X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=64b090af6ecdd1f721e69617b022625c1ef5df26;hp=8e641caf2ddec551ccfd6f86308649b5690b9d06;hb=70a32266cc1ada19b307b859305f215b5297bc7c;hpb=e78622a06f749a124b007aa7b969de02fcc9c3d2 diff --git a/ginac/mul.cpp b/ginac/mul.cpp index 8e641caf..64b090af 100644 --- a/ginac/mul.cpp +++ b/ginac/mul.cpp @@ -20,14 +20,15 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include #include #include "mul.h" #include "add.h" #include "power.h" +#include "matrix.h" #include "archive.h" -#include "debugmsg.h" #include "utils.h" namespace GiNaC { @@ -35,12 +36,11 @@ namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq) ////////// -// default ctor, dctor, copy ctor assignment operator and helpers +// default ctor, dtor, copy ctor, assignment operator and helpers ////////// mul::mul() { - debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; } @@ -55,34 +55,30 @@ DEFAULT_DESTROY(mul) mul::mul(const ex & lh, const ex & rh) { - debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; - overall_coeff = _ex1(); + overall_coeff = _ex1; construct_from_2_ex(lh,rh); GINAC_ASSERT(is_canonical()); } mul::mul(const exvector & v) { - debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; - overall_coeff = _ex1(); + overall_coeff = _ex1; construct_from_exvector(v); GINAC_ASSERT(is_canonical()); } mul::mul(const epvector & v) { - debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; - overall_coeff = _ex1(); + overall_coeff = _ex1; construct_from_epvector(v); GINAC_ASSERT(is_canonical()); } mul::mul(const epvector & v, const ex & oc) { - debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; overall_coeff = oc; construct_from_epvector(v); @@ -91,7 +87,6 @@ mul::mul(const epvector & v, const ex & oc) mul::mul(epvector * vp, const ex & oc) { - debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; GINAC_ASSERT(vp!=0); overall_coeff = oc; @@ -102,14 +97,13 @@ mul::mul(epvector * vp, const ex & oc) mul::mul(const ex & lh, const ex & mh, const ex & rh) { - debugmsg("mul ctor from ex,ex,ex",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; exvector factors; factors.reserve(3); factors.push_back(lh); factors.push_back(mh); factors.push_back(rh); - overall_coeff = _ex1(); + overall_coeff = _ex1; construct_from_exvector(factors); GINAC_ASSERT(is_canonical()); } @@ -121,53 +115,51 @@ mul::mul(const ex & lh, const ex & mh, const ex & rh) DEFAULT_ARCHIVING(mul) ////////// -// functions overriding virtual functions from bases classes +// functions overriding virtual functions from base classes ////////// // public void mul::print(const print_context & c, unsigned level) const { - debugmsg("mul print", LOGLEVEL_PRINT); - - if (is_of_type(c, print_tree)) { + if (is_a(c)) { inherited::print(c, level); - } else if (is_of_type(c, print_csrc)) { + } else if (is_a(c)) { if (precedence() <= level) c.s << "("; - if (!overall_coeff.is_equal(_ex1())) { - overall_coeff.bp->print(c, precedence()); + if (!overall_coeff.is_equal(_ex1)) { + overall_coeff.print(c, precedence()); c.s << "*"; } - + // Print arguments, separated by "*" or "/" epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { // If the first argument is a negative integer power, it gets printed as "1.0/" - if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) { - if (is_of_type(c, print_csrc_cl_N)) + if (it == seq.begin() && ex_to(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) { + if (is_a(c)) c.s << "recip("; else c.s << "1.0/"; } // If the exponent is 1 or -1, it is left out - if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0) + if (it->coeff.compare(_ex1) == 0 || it->coeff.compare(_num_1) == 0) it->rest.print(c, precedence()); else { // Outer parens around ex needed for broken gcc-2.95 parser: - (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).print(c, level); + (ex(power(it->rest, abs(ex_to(it->coeff))))).print(c, level); } // Separator is "/" for negative integer powers, "*" otherwise ++it; if (it != itend) { - if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) + if (ex_to(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) c.s << "/"; else c.s << "*"; @@ -180,7 +172,7 @@ void mul::print(const print_context & c, unsigned level) const } else { if (precedence() <= level) { - if (is_of_type(c, print_latex)) + if (is_a(c)) c.s << "{("; else c.s << "("; @@ -189,11 +181,11 @@ void mul::print(const print_context & c, unsigned level) const bool first = true; // First print the overall numeric coefficient - numeric coeff = ex_to_numeric(overall_coeff); + numeric coeff = ex_to(overall_coeff); if (coeff.csgn() == -1) c.s << '-'; - if (!coeff.is_equal(_num1()) && - !coeff.is_equal(_num_1())) { + if (!coeff.is_equal(_num1) && + !coeff.is_equal(_num_1)) { if (coeff.is_rational()) { if (coeff.is_negative()) (-coeff).print(c); @@ -205,7 +197,7 @@ void mul::print(const print_context & c, unsigned level) const else coeff.print(c, precedence()); } - if (is_of_type(c, print_latex)) + if (is_a(c)) c.s << ' '; else c.s << '*'; @@ -215,7 +207,7 @@ void mul::print(const print_context & c, unsigned level) const epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { if (!first) { - if (is_of_type(c, print_latex)) + if (is_a(c)) c.s << ' '; else c.s << '*'; @@ -223,11 +215,11 @@ void mul::print(const print_context & c, unsigned level) const first = false; } recombine_pair_to_ex(*it).print(c, precedence()); - it++; + ++it; } if (precedence() <= level) { - if (is_of_type(c, print_latex)) + if (is_a(c)) c.s << ")}"; else c.s << ")"; @@ -244,16 +236,20 @@ bool mul::info(unsigned inf) const case info_flags::rational_polynomial: case info_flags::crational_polynomial: case info_flags::rational_function: { - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { if (!(recombine_pair_to_ex(*i).info(inf))) return false; + ++i; } return overall_coeff.info(inf); } case info_flags::algebraic: { - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { if ((recombine_pair_to_ex(*i).info(inf))) return true; + ++i; } return false; } @@ -263,20 +259,26 @@ bool mul::info(unsigned inf) const int mul::degree(const ex & s) const { + // Sum up degrees of factors int deg_sum = 0; - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - if (ex_to_numeric(cit->coeff).is_integer()) - deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int(); + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + if (ex_to(i->coeff).is_integer()) + deg_sum += i->rest.degree(s) * ex_to(i->coeff).to_int(); + ++i; } return deg_sum; } int mul::ldegree(const ex & s) const { + // Sum up degrees of factors int deg_sum = 0; - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - if (ex_to_numeric(cit->coeff).is_integer()) - deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int(); + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + if (ex_to(i->coeff).is_integer()) + deg_sum += i->rest.ldegree(s) * ex_to(i->coeff).to_int(); + ++i; } return deg_sum; } @@ -289,97 +291,103 @@ ex mul::coeff(const ex & s, int n) const if (n==0) { // product of individual coeffs // if a non-zero power of s is found, the resulting product will be 0 - epvector::const_iterator it = seq.begin(); - while (it!=seq.end()) { - coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n)); - ++it; + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n)); + ++i; } coeffseq.push_back(overall_coeff); return (new mul(coeffseq))->setflag(status_flags::dynallocated); } - epvector::const_iterator it=seq.begin(); - bool coeff_found = 0; - while (it!