X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=2c8456510a44d35201f5659dec50f27f32206e02;hp=e156a0fff00c5ad50ff05a91cd77e2fcde1721ea;hb=5ef801553eb39aed7bd2df9dd1aff9d752c3ea9d;hpb=9c91319253425e66f9b6feb9e7036f841bc55e84 diff --git a/ginac/mul.cpp b/ginac/mul.cpp index e156a0ff..2c845651 100644 --- a/ginac/mul.cpp +++ b/ginac/mul.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's products of expressions. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2003 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 @@ -20,14 +20,18 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include #include +#include #include "mul.h" #include "add.h" #include "power.h" +#include "operators.h" +#include "matrix.h" +#include "lst.h" #include "archive.h" -#include "debugmsg.h" #include "utils.h" namespace GiNaC { @@ -35,54 +39,46 @@ namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq) ////////// -// default ctor, dctor, copy ctor assignment operator and helpers +// default constructor ////////// mul::mul() { - debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_mul; } -DEFAULT_COPY(mul) -DEFAULT_DESTROY(mul) - ////////// -// other ctors +// other constructors ////////// // public 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()); } @@ -121,104 +115,162 @@ 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 +{ + if (is_a(c)) { + + inherited::print(c, level); + + } else if (is_a(c)) { + + if (precedence() <= level) + c.s << "("; + + 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/" + bool needclosingparenthesis = false; + if (it == seq.begin() && it->coeff.info(info_flags::negint)) { + if (is_a(c)) { + c.s << "recip("; + needclosingparenthesis = true; + } else + c.s << "1.0/"; + } -void mul::print(std::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; + // If the exponent is 1 or -1, it is left out + if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) + it->rest.print(c, precedence()); + else if (it->coeff.info(info_flags::negint)) + // Outer parens around ex needed for broken GCC parser: + (ex(power(it->rest, -ex_to(it->coeff)))).print(c, level); else - os << coeff; - } else { - if (coeff.csgn()==-1) - (-coeff).print(os, precedence); + // Outer parens around ex needed for broken GCC parser: + (ex(power(it->rest, ex_to(it->coeff)))).print(c, level); + + if (needclosingparenthesis) + c.s << ")"; + + // Separator is "/" for negative integer powers, "*" otherwise + ++it; + if (it != itend) { + if (it->coeff.info(info_flags::negint)) + c.s << "/"; + else + c.s << "*"; + } + } + + if (precedence() <= level) + c.s << ")"; + + } else if (is_a(c)) { + c.s << class_name() << '('; + op(0).print(c); + for (size_t i=1; i(c)) + c.s << "{("; else - coeff.print(os, precedence); + c.s << "("; } - os << '*'; - } - // then proceed with the remaining factors: - for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) { - if (!first) { - os << '*'; - } else { - first=false; + + // First print the overall numeric coefficient + const 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_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_a(c)) + c.s << ' '; + else + c.s << '*'; } - recombine_pair_to_ex(*cit).print(os,precedence); - } - if (precedence<=upper_precedence) os << ")"; -} -void mul::printraw(std::ostream & os) const -{ - debugmsg("mul printraw",LOGLEVEL_PRINT); + // Then proceed with the remaining factors + epvector::const_iterator it = seq.begin(), itend = seq.end(); + if (is_a(c)) { + + // Separate factors into those with negative numeric exponent + // and all others + exvector neg_powers, others; + while (it != itend) { + GINAC_ASSERT(is_exactly_a(it->coeff)); + if (ex_to(it->coeff).is_negative()) + neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff)))); + else + others.push_back(recombine_pair_to_ex(*it)); + ++it; + } - 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 << ")"; -} + if (!neg_powers.empty()) { -void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const -{ - debugmsg("mul print csrc", LOGLEVEL_PRINT); - if (precedence <= upper_precedence) - os << "("; + // Factors with negative exponent are printed as a fraction + c.s << "\\frac{"; + mul(others).eval().print(c); + c.s << "}{"; + mul(neg_powers).eval().print(c); + c.s << "}"; - 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/"; + } else { + + // All other factors are printed in the ordinary way + exvector::const_iterator vit = others.begin(), vitend = others.end(); + while (vit != vitend) { + c.s << ' '; + vit->print(c, precedence()); + ++vit; + } + } + + } else { + + bool first = true; + while (it != itend) { + if (!first) + c.s << '*'; + else + first = false; + recombine_pair_to_ex(*it).print(c, precedence()); + ++it; + } } - // 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 << "/"; + if (precedence() <= level) { + if (is_a(c)) + c.s << ")}"; else - os << "*"; + c.s << ")"; } } - if (precedence <= upper_precedence) - os << ")"; } bool mul::info(unsigned inf) const @@ -230,16 +282,20 @@ 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; } @@ -247,27 +303,33 @@ bool mul::info(unsigned inf) const return inherited::info(inf); } -int mul::degree(const symbol & s) 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 symbol & s) const +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; } -ex mul::coeff(const symbol & s, int n) const +ex mul::coeff(const ex & s, int n) const { exvector coeffseq; coeffseq.reserve(seq.size()+1); @@ -275,97 +337,103 @@ ex mul::coeff(const symbol & 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)) - printtree(std::cerr,0); - GINAC_ASSERT(!