 
+template<class R> ptr<const free_submodule<R> >
+free_submodule<R>::intersection (ptr<const free_submodule<R> > m) const
+{
+  assert (parent == m->parent);
+  
+  unsigned md = m->dim (),
+    d = dim ();
+  
+  basedvector<linear_combination<R>, 1> intr;
+  
+  basedvector<linear_combination<R>, 1> hperp,
+    hproj;
+  basedvector<unsigned, 1> hpivots;
+  for (unsigned i = 1; i <= md; i ++)
+    {
+      linear_combination<R> perp (COPY, m->gens[i]),
+	proj (parent);
+      
+      for (unsigned j = 1; j <= d; j ++)
+	{
+	  unsigned k = pivots[j];
+	  if (perp % k)
+	    {
+	      const linear_combination<R> &g = gens[j];
+	      R c = g(k);
+	      R d = perp(k);
+	      
+	      assert (c | d);
+	      R q = d.div (c);
+	      
+	      perp.mulsub (q, g);
+	      proj.mulsub (q, g);
+	      
+	      assert (! (perp % k));
+	    }
+	}
+      
+      for (unsigned j = 1; j <= hpivots.size (); j ++)
+	{
+	  unsigned k = hpivots[j];
+	  if (perp % k)
+	    {
+	      const linear_combination<R> &h = hperp[j];
+	      R c = h(k);
+	      R d = perp(k);
+	      
+	      assert (c | d);
+	      R q = d.div (c);
+	      
+	      perp.mulsub (q, h);
+	      proj.mulsub (q, hproj[j]);
+	      
+	      assert (! (perp % k));
+	    }
+	  
+	}
+      
+      if (perp == 0)
+	intr.append (proj);
+      else
+	{
+	  hperp.append (perp);
+	  hproj.append (proj);
+	  hpivots.append (perp.head ().first);
+	}
+    }
+  
+  mod_span<R> span (parent, intr);
+  return parent->submodule (span);
+}
+
+template<class R> ptr<const free_submodule<R> >
+free_submodule<R>::plus (ptr<const free_submodule<R> > m) const
+{
+  assert (parent == m->parent);
+  
+  basedvector<linear_combination<R>, 1> s;
+  for (unsigned i = 1; i <= dim (); i ++)
+    s.append (gens[i]);
+  
+  for (unsigned i = 1; i <= m->dim (); i ++)
+    s.append (m->gens[i]);
+  
+  mod_span<R> span (parent, s);
+  return parent->submodule (span);
+}
+
 template<class R> bool
 mod_map<R>::homogeneous () const
 {
@@ -1655,7 +1806,7 @@ mod_map<R>::kernel () const
     to = impl->to;
   
   basedvector<linear_combination<R>, 1> from_xs (from->dim ());
-  for (unsigned i = 1; i <= to->dim (); i ++)
+  for (unsigned i = 1; i <= from->dim (); i ++)
     {
       linear_combination<R> x (from);
       x.muladd (1, i);
@@ -1835,3 +1986,59 @@ mod_map<R>::display_self () const
       newline ();
     }
 }
+
+// ??? io
+
+template<class R> void
+writer::write_mod (ptr<const module<R> > m)
+{
+  pair<unsigned &, bool> p = aw->id_io_id.find (m->id_counter);
+  if (p.second)
+    {
+      write_int ((int)p.first);
+    }
+  else
+    {
+      ++ aw->io_id_counter;
+      unsigned io_id = aw->io_id_counter;
+      
+      p.first = io_id;
+      
+      write_int (- (int)io_id);
+      
+      unsigned n = m->dim (),
+	r = m->free_rank ();
+      write_unsigned (n);
+      write_unsigned (r);
+      for (unsigned i = 1; i <= n; i ++)
+	write (*this, m->generator_grading (i));
+      for (unsigned i = r + 1; i <= n; i ++)
+	write (*this, m->generator_ann (i));
+    }
+}
+
+template<class R> ptr<const module<R> > 
+reader::read_mod ()
+{
+  int io_id = read_int ();
+  if (io_id < 0)
+    {
+      unsigned n = read_unsigned ();
+      unsigned r = read_unsigned ();
+      basedvector<grading, 1> gr (n);
+      for (unsigned i = 1; i <= n; i ++)
+	gr[i] = grading (*this);
+      basedvector<R, 1> ann (n - r);
+      for (unsigned i = r + 1; i <= n; i ++)
+	ann[i - r] = R (*this);
+      
+      ptr<const module<R> > m = new explicit_module<R> (r, ann, gr);
+      ar->io_id_id.push ((unsigned)(-io_id), m->id);
+      return m;
+    }
+  else
+    {
+      unsigned id = ar->io_id_id(io_id);
+      return module<R>::id_module[id];
+    }
+}

