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sseq.h
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sseq.h
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class sseq_bounds
{
public:
int minh, maxh,
minq, maxq;
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_)
{ }
sseq_bounds (const sseq_bounds &b)
: minh(b.minh), maxh(b.maxh), minq(b.minq), maxq(b.maxq)
{ }
~sseq_bounds () { }
sseq_bounds &operator = (const sseq_bounds &b)
{
minh = b.minh;
maxh = b.maxh;
minq = b.minq;
maxq = b.maxq;
return *this;
}
unsigned width () const { return maxh - minh + 1; }
unsigned height () const { return maxq - minq + 1; }
bool operator == (const sseq_bounds &b) const
{
return minh == b.minh
&& maxh == b.maxh
&& minq == b.minq
&& maxq == b.maxq;
}
bool operator != (const sseq_bounds &b) const { return !operator == (b); }
};
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)
: 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 k == pg.k
&& dk_gr == pg.dk_gr
&& rank == pg.rank
&& im_rank == pg.im_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;
multivariate_laurentpoly<Z> delta_poincare_polynomial (const sseq_bounds &b) const;
unsigned homological_width (const sseq_bounds &b) const;
void addeq (const sseq_bounds &b, const sseq_bounds &b2, const sseq_page &pg2);
void otimes_addeq (const sseq_bounds &b,
const sseq_bounds &b1, const sseq_page &pg1,
const sseq_bounds &b2, const sseq_page &pg2);
template<class M> void texshow (FILE *fp, const sseq_bounds &b, const char *label, M m);
};
class sseq
{
public:
sseq_bounds bounds;
basedvector<sseq_page, 1> pages;
public:
sseq () { }
sseq (const sseq_bounds &b,
const basedvector<sseq_page, 1> &pages_)
: bounds(b),
pages(pages_)
{ }
sseq (const sseq_bounds &b)
: bounds(b)
{ }
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 &ss2) const; // direct sum
sseq otimes (const sseq &ss2) const; // tensor product
sseq shift (int dh, int dq) const;
unsigned e2_rank () const { return pages[1].total_rank (); }
unsigned einf_rank () const { return pages[pages.size ()].total_rank (); }
unsigned homological_width () const { return pages[1].homological_width (bounds); }
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);
};
template<class R, class M>
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 ())
{
dk.check_grading (dk_gr);
grading m_dk_gr = m.map_delta(dk_gr);
for (unsigned i = 0; i < b.width (); i ++)
{
vector<unsigned> r (b.height ()),
im_r (b.height ());
for (unsigned j = 0; j < b.height (); j ++)
r[j] = im_r[j] = 0;
rank[i] = r;
im_rank[i] = im_r;
}
ptr<const module<R> > C = dk.domain ();
for (unsigned i = 1; i <= C->dim (); i ++)
{
grading gr = m(C->generator_grading (i));
rank[(unsigned)(gr.h - b.minh)][(unsigned)(gr.q - b.minq)] ++;
}
ptr<const free_submodule<R> > im = dk.image ();
for (unsigned i = 1; i <= im->dim (); i ++)
{
grading gr = m(im->generator_grading (i));
im_rank[(unsigned)(gr.h - m_dk_gr.h - b.minh)][(unsigned)(gr.q - m_dk_gr.q - b.minq)] ++;
}
}
template<class M> void
sseq_page::texshow (FILE *fp, const sseq_bounds &b, const char *label, M m)
{
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 ++)
{
if (i == n)
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 ());
}
for (unsigned i = 1; i <= n; i ++)
{
char buf[1000];
if (i == n)
sprintf (buf, "$E_\\infty = E_{%d}$", pages[i].k);
else
sprintf (buf, "$E_{%d}$", pages[i].k);
pages[i].texshow (fp, bounds, buf, m);
}
}
class sseq_builder
{
private:
typedef Z2::linear_combination linear_combination;
// typedef Z2::linear_combination_iter linear_combination_iter;
typedef Z2::linear_combination_const_iter linear_combination_const_iter;
public:
ptr<const module<Z2> > C;
ullmanset<1> present;
basedvector<set<unsigned>, 1> im, preim;
void cancel (unsigned i, unsigned j);
void cancel (unsigned d);
linear_combination lc (const set<unsigned> &s);
bool im_zero ();
public:
sseq_builder (const ptr<const module<Z2> > &C_, const mod_map<Z2> &d);
sseq build_sseq ();
};