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