genfun.cc

   1 #include <iostream>
   2 #include <iomanip>
   3 #include <vector>
   4 #include <assert.h>
   5 #include <barvinok/genfun.h>
   6 #include <barvinok/barvinok.h>
   7 #include "conversion.h"
   8 #include "genfun_constructor.h"
   9 #include "mat_util.h"
  10 #include "matrix_read.h"
  11
  12 using std::cout;
  13 using std::cerr;
  14 using std::endl;
  15 using std::pair;
  16 using std::vector;
  17
  18 bool short_rat_lex_smaller_denominator::operator()(const short_rat* r1,
  19                                                    const short_rat* r2) const
  20 {
  21     return lex_cmp(r1->d.power, r2->d.power) < 0;
  22 }
  23
  24 static void lex_order_terms(struct short_rat* rat)
  25 {
  26     for (int i = 0; i < rat->n.power.NumRows(); ++i) {
  27         int m = i;
  28         for (int j = i+1; j < rat->n.power.NumRows(); ++j)
  29             if (lex_cmp(rat->n.power[j], rat->n.power[m]) < 0)
  30                 m = j;
  31         if (m != i) {
  32             vec_ZZ tmp = rat->n.power[m];
  33             rat->n.power[m] = rat->n.power[i];
  34             rat->n.power[i] = tmp;
  35             QQ tmp_coeff = rat->n.coeff[m];
  36             rat->n.coeff[m] = rat->n.coeff[i];
  37             rat->n.coeff[i] = tmp_coeff;
  38         }
  39     }
  40 }
  41
  42 short_rat::short_rat(const short_rat& r)
  43 {
  44     n.coeff = r.n.coeff;
  45     n.power = r.n.power;
  46     d.power = r.d.power;
  47 }
  48
  49 short_rat::short_rat(Value c)
  50 {
  51     n.coeff.SetLength(1);
  52     value2zz(c, n.coeff[0].n);
  53     n.coeff[0].d = 1;
  54     n.power.SetDims(1, 0);
  55     d.power.SetDims(0, 0);
  56 }
  57
  58 short_rat::short_rat(const QQ& c, const vec_ZZ& num, const mat_ZZ& den)
  59 {
  60     n.coeff.SetLength(1);
  61     ZZ g = GCD(c.n, c.d);
  62     n.coeff[0].n = c.n/g;
  63     n.coeff[0].d = c.d/g;
  64     n.power.SetDims(1, num.length());
  65     n.power[0] = num;
  66     d.power = den;
  67     normalize();
  68 }
  69
  70 short_rat::short_rat(const vec_QQ& c, const mat_ZZ& num, const mat_ZZ& den)
  71 {
  72     n.coeff = c;
  73     n.power = num;
  74     d.power = den;
  75     normalize();
  76 }
  77
  78 void short_rat::normalize()
  79 {
  80     /* Make all powers in denominator reverse-lexico-positive */
  81     for (int i = 0; i < d.power.NumRows(); ++i) {
  82         int j;
  83         for (j = d.power.NumCols()-1; j >= 0; --j)
  84             if (!IsZero(d.power[i][j]))
  85                 break;
  86         assert(j >= 0);
  87         if (sign(d.power[i][j]) < 0) {
  88             negate(d.power[i], d.power[i]);
  89             for (int k = 0; k < n.coeff.length(); ++k) {
  90                 negate(n.coeff[k].n, n.coeff[k].n);
  91                 n.power[k] += d.power[i];
  92             }
  93         }
  94     }
  95
  96     /* Order powers in denominator */
  97     lex_order_rows(d.power);
  98 }
  99
 100 void short_rat::add(const short_rat *r)
 101 {
 102     for (int i = 0; i < r->n.power.NumRows(); ++i) {
 103         int len = n.coeff.length();
 104         int j;
 105         for (j = 0; j < len; ++j)
 106             if (r->n.power[i] == n.power[j])
 107                 break;
 108         if (j < len) {
 109             n.coeff[j] += r->n.coeff[i];
 110             if (n.coeff[j].n == 0) {
 111                 if (j < len-1) {
 112                     n.power[j] = n.power[len-1];
 113                     n.coeff[j] = n.coeff[len-1];
 114                 }
 115                 int dim = n.power.NumCols();
 116                 n.coeff.SetLength(len-1);
 117                 n.power.SetDims(len-1, dim);
 118             }
 119         } else {
 120             int dim = n.power.NumCols();
 121             n.coeff.SetLength(len+1);
 122             n.power.SetDims(len+1, dim);
 123             n.coeff[len] = r->n.coeff[i];
 124             n.power[len] = r->n.power[i];
 125         }