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_exactly_a(recombine_pair_to_ex(*i))) + print(print_tree(std::cerr)); + 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())) { + is_exactly_a((*seq.begin()).rest) && + 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(); @@ -379,20 +447,196 @@ 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::simplify_ncmul(const exvector & v) const +ex mul::evalm() const { - throw(std::logic_error("mul::simplify_ncmul() should never have been called!")); + // numeric*matrix + if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1) + && is_a(seq[0].rest)) + 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_a(m)) { + 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::eval_ncmul(const exvector & v) const +{ + if (seq.empty()) + return inherited::eval_ncmul(v); + + // Find first noncommutative element and call its eval_ncmul() + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + if (i->rest.return_type() == return_types::noncommutative) + return i->rest.eval_ncmul(v); + ++i; + } + return inherited::eval_ncmul(v); +} + +bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls) +{ + ex origbase; + int origexponent; + int origexpsign; + + if (is_exactly_a(origfactor) && origfactor.op(1).info(info_flags::integer)) { + origbase = origfactor.op(0); + int expon = ex_to(origfactor.op(1)).to_int(); + origexponent = expon > 0 ? expon : -expon; + origexpsign = expon > 0 ? 1 : -1; + } else { + origbase = origfactor; + origexponent = 1; + origexpsign = 1; + } + + ex patternbase; + int patternexponent; + int patternexpsign; + + if (is_exactly_a(patternfactor) && patternfactor.op(1).info(info_flags::integer)) { + patternbase = patternfactor.op(0); + int expon = ex_to(patternfactor.op(1)).to_int(); + patternexponent = expon > 0 ? expon : -expon; + patternexpsign = expon > 0 ? 1 : -1; + } else { + patternbase = patternfactor; + patternexponent = 1; + patternexpsign = 1; + } + + lst saverepls = repls; + if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls)) + return false; + repls = saverepls; + + int newnummatches = origexponent / patternexponent; + if (newnummatches < nummatches) + nummatches = newnummatches; + return true; +} + +ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const +{ + std::vector subsed(seq.size(), false); + exvector subsresult(seq.size()); + + for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) { + + if (is_exactly_a(it->first)) { + + int nummatches = std::numeric_limits::max(); + std::vector currsubsed(seq.size(), false); + bool succeed = true; + lst repls; + + for (size_t j=0; jfirst.nops(); j++) { + bool found=false; + for (size_t k=0; kfirst.op(j), nummatches, repls)) { + currsubsed[k] = true; + found = true; + break; + } + } + if (!found) { + succeed = false; + break; + } + } + if (!succeed) + continue; + + bool foundfirstsubsedfactor = false; + for (size_t j=0; jsecond.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches); + } + subsed[j] = true; + } + } + + } else { + + int nummatches = std::numeric_limits::max(); + lst repls; + + for (size_t j=0; jnops(); j++) { + if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) { + subsed[j] = true; + subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches); + } + } + } + } + + bool subsfound = false; + for (size_t i=0; isetflag(status_flags::dynallocated); } // protected @@ -401,15 +645,21 @@ ex mul::simplify_ncmul(const exvector & v) const * @see ex::diff */ ex mul::derivative(const symbol & s) const { + size_t 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); } @@ -419,51 +669,50 @@ int mul::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } -bool mul::is_equal_same_type(const basic & other) const -{ - return inherited::is_equal_same_type(other); -} - -unsigned mul::return_type(void) const +unsigned mul::return_type() 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; } -unsigned mul::return_type_tinfo(void) const +unsigned mul::return_type_tinfo() 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; @@ -471,22 +720,22 @@ 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); - if (is_ex_exactly_of_type(powerref.exponent,numeric)) + if (is_exactly_a(e)) { + const power & powerref = ex_to(e); + if (is_exactly_a(powerref.exponent)) 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, @@ -494,11 +743,11 @@ expair mul::combine_ex_with_coeff_to_pair(const ex & e, { // to avoid duplication of power simplification