X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=a4bb802ec9475c6b8f87ac4becbeaaf22b13cea5;hp=efabd3bee765406c92872be93445b97b0c3b75f0;hb=c8ba9c6cf819792cbf88d25b324406b67d5cc49a;hpb=aff6beb8e799e6827c40975ed2f22b51976b1cb8 diff --git a/ginac/mul.cpp b/ginac/mul.cpp index efabd3be..a4bb802e 100644 --- a/ginac/mul.cpp +++ b/ginac/mul.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's products of expressions. */ /* - * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -26,150 +26,100 @@ #include "mul.h" #include "add.h" #include "power.h" +#include "matrix.h" #include "archive.h" #include "debugmsg.h" #include "utils.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default ctor, dctor, copy ctor assignment operator and helpers ////////// -// public - mul::mul() { - debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_mul; -} - -mul::~mul() -{ - debugmsg("mul destructor",LOGLEVEL_DESTRUCT); - destroy(0); -} - -mul::mul(const mul & other) -{ - debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT); - copy(other); -} - -const mul & mul::operator=(const mul & other) -{ - debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT); - if (this != &other) { - destroy(1); - copy(other); - } - return *this; -} - -// protected - -void mul::copy(const mul & other) -{ - inherited::copy(other); + debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT); + tinfo_key = TINFO_mul; } -void mul::destroy(bool call_parent) -{ - if (call_parent) inherited::destroy(call_parent); -} +DEFAULT_COPY(mul) +DEFAULT_DESTROY(mul) ////////// -// other constructors +// other ctors ////////// // public mul::mul(const ex & lh, const ex & rh) { - debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_mul; - overall_coeff = _ex1(); - construct_from_2_ex(lh,rh); - GINAC_ASSERT(is_canonical()); + debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT); + tinfo_key = TINFO_mul; + overall_coeff = _ex1(); + construct_from_2_ex(lh,rh); + GINAC_ASSERT(is_canonical()); } mul::mul(const exvector & v) { - debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_mul; - overall_coeff = _ex1(); - construct_from_exvector(v); - GINAC_ASSERT(is_canonical()); + debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT); + tinfo_key = TINFO_mul; + overall_coeff = _ex1(); + construct_from_exvector(v); + GINAC_ASSERT(is_canonical()); } mul::mul(const epvector & v) { - debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_mul; - overall_coeff = _ex1(); - construct_from_epvector(v); - GINAC_ASSERT(is_canonical()); + debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT); + tinfo_key = TINFO_mul; + overall_coeff = _ex1(); + construct_from_epvector(v); + GINAC_ASSERT(is_canonical()); } mul::mul(const epvector & v, const ex & oc) { - debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_mul; - overall_coeff = oc; - construct_from_epvector(v); - GINAC_ASSERT(is_canonical()); + debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT); + tinfo_key = TINFO_mul; + overall_coeff = oc; + construct_from_epvector(v); + GINAC_ASSERT(is_canonical()); } mul::mul(epvector * vp, const ex & oc) { - debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_mul; - GINAC_ASSERT(vp!=0); - overall_coeff = oc; - construct_from_epvector(*vp); - delete vp; - GINAC_ASSERT(is_canonical()); + debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT); + tinfo_key = TINFO_mul; + GINAC_ASSERT(vp!=0); + overall_coeff = oc; + construct_from_epvector(*vp); + delete vp; + GINAC_ASSERT(is_canonical()); } mul::mul(const ex & lh, const ex & mh, const ex & rh) { - debugmsg("mul constructor 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(); - construct_from_exvector(factors); - GINAC_ASSERT(is_canonical()); + 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(); + construct_from_exvector(factors); + GINAC_ASSERT(is_canonical()); } ////////// // archiving ////////// -/** Construct object from archive_node. */ -mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) -{ - debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT); -} - -/** Unarchive the object. */ -ex mul::unarchive(const archive_node &n, const lst &sym_lst) -{ - return (new mul(n, sym_lst))->setflag(status_flags::dynallocated); -} - -/** Archive the object. */ -void mul::archive(archive_node &n) const -{ - inherited::archive(n); -} +DEFAULT_ARCHIVING(mul) ////////// // functions overriding virtual functions from bases classes @@ -177,576 +127,583 @@ void mul::archive(archive_node &n) const // public -basic * mul::duplicate() const -{ - debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT); - return new mul(*this); -} - -void mul::print(ostream & os, unsigned upper_precedence) const -{ - debugmsg("mul print",LOGLEVEL_PRINT); - if (precedence<=upper_precedence) os << "("; - bool first=true; - // first print the overall numeric coefficient: - numeric coeff = ex_to_numeric(overall_coeff); - if (coeff.csgn()==-1) os << '-'; - if (!coeff.is_equal(_num1()) && - !coeff.is_equal(_num_1())) { - if (coeff.is_rational()) { - if (coeff.is_negative()) - os << -coeff; - else - os << coeff; - } else { - if (coeff.csgn()==-1) - (-coeff).print(os, precedence); - else - coeff.print(os, precedence); - } - os << '*'; - } - // then proceed with the remaining factors: - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - if (!first) { - os << '*'; - } else { - first=false; - } - recombine_pair_to_ex(*cit).print(os,precedence); - } - if (precedence<=upper_precedence) os << ")"; -} - -void mul::printraw(ostream & os) const -{ - debugmsg("mul printraw",LOGLEVEL_PRINT); - - os << "*("; - for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) { - os << "("; - (*it).rest.bp->printraw(os); - os << ","; - (*it).coeff.bp->printraw(os); - os << "),"; - } - os << ",hash=" << hashvalue << ",flags=" << flags; - os << ")"; -} - -void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const -{ - debugmsg("mul print csrc", LOGLEVEL_PRINT); - if (precedence <= upper_precedence) - os << "("; - - if (!overall_coeff.is_equal(_ex1())) { - overall_coeff.bp->printcsrc(os,type,precedence); - os << "*"; - } - - // Print arguments, separated by "*" or "/" - epvector::const_iterator it = seq.begin(); - epvector::const_iterator 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 (type == csrc_types::ctype_cl_N) - os << "recip("; - else - os << "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) - it->rest.bp->printcsrc(os, type, precedence); - else - // outer parens around ex needed for broken gcc-2.95 parser: - (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence); - - // Separator is "/" for negative integer powers, "*" otherwise - it++; - if (it != itend) { - if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) - os << "/"; - else - os << "*"; - } - } - if (precedence <= upper_precedence) - os << ")"; +void mul::print(const print_context & c, unsigned level) const +{ + debugmsg("mul print", LOGLEVEL_PRINT); + + if (is_of_type(c, print_tree)) { + + inherited::print(c, level); + + } else if (is_of_type(c, print_csrc)) { + + if (precedence() <= level) + c.s << "("; + + if (!overall_coeff.is_equal(_ex1())) { + overall_coeff.bp->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)) + 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) + 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); + } + + // Separator is "/" for negative integer powers, "*" otherwise + ++it; + if (it != itend) { + if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) + c.s << "/"; + else + c.s << "*"; + } + } + + if (precedence() <= level) + c.s << ")"; + + } else { + + if (precedence() <= level) { + if (is_of_type(c, print_latex)) + c.s << "{("; + else + c.s << "("; + } + + bool first = true; + + // First print the overall numeric coefficient + numeric coeff = ex_to_numeric(overall_coeff); + if (coeff.csgn() == -1) + c.s << '-'; + if (!coeff.is_equal(_num1()) && + !coeff.is_equal(_num_1())) { + if (coeff.is_rational()) { + if (coeff.is_negative()) + (-coeff).print(c); + else + coeff.print(c); + } else { + if (coeff.csgn() == -1) + (-coeff).print(c, precedence()); + else + coeff.print(c, precedence()); + } + if (is_of_type(c, print_latex)) + c.s << ' '; + else + c.s << '*'; + } + + // Then proceed with the remaining factors + epvector::const_iterator it = seq.begin(), itend = seq.end(); + while (it != itend) { + if (!first) { + if (is_of_type(c, print_latex)) + c.s << ' '; + else + c.s << '*'; + } else { + first = false; + } + recombine_pair_to_ex(*it).print(c, precedence()); + it++; + } + + if (precedence() <= level) { + if (is_of_type(c, print_latex)) + c.s << ")}"; + else + c.s << ")"; + } + } } bool mul::info(unsigned inf) const { - // TODO: optimize - if (inf==info_flags::polynomial || - inf==info_flags::integer_polynomial || - inf==info_flags::cinteger_polynomial || - inf==info_flags::rational_polynomial || - inf==info_flags::crational_polynomial || - inf==info_flags::rational_function) { - for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) { - if (!