 126     }
 127 }
 128
 129 QQ short_rat::coefficient(Value* params, barvinok_options *options) const
 130 {
 131     unsigned nvar = d.power.NumRows();
 132     unsigned nparam = d.power.NumCols();
 133     Matrix *C = Matrix_Alloc(nparam + nvar, 1 + nvar + 1);
 134     Value tmp;
 135     value_init(tmp);
 136
 137     QQ c(0, 1);
 138
 139     for (int j = 0; j < n.coeff.length(); ++j) {
 140         C->NbRows = nparam+nvar;
 141         for (int r = 0; r < nparam; ++r) {
 142             value_set_si(C->p[r][0], 0);
 143             for (int c = 0; c < nvar; ++c) {
 144                 zz2value(d.power[c][r], C->p[r][1+c]);
 145             }
 146             zz2value(n.power[j][r], C->p[r][1+nvar]);
 147             value_subtract(C->p[r][1+nvar], C->p[r][1+nvar], params[r]);
 148         }
 149         for (int r = 0; r < nvar; ++r) {
 150             value_set_si(C->p[nparam+r][0], 1);
 151             Vector_Set(&C->p[nparam+r][1], 0, nvar + 1);
 152             value_set_si(C->p[nparam+r][1+r], 1);
 153         }
 154         Polyhedron *P = Constraints2Polyhedron(C, options->MaxRays);
 155         if (emptyQ2(P)) {
 156             Polyhedron_Free(P);
 157             continue;
 158         }
 159         barvinok_count_with_options(P, &tmp, options);
 160         Polyhedron_Free(P);
 161         if (value_zero_p(tmp))
 162             continue;
 163         QQ c2(0, 1);
 164         value2zz(tmp, c2.n);
 165         c2 *= n.coeff[j];
 166         c += c2;
 167     }
 168     Matrix_Free(C);
 169     value_clear(tmp);
 170     return c;
 171 }
 172
 173 bool short_rat::reduced()
 174 {
 175     int dim = n.power.NumCols();
 176     lex_order_terms(this);
 177     if (n.power.NumRows() % 2 == 0) {
 178         if (n.coeff[0].n == -n.coeff[1].n &&
 179             n.coeff[0].d == n.coeff[1].d) {
 180             vec_ZZ step = n.power[1] - n.power[0];
 181             int k;
 182             for (k = 1; k < n.power.NumRows()/2; ++k) {
 183                 if (n.coeff[2*k].n != -n.coeff[2*k+1].n ||
 184                     n.coeff[2*k].d != n.coeff[2*k+1].d)
 185                     break;
 186                 if (step != n.power[2*k+1] - n.power[2*k])
 187                     break;
 188             }
 189             if (k == n.power.NumRows()/2) {
 190                 for (k = 0; k < d.power.NumRows(); ++k)
 191                     if (d.power[k] == step)
 192                         break;
 193                 if (k < d.power.NumRows()) {
 194                     for (++k; k < d.power.NumRows(); ++k)
 195                         d.power[k-1] = d.power[k];
 196                     d.power.SetDims(k-1, dim);
 197                     for (k = 1; k < n.power.NumRows()/2; ++k) {
 198                         n.coeff[k] = n.coeff[2*k];
 199                         n.power[k] = n.power[2*k];
 200                     }
 201                     n.coeff.SetLength(k);
 202                     n.power.SetDims(k, dim);
 203                     return true;
 204                 }
 205             }
 206         }
 207     }
 208     return false;
 209 }
 210
 211 gen_fun::gen_fun(Value c)
 212 {
 213     short_rat *r = new short_rat(c);
 214     context = Universe_Polyhedron(0);
 215     term.insert(r);
 216 }
 217
 218 void gen_fun::add(const QQ& c, const vec_ZZ& num, const mat_ZZ& den)
 219 {
 220     if (c.n == 0)
 221         return;
 222
 223     add(new short_rat(c, num, den));
 224 }
 225
 226 void gen_fun::add(short_rat *r)
 227 {
 228     short_rat_list::iterator i = term.find(r);
 229     while (i != term.end()) {
 230         (*i)->add(r);
 231         if ((*i)->n.coeff.length() == 0) {
 232             delete *i;
 233             term.erase(i);
 234         } else if ((*i)->reduced()) {
 235             delete r;
 236             /* we've modified term[i], so remove it
 237              * and add it back again
 238              */
 239             r = *i;
 240             term.erase(i);