lib/io.cpp

@@ -1,5 +1,6 @@
 
-#include <lib/lib.h>
+// #include <lib/lib.h>
+#include <algebra/algebra.h>
 
 void
 writer::write_int (int x)

lib/io.h

@@ -1,12 +1,18 @@
 
+template<class R> class module;
+
+class algebra_writer;
+class algebra_reader;
+
 class writer
 {
-  // don't use leb128 enconding.  for backward compatibility.
+ public:
   bool raw;
+  algebra_writer *aw;
   
  public:
   writer (const writer &) = delete;
-  writer (bool raw_ = false) : raw(raw_)  { }
+  writer (bool raw_ = false) : raw(raw_), aw(0) { }
   virtual ~writer () = default;
   
   writer &operator = (const writer &) = delete;
@@ -19,16 +25,18 @@ class writer
   void write_int (int x);
   void write_unsigned (unsigned x);
   void write_uint64 (uint64 x);
-  virtual void write_mpz (const mpz_t x);
+  
+  template<class R> void write_mod (ptr<const module<R> > m);
 };
 
 class reader
 {
   bool raw;
+  algebra_reader *ar;
   
  public:
   reader (const reader &) = delete;
-  reader (bool raw_) : raw(raw_) { }
+  reader (bool raw_) : raw(raw_), ar(0) { }
   virtual ~reader () = default;
   
   reader &operator = (const reader &) = delete;
@@ -60,6 +68,8 @@ class reader
   unsigned read_unsigned ();
   uint64 read_uint64 ();
   virtual void read_mpz (mpz_t x);
+  
+  template<class R> ptr<const module<R> > read_mod ();
 };
 
 extern FILE *open_file (const std::string &file, const char *mode);

lib/lib.h

@@ -158,11 +158,6 @@ void stderror (const char *fmt, ...);
 
 int alpha_to_int (char c);
 
-#include <lib/io.h>
-
-#include <lib/show.h>
-#include <lib/refcount.h>
-
 using std::tuple;
 using std::get;
 using std::make_tuple;
@@ -170,6 +165,11 @@ using std::tie;
 using std::ignore;
 using std::initializer_list;
 
+#include <lib/show.h>
+#include <lib/refcount.h>
+
+#include <lib/io.h>
+
 #include <lib/pair.h>
 
 #include <lib/maybe.h>
@@ -194,7 +194,6 @@ inline int random_int (int from, int to)
 #include <lib/bitset.h>
 #include <lib/ullmanset.h>
 #include <lib/setcommon.h>
-
 #include <lib/map_wrapper.h>
 #include <lib/map.h>
 
@@ -212,3 +211,23 @@ struct hasher : public std::unary_function<K, hash_t>
 #include <lib/unionfind.h>
 #include <lib/priority_queue.h>
 #include <lib/directed_multigraph.h>
+
+// ??? io
+
+class algebra_writer
+{
+public:
+  // modules
+  unsigned io_id_counter;
+  map<unsigned, unsigned> id_io_id;
+  
+  algebra_writer () : io_id_counter(0) { }
+  ~algebra_writer () { }
+};
+
+class algebra_reader
+{
+public:
+  map<unsigned, unsigned> io_id_id;
+  
+};

