ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <vector>
  24 #include <stdexcept>
  25
  26 #include "mul.h"
  27 #include "add.h"
  28 #include "power.h"
  29 #include "matrix.h"
  30 #include "archive.h"
  31 #include "debugmsg.h"
  32 #include "utils.h"
  33
  34 namespace GiNaC {
  35
  36 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  37
  38 //////////
  39 // default ctor, dctor, copy ctor assignment operator and helpers
  40 //////////
  41
  42 mul::mul()
  43 {
  44         debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT);
  45         tinfo_key = TINFO_mul;
  46 }
  47
  48 DEFAULT_COPY(mul)
  49 DEFAULT_DESTROY(mul)
  50
  51 //////////
  52 // other ctors
  53 //////////
  54
  55 // public
  56
  57 mul::mul(const ex & lh, const ex & rh)
  58 {
  59         debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT);
  60         tinfo_key = TINFO_mul;
  61         overall_coeff = _ex1();
  62         construct_from_2_ex(lh,rh);
  63         GINAC_ASSERT(is_canonical());
  64 }
  65
  66 mul::mul(const exvector & v)
  67 {
  68         debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT);
  69         tinfo_key = TINFO_mul;
  70         overall_coeff = _ex1();
  71         construct_from_exvector(v);
  72         GINAC_ASSERT(is_canonical());
  73 }
  74
  75 mul::mul(const epvector & v)
  76 {
  77         debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT);
  78         tinfo_key = TINFO_mul;
  79         overall_coeff = _ex1();
  80         construct_from_epvector(v);
  81         GINAC_ASSERT(is_canonical());
  82 }
  83
  84 mul::mul(const epvector & v, const ex & oc)
  85 {
  86         debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
  87         tinfo_key = TINFO_mul;
  88         overall_coeff = oc;
  89         construct_from_epvector(v);
  90         GINAC_ASSERT(is_canonical());
  91 }
  92
  93 mul::mul(epvector * vp, const ex & oc)
  94 {
  95         debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
  96         tinfo_key = TINFO_mul;
  97         GINAC_ASSERT(vp!=0);
  98         overall_coeff = oc;
  99         construct_from_epvector(*vp);
 100         delete vp;
 101         GINAC_ASSERT(is_canonical());
 102 }
 103
 104 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 105 {
 106         debugmsg("mul ctor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 107         tinfo_key = TINFO_mul;
 108         exvector factors;
 109         factors.reserve(3);
 110         factors.push_back(lh);
 111         factors.push_back(mh);
 112         factors.push_back(rh);
 113         overall_coeff = _ex1();
 114         construct_from_exvector(factors);
 115         GINAC_ASSERT(is_canonical());
 116 }
 117
 118 //////////
 119 // archiving
 120 //////////
 121
 122 DEFAULT_ARCHIVING(mul)
 123
 124 //////////
 125 // functions overriding virtual functions from bases classes
 126 //////////
 127
 128 // public
 129
 130 void mul::print(const print_context & c, unsigned level) const
 131 {
 132         debugmsg("mul print", LOGLEVEL_PRINT);
 133
 134         if (is_a<print_tree>(c)) {
 135
 136                 inherited::print(c, level);
 137
 138         } else if (is_a<print_csrc>(c)) {
 139
 140                 if (precedence() <= level)
 141                         c.s << "(";
 142
 143                 if (!overall_coeff.is_equal(_ex1())) {
 144                         overall_coeff.bp->print(c, precedence());
 145                         c.s << "*";
 146                 }
 147
 148                 // Print arguments, separated by "*" or "/"
 149                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 150                 while (it != itend) {
 151
 152                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 153                         if (it == seq.begin() && ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 154                                 if (is_a<print_csrc_cl_N>(c))
 155                                         c.s << "recip(";
 156                                 else
 157                                         c.s << "1.0/";
 158                         }
 159
 160                         // If the exponent is 1 or -1, it is left out
 161                         if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 162                                 it->rest.print(c, precedence());
 163                         else {
 164                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 165                                 (ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
 166                         }
 167
 168                         // Separator is "/" for negative integer powers, "*" otherwise
 169                         ++it;
 170                         if (it != itend) {
 171                                 if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 172                                         c.s << "/";
 173                                 else
 174                                         c.s << "*";
 175                         }
 176                 }
 177
 178                 if (precedence() <= level)
 179                         c.s << ")";
 180
 181         } else {
 182
 183                 if (precedence() <= level) {
 184                         if (is_a<print_latex>(c))
 185                                 c.s << "{(";
 186                         else
 187                                 c.s << "(";
 188                 }
 189
 190                 bool first = true;
 191
 192                 // First print the overall numeric coefficient
 193                 numeric coeff = ex_to<numeric>(overall_coeff);
 194                 if (coeff.csgn() == -1)
 195                         c.s << '-';
 196                 if (!coeff.is_equal(_num1()) &&
 197                         !coeff.is_equal(_num_1())) {
 198                         if (coeff.is_rational()) {
 199                                 if (coeff.is_negative())
 200                                         (-coeff).print(c);
 201                                 else
 202                                         coeff.print(c);
 203                         } else {
 204                                 if (coeff.csgn() == -1)
 205                                         (-coeff).print(c, precedence());
 206                                 else
 207                                         coeff.print(c, precedence());
 208                         }
 209                         if (is_a<print_latex>(c))
 210                                 c.s << ' ';
 211                         else
 212                                 c.s << '*';
 213                 }
 214
 215                 // Then proceed with the remaining factors
 216                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 217                 while (it != itend) {
 218                         if (!first) {
 219                                 if (is_a<print_latex>(c))
 220                                         c.s << ' ';
 221                                 else
 222                                         c.s << '*';
 223                         } else {
 224                                 first = false;
 225                         }
 226                         recombine_pair_to_ex(*it).print(c, precedence());
 227                         ++it;
 228                 }
 229
 230                 if (precedence() <= level) {
 231                         if (is_a<print_latex>(c))
 232                                 c.s << ")}";
 233                         else
 234                                 c.s << ")";
 235                 }
 236         }
 237 }
 238
 239 bool mul::info(unsigned inf) const
 240 {
 241         switch (inf) {
 242                 case info_flags::polynomial:
 243                 case info_flags::integer_polynomial:
 244                 case info_flags::cinteger_polynomial:
 245                 case info_flags::rational_polynomial:
 246                 case info_flags::crational_polynomial:
 247                 case info_flags::rational_function: {
 248                         epvector::const_iterator i = seq.begin(), end = seq.end();
 249                         while (i != end) {
 250                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 251                                         return false;
 252                                 ++i;
 253                         }
 254                         return overall_coeff.info(inf);
 255                 }
 256                 case info_flags::algebraic: {
 257                         epvector::const_iterator i = seq.begin(), end = seq.end();
 258                         while (i != end) {
 259                                 if ((recombine_pair_to_ex(*i).info(inf)))
 260                                         return true;
 261                                 ++i;
 262                         }
 263                         return false;
 264                 }
 265         }
 266         return inherited::info(inf);
 267 }
 268
 269 int mul::degree(const ex & s) const
 270 {
 271         // Sum up degrees of factors
 272         int deg_sum = 0;
 273         epvector::const_iterator i = seq.begin(), end = seq.end();
 274         while (i != end) {
 275                 if (ex_to<numeric>(i->coeff).is_integer())
 276                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 277                 ++i;
 278         }
 279         return deg_sum;
 280 }
 281
 282 int mul::ldegree(const ex & s) const
 283 {
 284         // Sum up degrees of factors
 285         int deg_sum = 0;
 286         epvector::const_iterator i = seq.begin(), end = seq.end();
 287         while (i != end) {
 288                 if (ex_to<numeric>(i->coeff).is_integer())
 289                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 290                 ++i;
 291         }
 292         return deg_sum;
 293 }
 294
 295 ex mul::coeff(const ex & s, int n) const
 296 {
 297         exvector coeffseq;
 298         coeffseq.reserve(seq.size()+1);
 299
 300         if (n==0) {
 301                 // product of individual coeffs
 302                 // if a non-zero power of s is found, the resulting product will be 0
 303                 epvector::const_iterator i = seq.begin(), end = seq.end();
 304                 while (i != end) {
 305                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 306                         ++i;
 307                 }
 308                 coeffseq.push_back(overall_coeff);
 309                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 310         }
 311
 312         epvector::const_iterator i = seq.begin(), end = seq.end();
 313         bool coeff_found = false;
 314         while (i != end) {
 315                 ex t = recombine_pair_to_ex(*i);
 316                 ex c = t.coeff(s, n);
 317                 if (!c.is_zero()) {
 318                         coeffseq.push_back(c);
 319                         coeff_found = 1;
 320                 } else {
 321                         coeffseq.push_back(t);
 322                 }
 323                 ++i;
 324         }
 325         if (coeff_found) {
 326                 coeffseq.push_back(overall_coeff);
 327                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 328         }
 329
 330         return _ex0();
 331 }
 332
 333 ex mul::eval(int level) const
 334 {
 335         // simplifications  *(...,x;0) -> 0
 336         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 337         //                  *(x;1) -> x
 338         //                  *(;c) -> c
 339
 340         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 341
 342         epvector *evaled_seqp = evalchildren(level);
 343         if (evaled_seqp) {
 344                 // do more evaluation later
 345                 return (new mul(evaled_seqp,overall_coeff))->
 346                            setflag(status_flags::dynallocated);
 347         }
 348
 349 #ifdef DO_GINAC_ASSERT
 350         epvector::const_iterator i = seq.begin(), end = seq.end();
 351         while (i != end) {
 352                 GINAC_ASSERT((!is_ex_exactly_of_type(i->rest, mul)) ||
 353                              (!(ex_to<numeric>(i->coeff).is_integer())));
 354                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 355                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 356                     print(print_tree(std::cerr));
 357                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric));
 358                 /* for paranoia */
 359                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 360                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 361                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 362                 /* end paranoia */
 363                 ++i;
 364         }
 365 #endif // def DO_GINAC_ASSERT
 366
 367         if (flags & status_flags::evaluated) {
 368                 GINAC_ASSERT(seq.size()>0);
 369                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1()));
 370                 return *this;
 371         }
 372
 373         int seq_size = seq.size();
 374         if (overall_coeff.is_zero()) {
 375                 // *(...,x;0) -> 0
 376                 return _ex0();
 377         } else if (seq_size==0) {
 378                 // *(;c) -> c
 379                 return overall_coeff;
 380         } else if (seq_size==1 && overall_coeff.is_equal(_ex1())) {
 381                 // *(x;1) -> x
 382                 return recombine_pair_to_ex(*(seq.begin()));
 383         } else if ((seq_size==1) &&
 384                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 385                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1())) {
 386                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 387                 const add & addref = ex_to<add>((*seq.begin()).rest);
 388                 epvector *distrseq = new epvector();
 389                 distrseq->reserve(addref.seq.size());
 390                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 391                 while (i != end) {
 392                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 393                         ++i;
 394                 }
 395                 return (new add(distrseq,
 396                                 ex_to<numeric>(addref.overall_coeff).
 397                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 398                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 399         }
 400         return this->hold();
 401 }
 402
 403 ex mul::evalf(int level) const
 404 {
 405         if (level==1)
 406                 return mul(seq,overall_coeff);
 407
 408         if (level==-max_recursion_level)
 409                 throw(std::runtime_error("max recursion level reached"));
 410
 411         epvector *s = new epvector();
 412         s->reserve(seq.size());
 413
 414         --level;
 415         epvector::const_iterator i = seq.begin(), end = seq.end();
 416         while (i != end) {
 417                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 418                                                            i->coeff));
 419                 ++i;
 420         }
 421         return mul(s, overall_coeff.evalf(level));
 422 }
 423
 424 ex mul::evalm(void) const
 425 {
 426         // numeric*matrix
 427         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1())
 428          && is_ex_of_type(seq[0].rest, matrix))
 429                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 430
 431         // Evaluate children first, look whether there are any matrices at all
 432         // (there can be either no matrices or one matrix; if there were more
 433         // than one matrix, it would be a non-commutative product)
 434         epvector *s = new epvector;
 435         s->reserve(seq.size());
 436
 437         bool have_matrix = false;
 438         epvector::iterator the_matrix;
 439
 440         epvector::const_iterator i = seq.begin(), end = seq.end();
 441         while (i != end) {
 442                 const ex &m = recombine_pair_to_ex(*i).evalm();
 443                 s->push_back(split_ex_to_pair(m));
 444                 if (is_ex_of_type(m, matrix)) {
 445                         have_matrix = true;
 446                         the_matrix = s->end() - 1;
 447                 }
 448                 ++i;
 449         }
 450
 451         if (have_matrix) {
 452
 453                 // The product contained a matrix. We will multiply all other factors
 454                 // into that matrix.
 455                 matrix m = ex_to<matrix>(the_matrix->rest);
 456                 s->erase(the_matrix);
 457                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 458                 return m.mul_scalar(scalar);
 459
 460         } else
 461                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 462 }
 463
 464 ex mul::simplify_ncmul(const exvector & v) const
 465 {
 466         if (seq.empty())
 467                 return inherited::simplify_ncmul(v);
 468
 469         // Find first noncommutative element and call its simplify_ncmul()
 470         epvector::const_iterator i = seq.begin(), end = seq.end();
 471         while (i != end) {
 472                 if (i->rest.return_type() == return_types::noncommutative)
 473                         return i->rest.simplify_ncmul(v);
 474                 ++i;
 475         }
 476         return inherited::simplify_ncmul(v);
 477 }
 478
 479 // protected
 480
 481 /** Implementation of ex::diff() for a product.  It applies the product rule.
 482  *  @see ex::diff */
 483 ex mul::derivative(const symbol & s) const
 484 {
 485         unsigned num = seq.size();
 486         exvector addseq;
 487         addseq.reserve(num);
 488
 489         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 490         epvector mulseq = seq;
 491         epvector::const_iterator i = seq.begin(), end = seq.end();
 492         epvector::iterator i2 = mulseq.begin();
 493         while (i != end) {
 494                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1()) *
 495                                              i->rest.diff(s));
 496                 ep.swap(*i2);
 497                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 498                 ep.swap(*i2);
 499                 ++i; ++i2;
 500         }
 501         return (new add(addseq))->setflag(status_flags::dynallocated);
 502 }
 503
 504 int mul::compare_same_type(const basic & other) const
 505 {
 506         return inherited::compare_same_type(other);
 507 }
 508
 509 bool mul::is_equal_same_type(const basic & other) const
 510 {
 511         return inherited::is_equal_same_type(other);
 512 }
 513
 514 unsigned mul::return_type(void) const
 515 {
 516         if (seq.empty()) {
 517                 // mul without factors: should not happen, but commutes
 518                 return return_types::commutative;
 519         }
 520
 521         bool all_commutative = true;
 522         epvector::const_iterator noncommutative_element; // point to first found nc element
 523
 524         epvector::const_iterator i = seq.begin(), end = seq.end();
 525         while (i != end) {
 526                 unsigned rt = i->rest.return_type();
 527                 if (rt == return_types::noncommutative_composite)
 528                         return rt; // one ncc -> mul also ncc
 529                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 530                         // first nc element found, remember position
 531                         noncommutative_element = i;
 532                         all_commutative = false;
 533                 }
 534                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 535                         // another nc element found, compare type_infos
 536                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 537                                 // diffent types -> mul is ncc
 538                                 return return_types::noncommutative_composite;
 539                         }
 540                 }
 541                 ++i;
 542         }
 543         // all factors checked
 544         return all_commutative ? return_types::commutative : return_types::noncommutative;
 545 }
 546
 547 unsigned mul::return_type_tinfo(void) const
 548 {
 549         if (seq.empty())
 550                 return tinfo_key;  // mul without factors: should not happen
 551
 552         // return type_info of first noncommutative element
 553         epvector::const_iterator i = seq.begin(), end = seq.end();
 554         while (i != end) {
 555                 if (i->rest.return_type() == return_types::noncommutative)
 556                         return i->rest.return_type_tinfo();
 557                 ++i;
 558         }
 559         // no noncommutative element found, should not happen
 560         return tinfo_key;
 561 }
 562
 563 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 564 {
 565         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 566 }
 567
 568 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 569 {
 570         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 571 }
 572
 573 expair mul::split_ex_to_pair(const ex & e) const
 574 {
 575         if (is_ex_exactly_of_type(e,power)) {
 576                 const power & powerref = ex_to<power>(e);
 577                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 578                         return expair(powerref.basis,powerref.exponent);
 579         }
 580         return expair(e,_ex1());
 581 }
 582
 583 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 584                                           const ex & c) const
 585 {
 586         // to avoid duplication of power simplification rules,
 587         // we create a temporary power object
 588         // otherwise it would be hard to correctly simplify
 589         // expression like (4^(1/3))^(3/2)
 590         if (are_ex_trivially_equal(c,_ex1()))
 591                 return split_ex_to_pair(e);
 592
 593         return split_ex_to_pair(power(e,c));
 594 }
 595
 596 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 597                                             const ex & c) const
 598 {
 599         // to avoid duplication of power simplification rules,
 600         // we create a temporary power object
 601         // otherwise it would be hard to correctly simplify
 602         // expression like (4^(1/3))^(3/2)
 603         if (are_ex_trivially_equal(c,_ex1()))
 604                 return p;
 605
 606         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 607 }
 608
 609 ex mul::recombine_pair_to_ex(const expair & p) const
 610 {
 611         if (ex_to<numeric>(p.coeff).is_equal(_num1()))
 612                 return p.rest;
 613         else
 614                 return power(p.rest,p.coeff);
 615 }
 616
 617 bool mul::expair_needs_further_processing(epp it)
 618 {
 619         if (is_ex_exactly_of_type((*it).rest,mul) &&
 620                 ex_to<numeric>((*it).coeff).is_integer()) {
 621                 // combined pair is product with integer power -> expand it
 622                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 623                 return true;
 624         }
 625         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 626                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 627                 if (!ep.is_equal(*it)) {
 628                         // combined pair is a numeric power which can be simplified
 629                         *it = ep;
 630                         return true;
 631                 }
 632                 if (ex_to<numeric>((*it).coeff).is_equal(_num1())) {
 633                         // combined pair has coeff 1 and must be moved to the end
 634                         return true;
 635                 }
 636         }
 637         return false;
 638 }
 639
 640 ex mul::default_overall_coeff(void) const
 641 {
 642         return _ex1();
 643 }
 644
 645 void mul::combine_overall_coeff(const ex & c)
 646 {
 647         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 648         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 649         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 650 }
 651
 652 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 653 {
 654         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 655         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 656         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 657         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 658 }
 659
 660 bool mul::can_make_flat(const expair & p) const
 661 {
 662         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 663         // this assertion will probably fail somewhere
 664         // it would require a more careful make_flat, obeying the power laws
 665         // probably should return true only if p.coeff is integer
 666         return ex_to<numeric>(p.coeff).is_equal(_num1());
 667 }
 668
 669 ex mul::expand(unsigned options) const
 670 {
 671         // First, expand the children
 672         epvector * expanded_seqp = expandchildren(options);