 241             i = term.find(r);
 242             continue;
 243         }
 244         delete r;
 245         return;
 246     }
 247
 248     term.insert(r);
 249 }
 250
 251 void gen_fun::add(const QQ& c, const gen_fun *gf, barvinok_options *options)
 252 {
 253     Polyhedron *U = DomainUnion(context, gf->context, options->MaxRays);
 254     Polyhedron *C = DomainConvex(U, options->MaxRays);
 255     Domain_Free(U);
 256     Domain_Free(context);
 257     context = C;
 258
 259     add(c, gf);
 260 }
 261
 262 void gen_fun::add(const QQ& c, const gen_fun *gf)
 263 {
 264     QQ p;
 265     for (short_rat_list::iterator i = gf->term.begin(); i != gf->term.end(); ++i) {
 266         for (int j = 0; j < (*i)->n.power.NumRows(); ++j) {
 267             p = c;
 268             p *= (*i)->n.coeff[j];
 269             add(p, (*i)->n.power[j], (*i)->d.power);
 270         }
 271     }
 272 }
 273
 274 static void split_param_compression(Matrix *CP, mat_ZZ& map, vec_ZZ& offset)
 275 {
 276     Matrix *T = Transpose(CP);
 277     matrix2zz(T, map, T->NbRows-1, T->NbColumns-1);
 278     values2zz(T->p[T->NbRows-1], offset, T->NbColumns-1);
 279     Matrix_Free(T);
 280 }
 281
 282 /*
 283  * Perform the substitution specified by CP
 284  *
 285  * CP is a homogeneous matrix that maps a set of "compressed parameters"
 286  * to the original set of parameters.
 287  *
 288  * This function is applied to a gen_fun computed with the compressed parameters
 289  * and adapts it to refer to the original parameters.
 290  *
 291  * That is, if y are the compressed parameters and x = A y + b are the original
 292  * parameters, then we want the coefficient of the monomial t^y in the original
 293  * generating function to be the coefficient of the monomial u^x in the resulting
 294  * generating function.
 295  * The original generating function has the form
 296  *
 297  *        a t^m/(1-t^n) = a t^m + a t^{m+n} + a t^{m+2n} + ...
 298  *
 299  * Since each term t^y should correspond to a term u^x, with x = A y + b, we want
 300  *
 301  *         a u^{A m + b} + a u^{A (m+n) + b} + a u^{A (m+2n) +b} + ... =
 302  *
 303  *         = a u^{A m + b}/(1-u^{A n})
 304  *
 305  * Therefore, we multiply the powers m and n in both numerator and denominator by A
 306  * and add b to the power in the numerator.
 307  * Since the above powers are stored as row vectors m^T and n^T,
 308  * we compute, say, m'^T = m^T A^T to obtain m' = A m.
 309  *
 310  * The pair (map, offset) contains the same information as CP.
 311  * map is the transpose of the linear part of CP, while offset is the constant part.
 312  */
 313 void gen_fun::substitute(Matrix *CP)
 314 {
 315     mat_ZZ map;
 316     vec_ZZ offset;
 317     split_param_compression(CP, map, offset);
 318     Polyhedron *C = Polyhedron_Image(context, CP, 0);
 319     Polyhedron_Free(context);
 320     context = C;
 321
 322     short_rat_list new_term;
 323     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 324         short_rat *r = (*i);
 325         r->d.power *= map;
 326         r->n.power *= map;
 327         for (int j = 0; j < r->n.power.NumRows(); ++j)
 328             r->n.power[j] += offset;
 329         r->normalize();
 330         new_term.insert(r);
 331     }
 332     term.swap(new_term);
 333 }
 334
 335 struct parallel_cones {
 336     int     *pos;
 337     vector<pair<Vector *, QQ> >     vertices;
 338     parallel_cones(int *pos) : pos(pos) {}
 339 };
 340
 341 struct parallel_polytopes {
 342     gf_base *red;
 343     Polyhedron *context;
 344     Matrix *Constraints;
 345     Matrix *CP, *T;
 346     int dim;
 347     int nparam;
 348     vector<parallel_cones>    cones;
 349     barvinok_options    *options;
 350
 351     parallel_polytopes(int n, Polyhedron *context, int nparam,
 352                        barvinok_options *options) :
 353                         context(context), dim(-1), nparam(nparam),