main.cpp

@@ -277,6 +277,164 @@ load (map<knot_desc,
 int
 main ()
 {
+#if 0
+  knot_diagram kd (rolfsen_knot (8, 19));
+  show (kd); newline ();
+  
+  cube<Z2> c (kd);
+  mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
+  
+  chain_complex_simplifier<Z2> s (c.khC, d, 1);
+  
+  steenrod_square sq (c, d, s);
+  mod_map<Z2> sq1 = sq.sq1 ();
+  mod_map<Z2> sq2 = sq.sq2 ();
+  
+  assert (sq1.compose (sq1) == 0);
+  assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
+  
+  display ("sq1:\n", sq1);
+  display ("sq2:\n", sq2);
+  
+  writer w ("sqtest.dat");
+  write (w, sq1);
+  write (w, sq2);
+#endif
+  
+#if 1
+#if 0
+  reader r ("sqtest.dat");
+  
+  knot_desc kd (knot_desc::ROLFSEN, 8, 19);
+  mod_map<Z2> sq1 (r);
+  mod_map<Z2> sq2 (r);
+  
+  ptr<const module<Z2> > H = sq1.domain ();
+  
+  display ("sq1:\n", sq1);
+  display ("sq2:\n", sq2);
+#endif
+  
+  for (unsigned i = 1; i <= 10; i ++)
+    for (unsigned j = 1; j <= rolfsen_crossing_knots (i);  j ++)
+      {
+#if 0
+	// (Knot Atlas) L10n18 
+	int xings[10][4] = {
+	  { 6, 1, 7, 2 },
+	  { 18, 7, 19, 8 },
+	  { 4,19,1,20 },
+	  { 5,12,6,13 },
+	  { 8,4,9,3 },
+	  { 13,17,14,16 },
+	  { 9,15,10,14 },
+	  { 15,11,16,10 },
+	  { 11,20,12,5 },
+	  { 2,18,3,17 },
+	};
+	knot_diagram kd (planar_diagram ("L10n18", 10, xings));
+#endif
+	
+	// (Knot Atlas) L10n102
+	int xings[10][4] = {
+	  { 6,1,7,2 }, { 10,3,11,4 }, { 14,7,15,8 }, { 8,13,5,14 }, { 11,18,12,19 }, { 15,20,16,17 }, { 19,16,20,9 }, { 17,12,18,13 }, { 2,5,3,6 }, { 4,9,1,10 },
+	};
+	knot_diagram kd (planar_diagram ("L10n102", 10, xings));
+	
+	// knot_diagram kd (rolfsen_knot (i, j));
+	// knot_diagram kd (mt_link (10, 0, 18));
+	
+	// show (kd); newline ();
+	printf ("%s  ", kd.name.c_str ());
+	
+	cube<Z2> c (kd);
+	mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
+	
+	chain_complex_simplifier<Z2> s (c.khC, d, 1);
+	
+	steenrod_square sq (c, d, s);
+
+	mod_map<Z2> sq1 = sq.sq1 ();
+	mod_map<Z2> sq2 = sq.sq2 ();
+	
+	assert (sq1.compose (sq1) == 0);
+	assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
+	
+	ptr<const module<Z2> > H = sq1.domain ();
+	
+	bool first = 1;
+  
+	// ???
+	set<grading> gs = H->gradings ();
+	for (set_const_iter<grading> i = gs; i; i ++)
+	  {
+	    grading hq = i.val (),
+	      h1q (hq.h + 1, hq.q),
+	      h2q (hq.h + 2, hq.q);
+      
+	    // printf ("(%d, %d):\n", hq.h, hq.q);
+      
+	    ptr<const free_submodule<Z2> > H_hq = H->graded_piece (hq),
+	      H_h1q = H->graded_piece (h1q),
+	      H_h2q = H->graded_piece (h2q);
+      
+	    mod_map<Z2> whole = sq2.restrict (H_hq, H_h2q),
+	      tail = sq1.restrict (H_hq, H_h1q),
+	      head = sq1.restrict (H_h1q, H_h2q);
+      
+	    ptr<const free_submodule<Z2> > whole_im = whole.image (),
+	      tail_ker = tail.kernel (),
+	      head_im = head.image ();
+	    ptr<const free_submodule<Z2> > inter = whole_im->intersection (head_im);
+      
+	    mod_map<Z2> whole_res = whole.restrict_from (tail_ker);
+	    ptr<const free_submodule<Z2> > whole_res_im = whole_res.image ();
+      
+	    ptr<const free_submodule<Z2> > res_inter = whole_res_im->intersection (head_im);
+      
+	    int r1 = whole_im->dim ();
+	    int r2 = whole_res_im->dim ();
+	    int r3 = inter->dim ();
+	    int r4 = res_inter->dim ();
+      
+	    if (r1 == 0
+		&& r2 == 0
+		&& r3 == 0
+		&& r4 == 0)
+	      continue;
+      
+	    // printf ("  r = (%d, %d, %d, %d)\n", r1, r2, r3, r4);
+      
+	    int s1 = r2 - r4,
+	      s2 = r1 - r2 - r3 + r4,
+	      s3 = r4,
+	      s4 = r3 - r4;
+
+	    if (first)
+	      {
+#if 0
+		show (kd);
+		printf (":  ");
+#endif
+		first = 0;
+	      }
+	    else
+	      printf (", ");
+	    printf ("(%d, %d) -> (%d, %d, %d, %d)",
+		    hq.h, hq.q,
+		    s1, s2, s3, s4);
+	  }
+	// if (!first)
+	  newline ();
+      }
+#endif
+
+#if 0
+  // knot_diagram kd (htw_knot (12, 0, 48));
+  knot_diagram kd (htw_knot (10, 1, 23));
+  show (kd); newline ();
+#endif
+  
 #if 0
   for (int a = 1; a >= 0; a --)
     for (unsigned i = 1; i <= 9; i ++)
@@ -350,7 +508,7 @@ main ()
   }
 #endif
   