=seq.end()) { - ex t = recombine_pair_to_ex(*it); - ex c = t.coeff(s,n); + epvector::const_iterator i = seq.begin(), end = seq.end(); + bool coeff_found = false; + while (i != end) { + ex t = recombine_pair_to_ex(*i); + ex c = t.coeff(s, n); if (!c.is_zero()) { coeffseq.push_back(c); coeff_found = 1; } else { coeffseq.push_back(t); } - ++it; + ++i; } if (coeff_found) { coeffseq.push_back(overall_coeff); return (new mul(coeffseq))->setflag(status_flags::dynallocated); } - return _ex0(); + return _ex0; } +/** Perform automatic term rewriting rules in this class. In the following + * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2... + * stand for such expressions that contain a plain number. + * - *(...,x;0) -> 0 + * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...)) + * - *(x;1) -> x + * - *(;c) -> c + * + * @param level cut-off in recursive evaluation */ ex mul::eval(int level) const { - // simplifications *(...,x;0) -> 0 - // *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric()) - // *(x;1) -> x - // *(;c) -> c - - debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION); - - epvector * evaled_seqp = evalchildren(level); - if (evaled_seqp!=0) { + epvector *evaled_seqp = evalchildren(level); + if (evaled_seqp) { // do more evaluation later return (new mul(evaled_seqp,overall_coeff))-> setflag(status_flags::dynallocated); } #ifdef DO_GINAC_ASSERT - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul)) || - (!(ex_to_numeric((*cit).coeff).is_integer()))); - GINAC_ASSERT(!(cit->is_canonical_numeric())); - if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + GINAC_ASSERT((!is_exactly_a(i->rest)) || + (!(ex_to(i->coeff).is_integer()))); + GINAC_ASSERT(!(i->is_canonical_numeric())); + if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric)) print(print_tree(std::cerr)); - GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)); + GINAC_ASSERT(!is_exactly_a(recombine_pair_to_ex(*i))); /* for paranoia */ - expair p = split_ex_to_pair(recombine_pair_to_ex(*cit)); - GINAC_ASSERT(p.rest.is_equal((*cit).rest)); - GINAC_ASSERT(p.coeff.is_equal((*cit).coeff)); + expair p = split_ex_to_pair(recombine_pair_to_ex(*i)); + GINAC_ASSERT(p.rest.is_equal(i->rest)); + GINAC_ASSERT(p.coeff.is_equal(i->coeff)); /* end paranoia */ + ++i; } #endif // def DO_GINAC_ASSERT if (flags & status_flags::evaluated) { GINAC_ASSERT(seq.size()>0); - GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1())); + GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1)); return *this; } int seq_size = seq.size(); - if (overall_coeff.is_equal(_ex0())) { + if (overall_coeff.is_zero()) { // *(...,x;0) -> 0 - return _ex0(); + return _ex0; } else if (seq_size==0) { // *(;c) -> c return overall_coeff; - } else if (seq_size==1 && overall_coeff.is_equal(_ex1())) { + } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) { // *(x;1) -> x return recombine_pair_to_ex(*(seq.begin())); } else if ((seq_size==1) && is_ex_exactly_of_type((*seq.begin()).rest,add) && - ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) { + ex_to((*seq.begin()).coeff).is_equal(_num1)) { // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +()) - const add & addref = ex_to_add((*seq.begin()).rest); - epvector distrseq; - distrseq.reserve(addref.seq.size()); - for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) { - distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff)); + const add & addref = ex_to((*seq.begin()).rest); + epvector *distrseq = new epvector(); + distrseq->reserve(addref.seq.size()); + epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end(); + while (i != end) { + distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff)); + ++i; } return (new add(distrseq, - ex_to_numeric(addref.overall_coeff). - mul_dyn(ex_to_numeric(overall_coeff)))) + ex_to(addref.overall_coeff). + mul_dyn(ex_to(overall_coeff)))) ->setflag(status_flags::dynallocated | status_flags::evaluated); } return this->hold(); @@ -393,27 +401,70 @@ ex mul::evalf(int level) const if (level==-max_recursion_level) throw(std::runtime_error("max recursion level reached")); - epvector s; - s.reserve(seq.size()); - + epvector *s = new epvector(); + s->reserve(seq.size()); + --level; - for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) { - s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level), - (*it).coeff)); + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level), + i->coeff)); + ++i; } - return mul(s,overall_coeff.evalf(level)); + return