 354                         options(options) {
 355         red = NULL;
 356         Constraints = NULL;
 357         CP = NULL;
 358         T = NULL;
 359     }
 360     bool add(const QQ& c, Polyhedron *P) {
 361         int i;
 362
 363         for (i = 0; i < P->NbEq; ++i)
 364             if (First_Non_Zero(P->Constraint[i]+1,
 365                                P->Dimension-nparam) == -1)
 366                 break;
 367         if (i < P->NbEq)
 368             return false;
 369
 370         Polyhedron *Q = remove_equalities_p(Polyhedron_Copy(P), P->Dimension-nparam,
 371                                             NULL, options->MaxRays);
 372         POL_ENSURE_VERTICES(Q);
 373         if (emptyQ(Q)) {
 374             Polyhedron_Free(Q);
 375             return true;
 376         }
 377
 378         if (Q->NbEq != 0) {
 379             Polyhedron *R;
 380             if (!CP) {
 381                 Matrix *M;
 382                 M = Matrix_Alloc(Q->NbEq, Q->Dimension+2);
 383                 Vector_Copy(Q->Constraint[0], M->p[0], Q->NbEq * (Q->Dimension+2));
 384                 CP = compress_parms(M, nparam);
 385                 T = align_matrix(CP, Q->Dimension+1);
 386                 Matrix_Free(M);
 387             }
 388             R = Polyhedron_Preimage(Q, T, options->MaxRays);
 389             Polyhedron_Free(Q);
 390             Q = remove_equalities_p(R, R->Dimension-nparam, NULL,
 391                                     options->MaxRays);
 392         }
 393         assert(Q->NbEq == 0);
 394
 395         if (First_Non_Zero(Q->Constraint[Q->NbConstraints-1]+1, Q->Dimension) == -1)
 396             Q->NbConstraints--;
 397
 398         if (!Constraints) {
 399             dim = Q->Dimension;
 400             red = gf_base::create(Polyhedron_Copy(context), dim, nparam, options);
 401             red->base->init(Q);
 402             Constraints = Matrix_Alloc(Q->NbConstraints, Q->Dimension);
 403             for (int i = 0; i < Q->NbConstraints; ++i) {
 404                 Vector_Copy(Q->Constraint[i]+1, Constraints->p[i], Q->Dimension);
 405             }
 406         } else {
 407             assert(Q->Dimension == dim);
 408             for (int i = 0; i < Q->NbConstraints; ++i) {
 409                 int j;
 410                 for (j = 0; j < Constraints->NbRows; ++j)
 411                     if (Vector_Equal(Q->Constraint[i]+1, Constraints->p[j],
 412                                         Q->Dimension))
 413                         break;
 414                 assert(j < Constraints->NbRows);
 415             }
 416         }
 417
 418         for (int i = 0; i < Q->NbRays; ++i) {
 419             if (!value_pos_p(Q->Ray[i][dim+1]))
 420                 continue;
 421
 422             Polyhedron *C = supporting_cone(Q, i);
 423
 424             if (First_Non_Zero(C->Constraint[C->NbConstraints-1]+1,
 425                                C->Dimension) == -1)
 426                 C->NbConstraints--;
 427
 428             int *pos = new int[1+C->NbConstraints];
 429             pos[0] = C->NbConstraints;
 430             int l = 0;
 431             for (int k = 0; k < Constraints->NbRows; ++k) {
 432                 for (int j = 0; j < C->NbConstraints; ++j) {
 433                     if (Vector_Equal(C->Constraint[j]+1, Constraints->p[k],
 434                                      C->Dimension)) {
 435                         pos[1+l++] = k;
 436                         break;
 437                     }
 438                 }
 439             }
 440             assert(l == C->NbConstraints);
 441
 442             int j;
 443             for (j = 0; j < cones.size(); ++j)
 444                 if (!memcmp(pos, cones[j].pos, (1+C->NbConstraints)*sizeof(int)))
 445                     break;
 446             if (j == cones.size())
 447                 cones.push_back(parallel_cones(pos));
 448             else
 449                 delete [] pos;
 450
 451             Polyhedron_Free(C);