 673         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 674
 675         // Now, look for all the factors that are sums and multiply each one out
 676         // with the next one that is found while collecting the factors which are
 677         // not sums
 678         int number_of_adds = 0;
 679         ex last_expanded = _ex1();
 680         epvector non_adds;
 681         non_adds.reserve(expanded_seq.size());
 682         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 683         while (cit != last) {
 684                 if (is_ex_exactly_of_type(cit->rest, add) &&
 685                         (cit->coeff.is_equal(_ex1()))) {
 686                         ++number_of_adds;
 687                         if (is_ex_exactly_of_type(last_expanded, add)) {
 688                                 const add & add1 = ex_to<add>(last_expanded);
 689                                 const add & add2 = ex_to<add>(cit->rest);
 690                                 int n1 = add1.nops();
 691                                 int n2 = add2.nops();
 692                                 exvector distrseq;
 693                                 distrseq.reserve(n1*n2);
 694                                 for (int i1=0; i1<n1; ++i1) {
 695                                         for (int i2=0; i2<n2; ++i2) {
 696                                                 distrseq.push_back(add1.op(i1) * add2.op(i2));
 697                                         }
 698                                 }
 699                                 last_expanded = (new add(distrseq))->
 700                                                  setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 701                         } else {
 702                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 703                                 last_expanded = cit->rest;
 704                         }
 705                 } else {
 706                         non_adds.push_back(*cit);
 707                 }
 708                 ++cit;
 709         }
 710         if (expanded_seqp)
 711                 delete expanded_seqp;
 712
 713         // Now the only remaining thing to do is to multiply the factors which
 714         // were not sums into the "last_expanded" sum
 715         if (is_ex_exactly_of_type(last_expanded, add)) {
 716                 const add & finaladd = ex_to<add>(last_expanded);
 717                 exvector distrseq;
 718                 int n = finaladd.nops();
 719                 distrseq.reserve(n);
 720                 for (int i=0; i<n; ++i) {
 721                         epvector factors = non_adds;
 722                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 723                         distrseq.push_back((new mul(factors, overall_coeff))->
 724                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 725                 }
 726                 return ((new add(distrseq))->
 727                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 728         }
 729         non_adds.push_back(split_ex_to_pair(last_expanded));
 730         return (new mul(non_adds, overall_coeff))->
 731                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 732 }
 733
 734
 735 //////////
 736 // new virtual functions which can be overridden by derived classes
 737 //////////
 738
 739 // none
 740
 741 //////////
 742 // non-virtual functions in this class
 743 //////////
 744
 745
 746 /** Member-wise expand the expairs representing this sequence.  This must be
 747  *  overridden from expairseq::expandchildren() and done iteratively in order
 748  *  to allow for early cancallations and thus safe memory.
 749  *
 750  *  @see mul::expand()
 751  *  @return pointer to epvector containing expanded representation or zero
 752  *  pointer, if sequence is unchanged. */
 753 epvector * mul::expandchildren(unsigned options) const
 754 {
 755         epvector::const_iterator last = seq.end();
 756         epvector::const_iterator cit = seq.begin();
 757         while (cit!=last) {
 758                 const ex & factor = recombine_pair_to_ex(*cit);
 759                 const ex & expanded_factor = factor.expand(options);
 760                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 761
 762                         // something changed, copy seq, eval and return it
 763                         epvector *s = new epvector;
 764                         s->reserve(seq.size());
 765
 766                         // copy parts of seq which are known not to have changed
 767                         epvector::const_iterator cit2 = seq.begin();
 768                         while (cit2!=cit) {
 769                                 s->push_back(*cit2);
 770                                 ++cit2;
 771                         }
 772                         // copy first changed element
 773                         s->push_back(split_ex_to_pair(expanded_factor));
 774                         ++cit2;
 775                         // copy rest
 776                         while (cit2!=last) {
 777                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 778                                 ++cit2;
 779                         }
 780                         return s;
 781                 }
 782                 ++cit;
 783         }
 784
 785         return 0; // nothing has changed
 786 }
 787
 788 } // namespace GiNaC