-#if 1
+#if 0
   compute_show_kh_sq (knot_desc (knot_desc::ROLFSEN, 8, 19));
   
   map<knot_desc,

mpimain.cpp

@@ -7,6 +7,8 @@
 #define CMD_DO 1
 #define CMD_DIE 2
 
+static const int block_size = 100;
+
 void
 master ()
 {
@@ -14,26 +16,29 @@ master ()
   
   work.append (knot_desc (TORUS, 0, 0));
   
-  for (int a = 1; a >= 0; a --)
+  for (unsigned i = 14; i >= 1; i --)
-    for (unsigned i = 1; i <= 10; i ++)
+    {
-      for (unsigned j = 1; j <= rolfsen_crossing_knots (i); j += 4000)
+      if (i <= 10)
+	{
+	  for (unsigned j = 1; j <= rolfsen_crossing_knots (i); j += block_size)
 	    {
 	      work.append (knot_desc (ROLFSEN, i, j));
 	    }
+	}
       
-  for (int a = 1; a >= 0; a --)
+      for (unsigned j = 1; j <= htw_knots (i); j += block_size)
-    for (unsigned i = 1; i <= 14; i ++)
-      for (unsigned j = 1; j <= htw_knots (i); j += 4000)
 	{
 	  work.append (knot_desc (HTW, i, j));
 	}
       
-  for (int a = 1; a >= 0; a --)
+      if (i <= 13)
-    for (unsigned i = 1; i <= 13; i ++)
+	{
-      for (unsigned j = 1; j <= mt_links (i); j += 4000)
+	  for (unsigned j = 1; j <= mt_links (i); j += block_size)
 	    {
 	      work.append (knot_desc (MT, i, j));
 	    }
+	}
+    }
   
   int ntasks = num_tasks ();
   
@@ -80,9 +85,7 @@ master ()
 
 void
 compute_kh_sq (map<knot_desc,
-		   triple<multivariate_laurentpoly<Z>,
+		   triple<ptr<const module<Z2> >, mod_map<Z2>, mod_map<Z2> > > &knot_kh_sq,
-			  multivariate_laurentpoly<Z>,
-			  multivariate_laurentpoly<Z> > > &knot_kh_sq,
 	       knot_desc &desc)
 {
   knot_diagram kd = desc.diagram ();
@@ -96,6 +99,7 @@ compute_kh_sq (map<knot_desc,
   mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
   
   chain_complex_simplifier<Z2> s (c.khC, d, 1);
+  assert (s.new_d == 0);
   
   steenrod_square sq (c, d, s);
   mod_map<Z2> sq1 = sq.sq1 ();
@@ -104,18 +108,8 @@ compute_kh_sq (map<knot_desc,
   assert (sq1.compose (sq1) == 0);
   assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
   
-  multivariate_laurentpoly<Z> P = s.new_C->free_poincare_polynomial ();
-  
-  ptr<const free_submodule<Z2> > sq1_im = sq1.image ();
-  multivariate_laurentpoly<Z> sq1_P = sq1_im->free_poincare_polynomial ();
-  
-  ptr<const free_submodule<Z2> > sq2_im = sq2.image ();
-  multivariate_laurentpoly<Z> sq2_P = sq2_im->free_poincare_polynomial ();
-  
   knot_kh_sq.push (desc,
-		   triple<multivariate_laurentpoly<Z>,
+		   triple<ptr<const module<Z2> >, mod_map<Z2>, mod_map<Z2> > (s.new_C, sq1, sq2));
-			  multivariate_laurentpoly<Z>,
-			  multivariate_laurentpoly<Z> > (P, sq1_P, sq2_P));
 }
 
 void
@@ -136,9 +130,7 @@ slave ()
 	    desc.j = (knot_desc::table)recv_int ();
 	    
 	    map<knot_desc,
-	      triple<multivariate_laurentpoly<Z>,
+		triple<ptr<const module<Z2> >, mod_map<Z2>, mod_map<Z2> > > knot_kh_sq;
-	             multivariate_laurentpoly<Z>,
-	             multivariate_laurentpoly<Z> > > knot_kh_sq;
 	    
 	    char buf[1000];
 	    if (desc.t == TORUS)
@@ -167,7 +159,7 @@ slave ()
 			 j0);
 		
 		for (unsigned j = j0;
-		     j <= std::min (j0 + 4000,
+		     j <= std::min (j0 + block_size - 1,
 				    desc.table_crossing_knots ());
 		     j ++)
 		  {