mul(s, overall_coeff.evalf(level)); +} + +ex mul::evalm(void) const +{ + // numeric*matrix + if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1) + && is_ex_of_type(seq[0].rest, matrix)) + return ex_to(seq[0].rest).mul(ex_to(overall_coeff)); + + // Evaluate children first, look whether there are any matrices at all + // (there can be either no matrices or one matrix; if there were more + // than one matrix, it would be a non-commutative product) + epvector *s = new epvector; + s->reserve(seq.size()); + + bool have_matrix = false; + epvector::iterator the_matrix; + + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + const ex &m = recombine_pair_to_ex(*i).evalm(); + s->push_back(split_ex_to_pair(m)); + if (is_ex_of_type(m, matrix)) { + have_matrix = true; + the_matrix = s->end() - 1; + } + ++i; + } + + if (have_matrix) { + + // The product contained a matrix. We will multiply all other factors + // into that matrix. + matrix m = ex_to(the_matrix->rest); + s->erase(the_matrix); + ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated); + return m.mul_scalar(scalar); + + } else + return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated); } ex mul::simplify_ncmul(const exvector & v) const { - if (seq.size()==0) { + if (seq.empty()) return inherited::simplify_ncmul(v); - } // Find first noncommutative element and call its simplify_ncmul() - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - if (cit->rest.return_type() == return_types::noncommutative) - return cit->rest.simplify_ncmul(v); + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + if (i->rest.return_type() == return_types::noncommutative) + return i->rest.simplify_ncmul(v); + ++i; } return inherited::simplify_ncmul(v); } @@ -424,15 +475,21 @@ ex mul::simplify_ncmul(const exvector & v) const * @see ex::diff */ ex mul::derivative(const symbol & s) const { + unsigned num = seq.size(); exvector addseq; - addseq.reserve(seq.size()); + addseq.reserve(num); // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c) - for (unsigned i=0; i!=seq.size(); ++i) { - epvector mulseq = seq; - mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) * - seq[i].rest.diff(s)); - addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated)); + epvector mulseq = seq; + epvector::const_iterator i = seq.begin(), end = seq.end(); + epvector::iterator i2 = mulseq.begin(); + while (i != end) { + expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) * + i->rest.diff(s)); + ep.swap(*i2); + addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated)); + ep.swap(*i2); + ++i; ++i2; } return (new add(addseq))->setflag(status_flags::dynallocated); } @@ -449,30 +506,32 @@ bool mul::is_equal_same_type(const basic & other) const unsigned mul::return_type(void) const { - if (seq.size()==0) { + if (seq.empty()) { // mul without factors: should not happen, but commutes return return_types::commutative; } - bool all_commutative = 1; - unsigned rt; - epvector::const_iterator cit_noncommutative_element; // point to first found nc element + bool all_commutative = true; + epvector::const_iterator noncommutative_element; // point to first found nc element - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - rt=(*cit).rest.return_type(); - if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc - if ((rt==return_types::noncommutative)&&(all_commutative)) { + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + unsigned rt = i->rest.return_type(); + if (rt == return_types::noncommutative_composite) + return rt; // one ncc -> mul also ncc + if ((rt == return_types::noncommutative) && (all_commutative)) { // first nc element found, remember position - cit_noncommutative_element = cit; - all_commutative = 0; + noncommutative_element = i; + all_commutative = false; } - if ((rt==return_types::noncommutative)&&(!all_commutative)) { + if ((rt == return_types::noncommutative) && (!all_commutative)) { // another nc element found, compare type_infos - if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) { + if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) { // diffent types -> mul is ncc return return_types::noncommutative_composite; } } + ++i; } // all factors checked return all_commutative ? return_types::commutative : return_types::noncommutative; @@ -480,13 +539,15 @@ unsigned mul::return_type(void) const unsigned mul::return_type_tinfo(void) const { - if (seq.size()==0) + if (seq.empty()) return tinfo_key; // mul without factors: should not happen // return type_info of first noncommutative element - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - if ((*cit).rest.return_type()==return_types::noncommutative) - return (*cit).rest.return_type_tinfo(); + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + if (i->rest.return_type() == return_types::noncommutative) + return i->rest.return_type_tinfo(); + ++i; } // no noncommutative element found, should not happen return tinfo_key; @@ -494,22 +555,22 @@ unsigned mul::return_type_tinfo(void) const ex mul::thisexpairseq(const epvector & v, const ex & oc) const { - return (new mul(v,oc))->setflag(status_flags::dynallocated); + return (new mul(v, oc))->setflag(status_flags::dynallocated); } ex mul::thisexpairseq(epvector * vp, const ex & oc) const { - return (new mul(vp,oc))->setflag(status_flags::dynallocated); + return (new mul(vp, oc))->setflag(status_flags::dynallocated); } expair mul::split_ex_to_pair(const ex & e) const { if (is_ex_exactly_of_type(e,power)) { - const power & powerref = ex_to_power(e); + const power & powerref = ex_to(e); if (is_ex_exactly_of_type(powerref.exponent,numeric)) return expair(powerref.basis,powerref.exponent); } - return expair(e,_ex1()); + return expair(e,_ex1); } expair mul::combine_ex_with_coeff_to_pair(const ex & e, @@ -519,7 +580,7 @@ expair mul::combine_ex_with_coeff_to_pair(const ex & e, // we create a temporary power object // otherwise it would be hard to correctly simplify // expression like (4^(1/3))^(3/2) - if (are_ex_trivially_equal(c,_ex1())) + if (are_ex_trivially_equal(c,_ex1)) return split_ex_to_pair(e); return split_ex_to_pair(power(e,c)); @@ -532,7 +593,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p, // we create a temporary power object // otherwise it would be hard to correctly simplify // expression like (4^(1/3))^(3/2) - if (are_ex_trivially_equal(c,_ex1())) + if (are_ex_trivially_equal(c,_ex1)) return p; return split_ex_to_pair(power(recombine_pair_to_ex(p),c)); @@ -540,7 +601,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p, ex mul::recombine_pair_to_ex(const expair & p) const { - if (ex_to_numeric(p.coeff).is_equal(_num1())) + if (ex_to(p.coeff).is_equal(_num1)) return p.rest; else return power(p.rest,p.coeff); @@ -549,7 +610,7 @@ ex mul::recombine_pair_to_ex(const expair & p) const bool mul::expair_needs_further_processing(epp it) { if (is_ex_exactly_of_type((*it).rest,mul) && - ex_to_numeric((*it).coeff).is_integer()) { + ex_to((*it).coeff).is_integer()) { // combined pair is product with integer power -> expand it *it = split_ex_to_pair(recombine_pair_to_ex(*it)); return true; @@ -561,7 +622,7 @@ bool mul::expair_needs_further_processing(epp it) *it = ep; return true; } - if (ex_to_numeric((*it).coeff).is_equal(_num1())) { + if (ex_to((*it).coeff).is_equal(_num1)) { // combined pair has coeff 1 and must be moved to the end return true; } @@ -571,71 +632,68 @@ bool mul::expair_needs_further_processing(epp it) ex mul::default_overall_coeff(void) const { - return _ex1(); + return _ex1; } void mul::combine_overall_coeff(const ex & c) { - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); - GINAC_ASSERT(is_ex_exactly_of_type(c,numeric)); - overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); + GINAC_ASSERT(is_exactly_a(c)); + overall_coeff = ex_to(overall_coeff).mul_dyn(ex_to(c)); } void mul::combine_overall_coeff(const ex & c1, const ex & c2) { - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); - GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric)); - GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric)); - overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2))); + GINAC_ASSERT(is_exactly_a(overall_coeff)); + GINAC_ASSERT(is_exactly_a(c1)); + GINAC_ASSERT(is_exactly_a(c2)); + overall_coeff = ex_to(overall_coeff).mul_dyn(ex_to(c1).power(ex_to(c2))); } bool mul::can_make_flat(const expair & p) const { - GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric)); + GINAC_ASSERT(is_exactly_a(p.coeff)); // this assertion will probably fail somewhere // it would require a more careful make_flat, obeying the power laws // probably should return true only if p.coeff is integer - return ex_to_numeric(p.coeff).is_equal(_num1()); + return ex_to(p.coeff).is_equal(_num1); } ex mul::expand(unsigned options) const { - if (flags & status_flags::expanded) - return *this; - - exvector sub_expanded_seq; - + // First, expand the children epvector * expanded_seqp = expandchildren(options); - - const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp; - + const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp; + + // Now, look for all the factors that are sums and multiply each one out + // with the next one that is found while collecting the factors which are + // not sums int number_of_adds = 0; + ex last_expanded = _ex1; epvector non_adds; non_adds.reserve(expanded_seq.size()); - epvector::const_iterator cit = expanded_seq.begin(); - epvector::const_iterator last = expanded_seq.end(); - ex last_expanded = _ex1(); - while (cit!=last) { - if (is_ex_exactly_of_type((*cit).rest,add) && - ((*cit).coeff.is_equal(_ex1()))) { + epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end(); + while (cit != last) { + if (is_ex_exactly_of_type(cit->rest, add) && + (cit->coeff.is_equal(_ex1))) { ++number_of_adds; - if (is_ex_exactly_of_type(last_expanded,add)) { - // expand adds - const add & add1 = ex_to_add(last_expanded); - const add & add2 = ex_to_add((*cit).rest); + if (is_ex_exactly_of_type(last_expanded, add)) { + const add & add1 = ex_to(last_expanded); + const add & add2 = ex_to(cit->rest); int n1 = add1.nops(); int n2 = add2.nops(); exvector distrseq; distrseq.reserve(n1*n2); for (int i1=0; i1setflag(status_flags::dynallocated | status_flags::expanded); + last_expanded = (new add(distrseq))-> + setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)); } else { non_adds.push_back(split_ex_to_pair(last_expanded)); - last_expanded = (*cit).rest; + last_expanded = cit->rest; } } else { non_adds.push_back(*cit); @@ -644,23 +702,26 @@ ex mul::expand(unsigned options) const } if (expanded_seqp) delete expanded_seqp; - - if (is_ex_exactly_of_type(last_expanded,add)) { - add const & finaladd = ex_to_add(last_expanded); + + // Now the only remaining thing to do is to multiply the factors which + // were not sums into the "last_expanded" sum + if (is_ex_exactly_of_type(last_expanded, add)) { + const add & finaladd = ex_to(last_expanded); exvector distrseq; int n = finaladd.nops(); distrseq.reserve(n); for (int i=0; isetflag(status_flags::dynallocated | status_flags::expanded)); + distrseq.push_back((new mul(factors, overall_coeff))-> + setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0))); } return ((new add(distrseq))-> - setflag(status_flags::dynallocated | status_flags::expanded)); + setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0))); } non_adds.push_back(split_ex_to_pair(last_expanded)); - return (new mul(non_adds,overall_coeff))-> - setflag(status_flags::dynallocated | status_flags::expanded); + return (new mul(non_adds, overall_coeff))-> + setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)); } @@ -684,7 +745,7 @@ ex mul::expand(unsigned options) const * pointer, if sequence is unchanged. */ epvector * mul::expandchildren(unsigned options) const { - epvector::const_iterator last = seq.end(); + const epvector::const_iterator last = seq.end(); epvector::const_iterator cit = seq.begin(); while (cit!=last) { const ex & factor = recombine_pair_to_ex(*cit);