(recombine_pair_to_ex(*it).info(inf))) - return false; - } - return overall_coeff.info(inf); - } else { - return inherited::info(inf); - } -} - -typedef vector intvector; - -int mul::degree(const symbol & s) const -{ - int deg_sum=0; - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int(); - } - return deg_sum; -} - -int mul::ldegree(const symbol & s) const -{ - int deg_sum=0; - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int(); - } - return deg_sum; -} - -ex mul::coeff(const symbol & s, int n) const -{ - exvector coeffseq; - coeffseq.reserve(seq.size()+1); - - 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; - } - 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); - if (!c.is_zero()) { - coeffseq.push_back(c); - coeff_found=1; - } else { - coeffseq.push_back(t); - } - ++it; - } - if (coeff_found) { - coeffseq.push_back(overall_coeff); - return (new mul(coeffseq))->setflag(status_flags::dynallocated); - } - - return _ex0(); + switch (inf) { + case info_flags::polynomial: + case info_flags::integer_polynomial: + case info_flags::cinteger_polynomial: + 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) { + if (!(recombine_pair_to_ex(*i).info(inf))) + return false; + } + return overall_coeff.info(inf); + } + case info_flags::algebraic: { + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + if ((recombine_pair_to_ex(*i).info(inf))) + return true; + } + return false; + } + } + return inherited::info(inf); +} + +int mul::degree(const ex & s) const +{ + 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(); + } + return deg_sum; +} + +int mul::ldegree(const ex & s) const +{ + 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(); + } + return deg_sum; +} + +ex mul::coeff(const ex & s, int n) const +{ + exvector coeffseq; + coeffseq.reserve(seq.size()+1); + + 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; + } + 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); + if (!c.is_zero()) { + coeffseq.push_back(c); + coeff_found = 1; + } else { + coeffseq.push_back(t); + } + ++it; + } + if (coeff_found) { + coeffseq.push_back(overall_coeff); + return (new mul(coeffseq))->setflag(status_flags::dynallocated); + } + + return _ex0(); } 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) { - // do more evaluation later - return (new mul(evaled_seqp,overall_coeff))-> - setflag(status_flags::dynallocated); - } - + // 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) { + // 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_numeric_with_coeff_1())); - if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) { - printtree(cerr,0); - } - GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)); - /* 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)); - /* end paranoia */ - } + 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)) + print(print_tree(std::cerr)); + GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)); + /* 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)); + /* end paranoia */ + } #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())); - return *this; - } - - int seq_size=seq.size(); - if (overall_coeff.is_equal(_ex0())) { - // *(...,x;0) -> 0 - return _ex0(); - } else if (seq_size==0) { - // *(;c) -> c - return overall_coeff; - } 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())) { - // *(+(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)); - } - return (new add(distrseq, - ex_to_numeric(addref.overall_coeff). - mul_dyn(ex_to_numeric(overall_coeff)))) - ->setflag(status_flags::dynallocated | - status_flags::evaluated ); - } - return this->hold(); + + if (flags & status_flags::evaluated) { + GINAC_ASSERT(seq.size()>0); + GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1())); + return *this; + } + + int seq_size = seq.size(); + if (overall_coeff.is_equal(_ex0())) { + // *(...,x;0) -> 0 + return _ex0(); + } else if (seq_size==0) { + // *(;c) -> c + return overall_coeff; + } 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())) { + // *(+(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)); + } + return (new add(distrseq, + ex_to_numeric(addref.overall_coeff). + mul_dyn(ex_to_numeric(overall_coeff)))) + ->setflag(status_flags::dynallocated | status_flags::evaluated); + } + return this->hold(); } ex mul::evalf(int level) const { - if (level==1) - return mul(seq,overall_coeff); - - if (level==-max_recursion_level) - throw(std::runtime_error("max recursion level reached")); - - epvector s; - 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)); - } - return mul(s,overall_coeff.evalf(level)); -} - -exvector mul::get_indices(void) const -{ - // return union of indices of factors - exvector iv; - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - exvector subiv=(*cit).rest.get_indices(); - iv.reserve(iv.size()+subiv.size()); - for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) { - iv.push_back(*cit2); - } - } - return iv; + if (level==1) + return mul(seq,overall_coeff); + + if (level==-max_recursion_level) + throw(std::runtime_error("max recursion level reached")); + + epvector s; + 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)); + } + return mul(s,overall_coeff.evalf(level)); +} + +ex mul::evalm(void) const +{ + // numeric*matrix + if (seq.size() == 1 && is_ex_of_type(seq[0].rest, matrix)) + return ex_to_matrix(seq[0].rest).mul(ex_to_numeric(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 it = seq.begin(), itend = seq.end(); + while (it != itend) { + const ex &m = recombine_pair_to_ex(*it).evalm(); + s->push_back(split_ex_to_pair(m)); + if (is_ex_of_type(m, matrix)) { + have_matrix = true; + the_matrix = s->end() - 1; + } + it++; + } + + if (have_matrix) { + + // The product contained a matrix. We will multiply all other factors + // into that matrix. + matrix m = ex_to_matrix(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 { - throw(std::logic_error("mul::simplify_ncmul() should never have been called!")); + if (seq.size()==0) { + 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); + } + return inherited::simplify_ncmul(v); } // protected -/** Implementation of ex::diff() for a product. It applies the product rule. +/** Implementation of ex::diff() for a product. It applies the product rule. * @see ex::diff */ ex mul::derivative(const symbol & s) const { - exvector new_seq; - new_seq.reserve(seq.size()); - - // 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 sub_seq=seq; - sub_seq[i] = split_ex_to_pair(sub_seq[i].coeff* - power(sub_seq[i].rest,sub_seq[i].coeff-1)* - sub_seq[i].rest.diff(s)); - new_seq.push_back((new mul(sub_seq,overall_coeff))->setflag(status_flags::dynallocated)); - } - return (new add(new_seq))->setflag(status_flags::dynallocated); + exvector addseq; + addseq.reserve(seq.size()); + + // 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)); + } + return (new add(addseq))->setflag(status_flags::dynallocated); } int mul::compare_same_type(const basic & other) const { - return inherited::compare_same_type(other); + return inherited::compare_same_type(other); } bool mul::is_equal_same_type(const basic & other) const { - return inherited::is_equal_same_type(other); + return inherited::is_equal_same_type(other); } unsigned mul::return_type(void) const { - if (seq.size()==0) { - // 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 - - 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)) { - // first nc element found, remember position - cit_noncommutative_element=cit; - all_commutative=0; - } - 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()) { - // diffent types -> mul is ncc - return return_types::noncommutative_composite; - } - } - } - // all factors checked - return all_commutative ? return_types::commutative : return_types::noncommutative; + if (seq.size()==0) { + // 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 + + 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)) { + // first nc element found, remember position + cit_noncommutative_element = cit; + all_commutative = 0; + } + 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()) { + // diffent types -> mul is ncc + return return_types::noncommutative_composite; + } + } + } + // all factors checked + return all_commutative ? return_types::commutative : return_types::noncommutative; } unsigned mul::return_type_tinfo(void) const { - if (seq.size()==0) { - // mul without factors: should not happen - return tinfo_key; - } - // 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(); - } - } - // no noncommutative element found, should not happen - return tinfo_key; + if (seq.size()==0) + 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(); + } + // no noncommutative element found, should not happen + return tinfo_key; } 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); - if (is_ex_exactly_of_type(powerref.exponent,numeric)) { - return expair(powerref.basis,powerref.exponent); - } - } - return expair(e,_ex1()); + if (is_ex_exactly_of_type(e,power)) { + const power & powerref = ex_to_power(e); + if (is_ex_exactly_of_type(powerref.exponent,numeric)) + return expair(powerref.basis,powerref.exponent); + } + return expair(e,_ex1()); } - + expair mul::combine_ex_with_coeff_to_pair(const ex & e, const ex & c) const { - // to avoid duplication of power simplification rules, - // 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())) { - return split_ex_to_pair(e); - } - return split_ex_to_pair(power(e,c)); + // to avoid duplication of power simplification rules, + // 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())) + return split_ex_to_pair(e); + + return split_ex_to_pair(power(e,c)); } - + expair mul::combine_pair_with_coeff_to_pair(const expair & p, const ex & c) const { - // to avoid duplication of power simplification rules, - // 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())) { - return p; - } - return split_ex_to_pair(power(recombine_pair_to_ex(p),c)); + // to avoid duplication of power simplification rules, + // 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())) + return p; + + return split_ex_to_pair(power(recombine_pair_to_ex(p),c)); } - + ex mul::recombine_pair_to_ex(const expair & p) const { - // if (p.coeff.compare(_ex1())==0) { - // if (are_ex_trivially_equal(p.coeff,_ex1())) { - if (ex_to_numeric(p.coeff).is_equal(_num1())) { - return p.rest; - } else { - return power(p.rest,p.coeff); - } + if (ex_to_numeric(p.coeff).is_equal(_num1())) + return p.rest; + else + return power(p.rest,p.coeff); } bool mul::expair_needs_further_processing(epp it) { - if (is_ex_exactly_of_type((*it).rest,mul) && - ex_to_numeric((*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; - } - if (is_ex_exactly_of_type((*it).rest,numeric)) { - expair ep=split_ex_to_pair(recombine_pair_to_ex(*it)); - if (!ep.is_equal(*it)) { - // combined pair is a numeric power which can be simplified - *it=ep; - return true; - } - if (ex_to_numeric((*it).coeff).is_equal(_num1())) { - // combined pair has coeff 1 and must be moved to the end - return true; - } - } - return false; + if (is_ex_exactly_of_type((*it).rest,mul) && + ex_to_numeric((*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; + } + if (is_ex_exactly_of_type((*it).rest,numeric)) { + expair ep=split_ex_to_pair(recombine_pair_to_ex(*it)); + if (!ep.is_equal(*it)) { + // combined pair is a numeric power which can be simplified + *it = ep; + return true; + } + if (ex_to_numeric((*it).coeff).is_equal(_num1())) { + // combined pair has coeff 1 and must be moved to the end + return true; + } + } + return false; } 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_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)); } 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_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))); } bool mul::can_make_flat(const expair & p) const { - GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric)); - // 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()); + GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric)); + // 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()); } ex mul::expand(unsigned options) const { - exvector sub_expanded_seq; - intvector positions_of_adds; - intvector number_of_add_operands; - - epvector * expanded_seqp = expandchildren(options); - - const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp; - - positions_of_adds.resize(expanded_seq.size()); - number_of_add_operands.resize(expanded_seq.size()); - - int number_of_adds = 0; - int number_of_expanded_terms = 1; - - unsigned current_position = 0; - epvector::const_iterator last = expanded_seq.end(); - for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) { - if (is_ex_exactly_of_type((*cit).rest,add)&& - (ex_to_numeric((*cit).coeff).is_equal(_num1()))) { - positions_of_adds[number_of_adds] = current_position; - const add & expanded_addref = ex_to_add((*cit).rest); - unsigned addref_nops = expanded_addref.nops(); - number_of_add_operands[number_of_adds] = addref_nops; - number_of_expanded_terms *= addref_nops; - number_of_adds++; - } - current_position++; - } - - if (number_of_adds==0) { - if (expanded_seqp==0) { - return this->setflag(status_flags::expanded); - } - return (new mul(expanded_seqp,overall_coeff))-> - setflag(status_flags::dynallocated || - status_flags::expanded); - } - - exvector distrseq; - distrseq.reserve(number_of_expanded_terms); - - intvector k; - k.resize(number_of_adds); - - int l; - for (l=0; l - setflag(status_flags::dynallocated | - status_flags::expanded)); - - // increment k[] - l=number_of_adds-1; - while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) { - k[l]=0; - l--; - } - if (l<0) break; - } - - if (expanded_seqp!