 452
 453             int k;
 454             for (k = 0; k < cones[j].vertices.size(); ++k)
 455                 if (Vector_Equal(Q->Ray[i]+1, cones[j].vertices[k].first->p,
 456                                  Q->Dimension+1))
 457                     break;
 458
 459             if (k == cones[j].vertices.size()) {
 460                 Vector *vertex = Vector_Alloc(Q->Dimension+1);
 461                 Vector_Copy(Q->Ray[i]+1, vertex->p, Q->Dimension+1);
 462                 cones[j].vertices.push_back(pair<Vector*,QQ>(vertex, c));
 463             } else {
 464                 cones[j].vertices[k].second += c;
 465                 if (cones[j].vertices[k].second.n == 0) {
 466                     int size = cones[j].vertices.size();
 467                     Vector_Free(cones[j].vertices[k].first);
 468                     if (k < size-1)
 469                         cones[j].vertices[k] = cones[j].vertices[size-1];
 470                     cones[j].vertices.pop_back();
 471                 }
 472             }
 473         }
 474
 475         Polyhedron_Free(Q);
 476         return true;
 477     }
 478     gen_fun *compute() {
 479         if (!red)
 480             return NULL;
 481         for (int i = 0; i < cones.size(); ++i) {
 482             Matrix *M = Matrix_Alloc(cones[i].pos[0], 1+Constraints->NbColumns+1);
 483             Polyhedron *Cone;
 484             for (int j = 0; j <cones[i].pos[0]; ++j) {
 485                 value_set_si(M->p[j][0], 1);
 486                 Vector_Copy(Constraints->p[cones[i].pos[1+j]], M->p[j]+1,
 487                             Constraints->NbColumns);
 488             }
 489             Cone = Constraints2Polyhedron(M, options->MaxRays);
 490             Matrix_Free(M);
 491             for (int j = 0; j < cones[i].vertices.size(); ++j) {
 492                 red->base->do_vertex_cone(cones[i].vertices[j].second,
 493                                           Polyhedron_Copy(Cone),
 494                                           cones[i].vertices[j].first->p, options);
 495             }
 496             Polyhedron_Free(Cone);
 497         }
 498         if (CP)
 499             red->gf->substitute(CP);
 500         return red->gf;
 501     }
 502     void print(std::ostream& os) const {
 503         for (int i = 0; i < cones.size(); ++i) {
 504             os << "[";
 505             for (int j = 0; j < cones[i].pos[0]; ++j) {
 506                 if (j)
 507                     os << ", ";
 508                 os << cones[i].pos[1+j];
 509             }
 510             os << "]" << endl;
 511             for (int j = 0; j < cones[i].vertices.size(); ++j) {
 512                 Vector_Print(stderr, P_VALUE_FMT, cones[i].vertices[j].first);
 513                 os << cones[i].vertices[j].second << endl;
 514             }
 515         }
 516     }
 517     ~parallel_polytopes() {
 518         for (int i = 0; i < cones.size(); ++i) {
 519             delete [] cones[i].pos;
 520             for (int j = 0; j < cones[i].vertices.size(); ++j)
 521                 Vector_Free(cones[i].vertices[j].first);
 522         }
 523         if (Constraints)
 524             Matrix_Free(Constraints);
 525         if (CP)
 526             Matrix_Free(CP);
 527         if (T)
 528             Matrix_Free(T);
 529         delete red;
 530     }
 531 };
 532
 533 gen_fun *gen_fun::Hadamard_product(const gen_fun *gf, barvinok_options *options)
 534 {
 535     QQ one(1, 1);
 536     Polyhedron *C = DomainIntersection(context, gf->context, options->MaxRays);
 537     Polyhedron *U = Universe_Polyhedron(C->Dimension);
 538     gen_fun *sum = new gen_fun(C);
 539     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 540         for (short_rat_list::iterator i2 = gf->term.begin(); i2 != gf->term.end();
 541                                                              ++i2) {
 542             int d = (*i)->d.power.NumCols();
 543             int k1 = (*i)->d.power.NumRows();
 544             int k2 = (*i2)->d.power.NumRows();
 545             assert((*i)->d.power.NumCols() == (*i2)->d.power.NumCols());
 546
 547             parallel_polytopes pp((*i)->n.power.NumRows() *
 548                                   (*i2)->n.power.NumRows(),
 549                                   sum->context, d, options);
 550
 551             for (int j = 0; j < (*i)->n.power.NumRows(); ++j) {
 552                 for (int j2 = 0; j2 < (*i2)->n.power.NumRows(); ++j2) {
 553                     Matrix *M = Matrix_Alloc(k1+k2+d+d, 1+k1+k2+d+1);
 554                     for (int k = 0; k < k1+k2; ++k) {
 555                         value_set_si(M->p[k][0], 1);
 556                         value_set_si(M->p[k][1+k], 1);
 557                     }
 558                     for (int k = 0; k < d; ++k) {
 559                         value_set_si(M->p[k1+k2+k][1+k1+k2+k], -1);
 560                         zz2value((*i)->n.power[j][k], M->p[k1+k2+k][1+k1+k2+d]);
 561                         for (int l = 0; l < k1; ++l)
 562                             zz2value((*i)->d.power[l][k], M->p[k1+k2+k][1+l]);
 563                     }
 564                     for (int k = 0; k < d; ++k) {
 565                         value_set_si(M->p[k1+k2+d+k][1+k1+k2+k], -1);
 566                         zz2value((*i2)->n.power[j2][k],
 567                                  M->p[k1+k2+d+k][1+k1+k2+d]);
 568                         for (int l = 0; l < k2; ++l)
 569                             zz2value((*i2)->d.power[l][k],
 570                                      M->p[k1+k2+d+k][1+k1+l]);
 571                     }
 572                     Polyhedron *P = Constraints2Polyhedron(M, options->MaxRays);
 573                     Matrix_Free(M);
 574
 575                     QQ c = (*i)->n.coeff[j];
 576                     c *= (*i2)->n.coeff[j2];
 577                     if (!pp.add(c, P)) {
 578                         gen_fun *t = barvinok_series_with_options(P, U, options);
 579                         sum->add(c, t);
 580                         delete t;
 581                     }
 582
 583                     Polyhedron_Free(P);
 584                 }
 585             }
 586
 587             gen_fun *t = pp.compute();
 588             if (t) {
 589                 sum->add(one, t);
 590                 delete t;
 591             }
 592         }
 593     }
 594     Polyhedron_Free(U);
 595     return sum;
 596 }
 597
 598 void gen_fun::add_union(gen_fun *gf, barvinok_options *options)
 599 {
 600     QQ one(1, 1), mone(-1, 1);
 601
 602     gen_fun *hp = Hadamard_product(gf, options);
 603     add(one, gf);
 604     add(mone, hp);
 605     delete hp;
 606 }
 607
 608 static void Polyhedron_Shift(Polyhedron *P, Vector *offset)
 609 {
 610     Value tmp;
 611     value_init(tmp);
 612     for (int i = 0; i < P->NbConstraints; ++i) {
 613         Inner_Product(P->Constraint[i]+1, offset->p, P->Dimension, &tmp);
 614         value_subtract(P->Constraint[i][1+P->Dimension],
 615                        P->Constraint[i][1+P->Dimension], tmp);
 616     }
 617     for (int i = 0; i < P->NbRays; ++i) {
 618         if (value_notone_p(P->Ray[i][0]))
 619             continue;
 620         if (value_zero_p(P->Ray[i][1+P->Dimension]))
 621             continue;
 622         Vector_Combine(P->Ray[i]+1, offset->p, P->Ray[i]+1,
 623                        P->Ray[i][0], P->Ray[i][1+P->Dimension], P->Dimension);
 624     }
 625     value_clear(tmp);
 626 }
 627
 628 void gen_fun::shift(const vec_ZZ& offset)
 629 {
 630     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 631         for (int j = 0; j < (*i)->n.power.NumRows(); ++j)
 632             (*i)->n.power[j] += offset;
 633
 634     Vector *v = Vector_Alloc(offset.length());
 635     zz2values(offset, v->p);
 636     Polyhedron_Shift(context, v);
 637     Vector_Free(v);
 638 }
 639
 640 /* Divide the generating functin by 1/(1-z^power).
 641  * The effect on the corresponding explicit function f(x) is
 642  * f'(x) = \sum_{i=0}^\infty f(x - i * power)
 643  */
 644 void gen_fun::divide(const vec_ZZ& power)
 645 {
 646     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 647         int r = (*i)->d.power.NumRows();
 648         int c = (*i)->d.power.NumCols();
 649         (*i)->d.power.SetDims(r+1, c);
 650         (*i)->d.power[r] = power;
 651     }
 652
 653     Vector *v = Vector_Alloc(1+power.length()+1);
 654     value_set_si(v->p[0], 1);
 655     zz2values(power, v->p+1);
 656     Polyhedron *C = AddRays(v->p, 1, context, context->NbConstraints+1);
 657     Vector_Free(v);
 658     Polyhedron_Free(context);
 659     context = C;
 660 }
 661
 662 static void print_power(std::ostream& os, const QQ& c, const vec_ZZ& p,
 663                         unsigned int nparam, char **param_name)
 664 {
 665     bool first = true;
 666
 667     for (int i = 0; i < p.length(); ++i) {
 668         if (p[i] == 0)
 669             continue;
 670         if (first) {
 671             if (c.n == -1 && c.d == 1)
 672                 os << "-";
 673             else if (c.n != 1 || c.d != 1) {
 674                 os << c.n;
 675                 if (c.d != 1)
 676                     os << "/" << c.d;
 677                 os << "*";
 678             }
 679             first = false;
 680         } else
 681             os << "*";
 682         if (i < nparam)
 683             os << param_name[i];
 684         else
 685             os << "x" << i;
 686         if (p[i] == 1)
 687             continue;
 688         if (p[i] < 0)
 689             os << "^(" << p[i] << ")";
 690         else
 691             os << "^" << p[i];
 692     }
 693     if (first) {
 694         os << c.n;
 695         if (c.d != 1)
 696             os << "/" << c.d;
 697     }
 698 }
 699
 700 void short_rat::print(std::ostream& os, unsigned int nparam, char **param_name) const
 701 {
 702     QQ mone(-1, 1);
 703     os << "(";
 704     for (int j = 0; j < n.coeff.length(); ++j) {
 705         if (j != 0 && n.coeff[j].n >= 0)
 706             os << "+";
 707         print_power(os, n.coeff[j], n.power[j], nparam, param_name);
 708     }
 709     os << ")/(";
 710     for (int j = 0; j < d.power.NumRows(); ++j) {
 711         if (j != 0)
 712             os << " * ";
 713         os << "(1";
 714         print_power(os, mone, d.power[j], nparam, param_name);
 715         os << ")";
 716     }
 717     os << ")";
 718 }
 719
 720 void gen_fun::print(std::ostream& os, unsigned int nparam, char **param_name) const
 721 {
 722     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 723         if (i != term.begin())
 724             os << " + ";
 725         (*i)->print(os, nparam, param_name);
 726     }
 727 }
 728
 729 std::ostream & operator<< (std::ostream & os, const short_rat& r)
 730 {
 731     os << r.n.coeff << endl;
 732     os << r.n.power << endl;
 733     os << r.d.power << endl;
 734     return os;
 735 }
 736
 737 std::ostream & operator<< (std::ostream & os, const Polyhedron& P)
 738 {
 739     char *str;
 740     void (*gmp_free)(void *, size_t);
 741     mp_get_memory_functions(NULL, NULL, &gmp_free);
 742     os << P.NbConstraints << " " << P.Dimension+2 << endl;
 743     for (int i = 0; i < P.NbConstraints; ++i) {
 744         for (int j = 0; j < P.Dimension+2; ++j) {
 745             str = mpz_get_str(0, 10, P.Constraint[i][j]);
 746             os << std::setw(4) << str << " ";
 747             (*gmp_free)(str, strlen(str)+1);
 748         }
 749         os << endl;
 750     }
 751     return os;
 752 }
 753
 754 std::ostream & operator<< (std::ostream & os, const gen_fun& gf)
 755 {
 756     os << *gf.context << endl;
 757     os << endl;
 758     os << gf.term.size() << endl;
 759     for (short_rat_list::iterator i = gf.term.begin(); i != gf.term.end(); ++i)
 760         os << **i;
 761     return os;
 762 }
 763
 764 gen_fun *gen_fun::read(std::istream& is, barvinok_options *options)
 765 {
 766     Matrix *M = Matrix_Read(is);
 767     Polyhedron *C = Constraints2Polyhedron(M, options->MaxRays);
 768     Matrix_Free(M);
 769
 770     gen_fun *gf = new gen_fun(C);
 771
 772     int n;
 773     is >> n;
 774
 775     vec_QQ c;
 776     mat_ZZ num;
 777     mat_ZZ den;
 778     for (int i = 0; i < n; ++i) {
 779         is >> c >> num >> den;
 780         gf->add(new short_rat(c, num, den));
 781     }
 782
 783     return gf;
 784 }
 785
 786 gen_fun::operator evalue *() const
 787 {
