genfun.cc

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