rules, // we create a temporary power object - // otherwise it would be hard to correctly simplify + // otherwise it would be hard to correctly evaluate // expression like (4^(1/3))^(3/2) - if (are_ex_trivially_equal(c,_ex1())) + if (c.is_equal(_ex1)) return split_ex_to_pair(e); - + return split_ex_to_pair(power(e,c)); } @@ -507,38 +756,38 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p, { // to avoid duplication of power simplification rules, // we create a temporary power object - // otherwise it would be hard to correctly simplify + // otherwise it would be hard to correctly evaluate // expression like (4^(1/3))^(3/2) - if (are_ex_trivially_equal(c,_ex1())) + if (c.is_equal(_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 (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); + return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated); } bool mul::expair_needs_further_processing(epp it) { - if (is_ex_exactly_of_type((*it).rest,mul) && - ex_to_numeric((*it).coeff).is_integer()) { + if (is_exactly_a(it->rest) && + 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; } - if (is_ex_exactly_of_type((*it).rest,numeric)) { - expair ep=split_ex_to_pair(recombine_pair_to_ex(*it)); + if (is_exactly_a(it->rest)) { + 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())) { + if (it->coeff.is_equal(_ex1)) { // combined pair has coeff 1 and must be moved to the end return true; } @@ -546,73 +795,110 @@ bool mul::expair_needs_further_processing(epp it) return false; } -ex mul::default_overall_coeff(void) const +ex mul::default_overall_coeff() 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_exactly_a(cit->rest) && + (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; i1(last_expanded)) { + + // Expand a product of two sums, aggressive version. + // Caring for the overall coefficients in separate loops can + // sometimes give a performance gain of up to 15%! + + const int sizedifference = ex_to(last_expanded).seq.size()-ex_to(cit->rest).seq.size(); + // add2 is for the inner loop and should be the bigger of the two sums + // in the presence of asymptotically good sorting: + const add& add1 = (sizedifference<0 ? ex_to(last_expanded) : ex_to(cit->rest)); + const add& add2 = (sizedifference<0 ? ex_to(cit->rest) : ex_to(last_expanded)); + const epvector::const_iterator add1begin = add1.seq.begin(); + const epvector::const_iterator add1end = add1.seq.end(); + const epvector::const_iterator add2begin = add2.seq.begin(); + const epvector::const_iterator add2end = add2.seq.end(); + epvector distrseq; + distrseq.reserve(add1.seq.size()+add2.seq.size()); + // Multiply add2 with the overall coefficient of add1 and append it to distrseq: + if (!add1.overall_coeff.is_zero()) { + if (add1.overall_coeff.is_equal(_ex1)) + distrseq.insert(distrseq.end(),add2begin,add2end); + else + for (epvector::const_iterator i=add2begin; i!=add2end; ++i) + distrseq.push_back(expair(i->rest, ex_to(i->coeff).mul_dyn(ex_to(add1.overall_coeff)))); + } + // Multiply add1 with the overall coefficient of add2 and append it to distrseq: + if (!add2.overall_coeff.is_zero()) { + if (add2.overall_coeff.is_equal(_ex1)) + distrseq.insert(distrseq.end(),add1begin,add1end); + else + for (epvector::const_iterator i=add1begin; i!=add1end; ++i) + distrseq.push_back(expair(i->rest, ex_to(i->coeff).mul_dyn(ex_to(add2.overall_coeff)))); + } + // Compute the new overall coefficient and put it together: + ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated); + // Multiply explicitly all non-numeric terms of add1 and add2: + for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) { + // We really have to combine terms here in order to compactify + // the result. Otherwise it would become waayy tooo bigg. + numeric oc; + distrseq.clear(); + for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) { + // Don't push_back expairs which might have a rest that evaluates to a numeric, + // since that would violate an invariant of expairseq: + const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated); + if (is_exactly_a(rest)) + oc += ex_to(rest).mul(ex_to(i1->coeff).mul(ex_to(i2->coeff))); + else + distrseq.push_back(expair(rest, ex_to(i1->coeff).mul_dyn(ex_to(i2->coeff)))); } + tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated); } - last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded); + last_expanded = tmp_accu; + } 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); @@ -621,23 +907,26 @@ 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_exactly_a(last_expanded)) { + const add & finaladd = ex_to(last_expanded); exvector distrseq; - int n = finaladd.nops(); + size_t 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)); } @@ -661,7 +950,7 @@ 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); @@ -694,12 +983,4 @@ epvector * mul::expandchildren(unsigned options) const return 0; // nothing has changed } -////////// -// static member variables -////////// - -// protected - -unsigned mul::precedence = 50; - } // namespace GiNaC