=0) { - delete expanded_seqp; - } - /* - cout << "mul::expand() distrseq begin" << endl; - for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) { - (*cit).printtree(cout); - } - cout << "mul::expand() distrseq end" << endl; - */ - - return (new add(distrseq))->setflag(status_flags::dynallocated | - status_flags::expanded); -} - + if (flags & status_flags::expanded) + return *this; + + exvector sub_expanded_seq; + + epvector * expanded_seqp = expandchildren(options); + + const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp; + + int number_of_adds = 0; + 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()))) { + ++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); + 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); + } else { + non_adds.push_back(split_ex_to_pair(last_expanded)); + last_expanded = (*cit).rest; + } + } else { + non_adds.push_back(*cit); + } + ++cit; + } + if (expanded_seqp) + delete expanded_seqp; + + if (is_ex_exactly_of_type(last_expanded,add)) { + add const & finaladd = ex_to_add(last_expanded); + exvector distrseq; + int n = finaladd.nops(); + distrseq.reserve(n); + for (int i=0; isetflag(status_flags::dynallocated | status_flags::expanded)); + } + return ((new add(distrseq))-> + setflag(status_flags::dynallocated | status_flags::expanded)); + } + non_adds.push_back(split_ex_to_pair(last_expanded)); + return (new mul(non_adds,overall_coeff))-> + setflag(status_flags::dynallocated | status_flags::expanded); +} + + ////////// // new virtual functions which can be overridden by derived classes ////////// @@ -757,57 +714,47 @@ ex mul::expand(unsigned options) const // non-virtual functions in this class ////////// + +/** Member-wise expand the expairs representing this sequence. This must be + * overridden from expairseq::expandchildren() and done iteratively in order + * to allow for early cancallations and thus safe memory. + * + * @see mul::expand() + * @return pointer to epvector containing expanded representation or zero + * pointer, if sequence is unchanged. */ epvector * mul::expandchildren(unsigned options) const { - epvector::const_iterator last = seq.end(); - epvector::const_iterator cit = seq.begin(); - while (cit!=last) { - const ex & factor = recombine_pair_to_ex(*cit); - const ex & expanded_factor = factor.expand(options); - if (!are_ex_trivially_equal(factor,expanded_factor)) { - - // something changed, copy seq, eval and return it - epvector *s=new epvector; - s->reserve(seq.size()); - - // copy parts of seq which are known not to have changed - epvector::const_iterator cit2 = seq.begin(); - while (cit2!=cit) { - s->push_back(*cit2); - ++cit2; - } - // copy first changed element - s->push_back(split_ex_to_pair(expanded_factor)); - ++cit2; - // copy rest - while (cit2!=last) { - s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options))); - ++cit2; - } - return s; - } - ++cit; - } - - return 0; // nothing has changed + epvector::const_iterator last = seq.end(); + epvector::const_iterator cit = seq.begin(); + while (cit!=last) { + const ex & factor = recombine_pair_to_ex(*cit); + const ex & expanded_factor = factor.expand(options); + if (!are_ex_trivially_equal(factor,expanded_factor)) { + + // something changed, copy seq, eval and return it + epvector *s = new epvector; + s->reserve(seq.size()); + + // copy parts of seq which are known not to have changed + epvector::const_iterator cit2 = seq.begin(); + while (cit2!=cit) { + s->push_back(*cit2); + ++cit2; + } + // copy first changed element + s->push_back(split_ex_to_pair(expanded_factor)); + ++cit2; + // copy rest + while (cit2!=last) { + s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options))); + ++cit2; + } + return s; + } + ++cit; + } + + return 0; // nothing has changed } - -////////// -// static member variables -////////// - -// protected - -unsigned mul::precedence=50; - - -////////// -// global constants -////////// - -const mul some_mul; -const type_info & typeid_mul=typeid(some_mul); -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC