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 base 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.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 /** Perform automatic term rewriting rules in this class.  In the following
 334  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 335  *  stand for such expressions that contain a plain number.
 336  *  - *(...,x;0) -> 0
 337  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 338  *  - *(x;1) -> x
 339  *  - *(;c) -> c
 340  *
 341  *  @param level cut-off in recursive evaluation */
 342 ex mul::eval(int level) const
 343 {
 344         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 345
 346         epvector *evaled_seqp = evalchildren(level);
 347         if (evaled_seqp) {
 348                 // do more evaluation later
 349                 return (new mul(evaled_seqp,overall_coeff))->
 350                            setflag(status_flags::dynallocated);
 351         }
 352
 353 #ifdef DO_GINAC_ASSERT
 354         epvector::const_iterator i = seq.begin(), end = seq.end();
 355         while (i != end) {
 356                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 357                              (!(ex_to<numeric>(i->coeff).is_integer())));
 358                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 359                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 360                     print(print_tree(std::cerr));
 361                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 362                 /* for paranoia */
 363                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 364                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 365                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 366                 /* end paranoia */
 367                 ++i;
 368         }
 369 #endif // def DO_GINAC_ASSERT
 370
 371         if (flags & status_flags::evaluated) {
 372                 GINAC_ASSERT(seq.size()>0);
 373                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1()));
 374                 return *this;
 375         }
 376
 377         int seq_size = seq.size();
 378         if (overall_coeff.is_zero()) {
 379                 // *(...,x;0) -> 0
 380                 return _ex0();
 381         } else if (seq_size==0) {
 382                 // *(;c) -> c
 383                 return overall_coeff;
 384         } else if (seq_size==1 && overall_coeff.is_equal(_ex1())) {
 385                 // *(x;1) -> x
 386                 return recombine_pair_to_ex(*(seq.begin()));
 387         } else if ((seq_size==1) &&
 388                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 389                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1())) {
 390                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 391                 const add & addref = ex_to<add>((*seq.begin()).rest);
 392                 epvector *distrseq = new epvector();
 393                 distrseq->reserve(addref.seq.size());
 394                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 395                 while (i != end) {
 396                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 397                         ++i;
 398                 }
 399                 return (new add(distrseq,
 400                                 ex_to<numeric>(addref.overall_coeff).
 401                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 402                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 403         }
 404         return this->hold();
 405 }
 406
 407 ex mul::evalf(int level) const
 408 {
 409         if (level==1)
 410                 return mul(seq,overall_coeff);
 411
 412         if (level==-max_recursion_level)
 413                 throw(std::runtime_error("max recursion level reached"));
 414
 415         epvector *s = new epvector();
 416         s->reserve(seq.size());
 417
 418         --level;
 419         epvector::const_iterator i = seq.begin(), end = seq.end();
 420         while (i != end) {
 421                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 422                                                            i->coeff));
 423                 ++i;
 424         }
 425         return mul(s, overall_coeff.evalf(level));
 426 }
 427
 428 ex mul::evalm(void) const
 429 {
 430         // numeric*matrix
 431         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1())
 432          && is_ex_of_type(seq[0].rest, matrix))
 433                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 434
 435         // Evaluate children first, look whether there are any matrices at all
 436         // (there can be either no matrices or one matrix; if there were more
 437         // than one matrix, it would be a non-commutative product)
 438         epvector *s = new epvector;
 439         s->reserve(seq.size());
 440
 441         bool have_matrix = false;
 442         epvector::iterator the_matrix;
 443
 444         epvector::const_iterator i = seq.begin(), end = seq.end();
 445         while (i != end) {
 446                 const ex &m = recombine_pair_to_ex(*i).evalm();
 447                 s->push_back(split_ex_to_pair(m));
 448                 if (is_ex_of_type(m, matrix)) {
 449                         have_matrix = true;
 450                         the_matrix = s->end() - 1;
 451                 }
 452                 ++i;
 453         }
 454
 455         if (have_matrix) {
 456
 457                 // The product contained a matrix. We will multiply all other factors
 458                 // into that matrix.
 459                 matrix m = ex_to<matrix>(the_matrix->rest);
 460                 s->erase(the_matrix);
 461                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 462                 return m.mul_scalar(scalar);
 463
 464         } else
 465                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 466 }
 467
 468 ex mul::simplify_ncmul(const exvector & v) const
 469 {
 470         if (seq.empty())
 471                 return inherited::simplify_ncmul(v);
 472
 473         // Find first noncommutative element and call its simplify_ncmul()
 474         epvector::const_iterator i = seq.begin(), end = seq.end();
 475         while (i != end) {
 476                 if (i->rest.return_type() == return_types::noncommutative)
 477                         return i->rest.simplify_ncmul(v);
 478                 ++i;
 479         }
 480         return inherited::simplify_ncmul(v);
 481 }
 482
 483 // protected
 484
 485 /** Implementation of ex::diff() for a product.  It applies the product rule.
 486  *  @see ex::diff */
 487 ex mul::derivative(const symbol & s) const
 488 {
 489         unsigned num = seq.size();
 490         exvector addseq;
 491         addseq.reserve(num);
 492
 493         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 494         epvector mulseq = seq;
 495         epvector::const_iterator i = seq.begin(), end = seq.end();
 496         epvector::iterator i2 = mulseq.begin();
 497         while (i != end) {
 498                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1()) *
 499                                              i->rest.diff(s));
 500                 ep.swap(*i2);
 501                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 502                 ep.swap(*i2);
 503                 ++i; ++i2;
 504         }
 505         return (new add(addseq))->setflag(status_flags::dynallocated);
 506 }
 507
 508 int mul::compare_same_type(const basic & other) const
 509 {
 510         return inherited::compare_same_type(other);
 511 }
 512
 513 bool mul::is_equal_same_type(const basic & other) const
 514 {
 515         return inherited::is_equal_same_type(other);
 516 }
 517
 518 unsigned mul::return_type(void) const
 519 {
 520         if (seq.empty()) {
 521                 // mul without factors: should not happen, but commutes
 522                 return return_types::commutative;
 523         }
 524
 525         bool all_commutative = true;
 526         epvector::const_iterator noncommutative_element; // point to first found nc element
 527
 528         epvector::const_iterator i = seq.begin(), end = seq.end();
 529         while (i != end) {
 530                 unsigned rt = i->rest.return_type();
 531                 if (rt == return_types::noncommutative_composite)
 532                         return rt; // one ncc -> mul also ncc
 533                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 534                         // first nc element found, remember position
 535                         noncommutative_element = i;
 536                         all_commutative = false;
 537                 }
 538                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 539                         // another nc element found, compare type_infos
 540                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 541                                 // diffent types -> mul is ncc
 542                                 return return_types::noncommutative_composite;
 543                         }
 544                 }
 545                 ++i;
 546         }
 547         // all factors checked
 548         return all_commutative ? return_types::commutative : return_types::noncommutative;
 549 }
 550
 551 unsigned mul::return_type_tinfo(void) const
 552 {
 553         if (seq.empty())
 554                 return tinfo_key;  // mul without factors: should not happen
 555
 556         // return type_info of first noncommutative element
 557         epvector::const_iterator i = seq.begin(), end = seq.end();
 558         while (i != end) {
 559                 if (i->rest.return_type() == return_types::noncommutative)
 560                         return i->rest.return_type_tinfo();
 561                 ++i;
 562         }
 563         // no noncommutative element found, should not happen
 564         return tinfo_key;
 565 }
 566
 567 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 568 {
 569         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 570 }
 571
 572 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 573 {
 574         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 575 }
 576
 577 expair mul::split_ex_to_pair(const ex & e) const
 578 {
 579         if (is_ex_exactly_of_type(e,power)) {
 580                 const power & powerref = ex_to<power>(e);
 581                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 582                         return expair(powerref.basis,powerref.exponent);
 583         }
 584         return expair(e,_ex1());
 585 }
 586
 587 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 588                                           const ex & c) const
 589 {
 590         // to avoid duplication of power simplification rules,
 591         // we create a temporary power object
 592         // otherwise it would be hard to correctly simplify
 593         // expression like (4^(1/3))^(3/2)
 594         if (are_ex_trivially_equal(c,_ex1()))
 595                 return split_ex_to_pair(e);
 596
 597         return split_ex_to_pair(power(e,c));
 598 }
 599
 600 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 601                                             const ex & c) const
 602 {
 603         // to avoid duplication of power simplification rules,
 604         // we create a temporary power object
 605         // otherwise it would be hard to correctly simplify
 606         // expression like (4^(1/3))^(3/2)
 607         if (are_ex_trivially_equal(c,_ex1()))
 608                 return p;
 609
 610         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 611 }
 612
 613 ex mul::recombine_pair_to_ex(const expair & p) const
 614 {
 615         if (ex_to<numeric>(p.coeff).is_equal(_num1()))
 616                 return p.rest;
 617         else
 618                 return power(p.rest,p.coeff);
 619 }
 620
 621 bool mul::expair_needs_further_processing(epp it)
 622 {
 623         if (is_ex_exactly_of_type((*it).rest,mul) &&
 624                 ex_to<numeric>((*it).coeff).is_integer()) {
 625                 // combined pair is product with integer power -> expand it
 626                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 627                 return true;
 628         }
 629         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 630                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 631                 if (!ep.is_equal(*it)) {
 632                         // combined pair is a numeric power which can be simplified
 633                         *it = ep;
 634                         return true;
 635                 }
 636                 if (ex_to<numeric>((*it).coeff).is_equal(_num1())) {
 637                         // combined pair has coeff 1 and must be moved to the end
 638                         return true;
 639                 }
 640         }
 641         return false;
 642 }
 643
 644 ex mul::default_overall_coeff(void) const
 645 {
 646         return _ex1();
 647 }
 648
 649 void mul::combine_overall_coeff(const ex & c)
 650 {
 651         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 652         GINAC_ASSERT(is_exactly_a<numeric>(c));
 653         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 654 }
 655
 656 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 657 {
 658         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 659         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 660         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 661         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 662 }
 663
 664 bool mul::can_make_flat(const expair & p) const
 665 {
 666         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 667         // this assertion will probably fail somewhere
 668         // it would require a more careful make_flat, obeying the power laws
 669         // probably should return true only if p.coeff is integer
 670         return ex_to<numeric>(p.coeff).is_equal(_num1());
 671 }
 672
 673 ex mul::expand(unsigned options) const
 674 {
 675         // First, expand the children
 676         epvector * expanded_seqp = expandchildren(options);
 677         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 678
 679         // Now, look for all the factors that are sums and multiply each one out
 680         // with the next one that is found while collecting the factors which are
 681         // not sums
 682         int number_of_adds = 0;
 683         ex last_expanded = _ex1();
 684         epvector non_adds;
 685         non_adds.reserve(expanded_seq.size());
 686         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 687         while (cit != last) {
 688                 if (is_ex_exactly_of_type(cit->rest, add) &&
 689                         (cit->coeff.is_equal(_ex1()))) {
 690                         ++number_of_adds;
 691                         if (is_ex_exactly_of_type(last_expanded, add)) {
 692                                 const add & add1 = ex_to<add>(last_expanded);
 693                                 const add & add2 = ex_to<add>(cit->rest);
 694                                 int n1 = add1.nops();
 695                                 int n2 = add2.nops();
 696                                 exvector distrseq;
 697                                 distrseq.reserve(n1*n2);
 698                                 for (int i1=0; i1<n1; ++i1) {
 699                                         for (int i2=0; i2<n2; ++i2) {
 700                                                 distrseq.push_back(add1.op(i1) * add2.op(i2));
 701                                         }
 702                                 }
 703                                 last_expanded = (new add(distrseq))->
 704                                                  setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 705                         } else {
 706                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 707                                 last_expanded = cit->rest;
 708                         }
 709                 } else {
 710                         non_adds.push_back(*cit);
 711                 }
 712                 ++cit;
 713         }
 714         if (expanded_seqp)
 715                 delete expanded_seqp;
 716
 717         // Now the only remaining thing to do is to multiply the factors which
 718         // were not sums into the "last_expanded" sum
 719         if (is_ex_exactly_of_type(last_expanded, add)) {
 720                 const add & finaladd = ex_to<add>(last_expanded);
 721                 exvector distrseq;
 722                 int n = finaladd.nops();
 723                 distrseq.reserve(n);
 724                 for (int i=0; i<n; ++i) {
 725                         epvector factors = non_adds;
 726                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 727                         distrseq.push_back((new mul(factors, overall_coeff))->
 728                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 729                 }
 730                 return ((new add(distrseq))->
 731                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 732         }
 733         non_adds.push_back(split_ex_to_pair(last_expanded));
 734         return (new mul(non_adds, overall_coeff))->
 735                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 736 }
 737
 738
 739 //////////
 740 // new virtual functions which can be overridden by derived classes
 741 //////////
 742
 743 // none
 744
 745 //////////
 746 // non-virtual functions in this class
 747 //////////
 748
 749
 750 /** Member-wise expand the expairs representing this sequence.  This must be
 751  *  overridden from expairseq::expandchildren() and done iteratively in order
 752  *  to allow for early cancallations and thus safe memory.
 753  *
 754  *  @see mul::expand()
 755  *  @return pointer to epvector containing expanded representation or zero
 756  *  pointer, if sequence is unchanged. */
 757 epvector * mul::expandchildren(unsigned options) const
 758 {
 759         epvector::const_iterator last = seq.end();
 760         epvector::const_iterator cit = seq.begin();
 761         while (cit!=last) {
 762                 const ex & factor = recombine_pair_to_ex(*cit);
 763                 const ex & expanded_factor = factor.expand(options);
 764                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 765
 766                         // something changed, copy seq, eval and return it
 767                         epvector *s = new epvector;
 768                         s->reserve(seq.size());
 769
 770                         // copy parts of seq which are known not to have changed
 771                         epvector::const_iterator cit2 = seq.begin();
 772                         while (cit2!=cit) {
 773                                 s->push_back(*cit2);
 774                                 ++cit2;
 775                         }
 776                         // copy first changed element
 777                         s->push_back(split_ex_to_pair(expanded_factor));
 778                         ++cit2;
 779                         // copy rest
 780                         while (cit2!=last) {
 781                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 782                                 ++cit2;
 783                         }
 784                         return s;
 785                 }
 786                 ++cit;
 787         }
 788
 789         return 0; // nothing has changed
 790 }
 791
 792 } // namespace GiNaC