 788     evalue *EP = NULL;
 789     evalue factor;
 790     value_init(factor.d);
 791     value_init(factor.x.n);
 792     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 793         unsigned nvar = (*i)->d.power.NumRows();
 794         unsigned nparam = (*i)->d.power.NumCols();
 795         Matrix *C = Matrix_Alloc(nparam + nvar, 1 + nvar + nparam + 1);
 796         mat_ZZ& d = (*i)->d.power;
 797         Polyhedron *U = context;
 798
 799         for (int j = 0; j < (*i)->n.coeff.length(); ++j) {
 800             for (int r = 0; r < nparam; ++r) {
 801                 value_set_si(C->p[r][0], 0);
 802                 for (int c = 0; c < nvar; ++c) {
 803                     zz2value(d[c][r], C->p[r][1+c]);
 804                 }
 805                 Vector_Set(&C->p[r][1+nvar], 0, nparam);
 806                 value_set_si(C->p[r][1+nvar+r], -1);
 807                 zz2value((*i)->n.power[j][r], C->p[r][1+nvar+nparam]);
 808             }
 809             for (int r = 0; r < nvar; ++r) {
 810                 value_set_si(C->p[nparam+r][0], 1);
 811                 Vector_Set(&C->p[nparam+r][1], 0, nvar + nparam + 1);
 812                 value_set_si(C->p[nparam+r][1+r], 1);
 813             }
 814             Polyhedron *P = Constraints2Polyhedron(C, 0);
 815             evalue *E = barvinok_enumerate_ev(P, U, 0);
 816             Polyhedron_Free(P);
 817             if (EVALUE_IS_ZERO(*E)) {
 818                 evalue_free(E);
 819                 continue;
 820             }
 821             zz2value((*i)->n.coeff[j].n, factor.x.n);
 822             zz2value((*i)->n.coeff[j].d, factor.d);
 823             emul(&factor, E);
 824             if (!EP)
 825                 EP = E;
 826             else {
 827                 eadd(E, EP);
 828                 evalue_free(E);
 829             }
 830         }
 831         Matrix_Free(C);
 832     }
 833     value_clear(factor.d);
 834     value_clear(factor.x.n);
 835     return EP ? EP : evalue_zero();
 836 }
 837
 838 ZZ gen_fun::coefficient(Value* params, barvinok_options *options) const
 839 {
 840     if (!in_domain(context, params))
 841         return ZZ::zero();
 842
 843     QQ sum(0, 1);
 844
 845     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 846         sum += (*i)->coefficient(params, options);
 847
 848     assert(sum.d == 1);
 849     return sum.n;
 850 }
 851
 852 void gen_fun::coefficient(Value* params, Value* c) const
 853 {
 854     barvinok_options *options = barvinok_options_new_with_defaults();
 855
 856     ZZ coeff = coefficient(params, options);
 857
 858     zz2value(coeff, *c);
 859
 860     barvinok_options_free(options);
 861 }
 862
 863 gen_fun *gen_fun::summate(int nvar, barvinok_options *options) const
 864 {
 865     int dim = context->Dimension;
 866     int nparam = dim - nvar;
 867     reducer *red;
 868     gen_fun *gf;
 869
 870     if (options->incremental_specialization == 1) {
 871         red = new partial_ireducer(Polyhedron_Project(context, nparam), dim, nparam);
 872     } else
 873         red = new partial_reducer(Polyhedron_Project(context, nparam), dim, nparam);
 874     for (;;) {
 875         try {
 876             red->init(context);
 877             for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 878                 red->reduce((*i)->n.coeff, (*i)->n.power, (*i)->d.power);
 879             break;
 880         } catch (OrthogonalException &e) {
 881             red->reset();
 882         }
 883     }
 884     gf = red->get_gf();
 885     delete red;
 886     return gf;
 887 }
 888
 889 /* returns true if the set was finite and false otherwise */
 890 bool gen_fun::summate(Value *sum) const
 891 {
 892     if (term.size() == 0) {
 893         value_set_si(*sum, 0);
 894         return true;
 895     }
 896
 897     int maxlen = 0;
 898     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 899         if ((*i)->d.power.NumRows() > maxlen)
 900             maxlen = (*i)->d.power.NumRows();
 901
 902     infinite_icounter cnt((*term.begin())->d.power.NumCols(), maxlen);
 903     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 904         cnt.reduce((*i)->n.coeff, (*i)->n.power, (*i)->d.power);
 905
 906     for (int i = 1; i <= maxlen; ++i)
 907         if (value_notzero_p(mpq_numref(cnt.count[i]))) {
 908             value_set_si(*sum, -1);
 909             return false;
 910         }
 911
 912     assert(value_one_p(mpq_denref(cnt.count[0])));
 913     value_assign(*sum, mpq_numref(cnt.count[0]));
 914     return true;
 915 }