X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=063722b10dd90e34e0b7afec1eb0365db0202b5c;hp=3188dd2297790c801c9e3c1b219300353919e92b;hb=05d274b894f2f84217d308bf4d4f2202b9627c63;hpb=7d870583a6bf21a2ffb7b6f051b702064623892e diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 3188dd22..063722b1 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2019 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 @@ -21,10 +21,6 @@ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include -#include -#include - #include "pseries.h" #include "add.h" #include "inifcns.h" // for Order function @@ -38,6 +34,10 @@ #include "archive.h" #include "utils.h" +#include +#include +#include + namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, @@ -52,7 +52,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, * Default constructor */ -pseries::pseries() : inherited(&pseries::tinfo_static) { } +pseries::pseries() { } /* @@ -68,8 +68,43 @@ pseries::pseries() : inherited(&pseries::tinfo_static) { } * @param rel_ expansion variable and point (must hold a relational) * @param ops_ vector of {coefficient, power} pairs (coefficient must not be zero) * @return newly constructed pseries */ -pseries::pseries(const ex &rel_, const epvector &ops_) : basic(&pseries::tinfo_static), seq(ops_) +pseries::pseries(const ex &rel_, const epvector &ops_) + : seq(ops_) +{ +#ifdef DO_GINAC_ASSERT + auto i = seq.begin(); + while (i != seq.end()) { + auto ip1 = i+1; + if (ip1 != seq.end()) + GINAC_ASSERT(!is_order_function(i->rest)); + else + break; + GINAC_ASSERT(is_a(i->coeff)); + GINAC_ASSERT(ex_to(i->coeff) < ex_to(ip1->coeff)); + ++i; + } +#endif // def DO_GINAC_ASSERT + GINAC_ASSERT(is_a(rel_)); + GINAC_ASSERT(is_a(rel_.lhs())); + point = rel_.rhs(); + var = rel_.lhs(); +} +pseries::pseries(const ex &rel_, epvector &&ops_) + : seq(std::move(ops_)) { +#ifdef DO_GINAC_ASSERT + auto i = seq.begin(); + while (i != seq.end()) { + auto ip1 = i+1; + if (ip1 != seq.end()) + GINAC_ASSERT(!is_order_function(i->rest)); + else + break; + GINAC_ASSERT(is_a(i->coeff)); + GINAC_ASSERT(ex_to(i->coeff) < ex_to(ip1->coeff)); + ++i; + } +#endif // def DO_GINAC_ASSERT GINAC_ASSERT(is_a(rel_)); GINAC_ASSERT(is_a(rel_.lhs())); point = rel_.rhs(); @@ -81,19 +116,18 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(&pseries::tinfo_s * Archiving */ -pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) +void pseries::read_archive(const archive_node &n, lst &sym_lst) { - archive_node::archive_node_cit first = n.find_first("coeff"); - archive_node::archive_node_cit last = n.find_last("power"); - ++last; - seq.reserve((last-first)/2); + inherited::read_archive(n, sym_lst); + auto range = n.find_property_range("coeff", "power"); + seq.reserve((range.end-range.begin)/2); - for (archive_node::archive_node_cit loc = first; loc < last;) { + for (auto loc = range.begin; loc < range.end;) { ex rest; ex coeff; n.find_ex_by_loc(loc++, rest, sym_lst); n.find_ex_by_loc(loc++, coeff, sym_lst); - seq.push_back(expair(rest, coeff)); + seq.emplace_back(expair(rest, coeff)); } n.find_ex("var", var, sym_lst); @@ -103,17 +137,14 @@ pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) void pseries::archive(archive_node &n) const { inherited::archive(n); - epvector::const_iterator i = seq.begin(), iend = seq.end(); - while (i != iend) { - n.add_ex("coeff", i->rest); - n.add_ex("power", i->coeff); - ++i; + for (auto & it : seq) { + n.add_ex("coeff", it.rest); + n.add_ex("power", it.coeff); } n.add_ex("var", var); n.add_ex("point", point); } -DEFAULT_UNARCHIVE(pseries) ////////// // functions overriding virtual functions from base classes @@ -129,7 +160,7 @@ void pseries::print_series(const print_context & c, const char *openbrace, const if (seq.empty()) c.s << '0'; - epvector::const_iterator i = seq.begin(), end = seq.end(); + auto i = seq.begin(), end = seq.end(); while (i != end) { // print a sign, if needed @@ -170,7 +201,7 @@ void pseries::print_series(const print_context & c, const char *openbrace, const } } } else - Order(power(var-point,i->coeff)).print(c); + Order(pow(var - point, i->coeff)).print(c); ++i; } @@ -248,7 +279,7 @@ int pseries::compare_same_type(const basic & other) const return cmpval; // ...and if that failed the individual elements - epvector::const_iterator it = seq.begin(), o_it = o.seq.begin(); + auto it = seq.begin(), o_it = o.seq.begin(); while (it!=seq.end() && o_it!=o.seq.end()) { cmpval = it->compare(*o_it); if (cmpval) @@ -274,8 +305,8 @@ ex pseries::op(size_t i) const throw (std::out_of_range("op() out of range")); if (is_order_function(seq[i].rest)) - return Order(power(var-point, seq[i].coeff)); - return seq[i].rest * power(var - point, seq[i].coeff); + return Order(pow(var-point, seq[i].coeff)); + return seq[i].rest * pow(var - point, seq[i].coeff); } /** Return degree of highest power of the series. This is usually the exponent @@ -283,25 +314,17 @@ ex pseries::op(size_t i) const * series is examined termwise. */ int pseries::degree(const ex &s) const { - if (var.is_equal(s)) { - // Return last exponent - if (seq.size()) - return ex_to((seq.end()-1)->coeff).to_int(); - else - return 0; - } else { - epvector::const_iterator it = seq.begin(), itend = seq.end(); - if (it == itend) - return 0; - int max_pow = std::numeric_limits::min(); - while (it != itend) { - int pow = it->rest.degree(s); - if (pow > max_pow) - max_pow = pow; - ++it; - } - return max_pow; - } + if (seq.empty()) + return 0; + + if (var.is_equal(s)) + // Return last/greatest exponent + return ex_to((seq.end()-1)->coeff).to_int(); + + int max_pow = std::numeric_limits::min(); + for (auto & it : seq) + max_pow = std::max(max_pow, it.rest.degree(s)); + return max_pow; } /** Return degree of lowest power of the series. This is usually the exponent @@ -311,25 +334,17 @@ int pseries::degree(const ex &s) const * I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */ int pseries::ldegree(const ex &s) const { - if (var.is_equal(s)) { - // Return first exponent - if (seq.size()) - return ex_to((seq.begin())->coeff).to_int(); - else - return 0; - } else { - epvector::const_iterator it = seq.begin(), itend = seq.end(); - if (it == itend) - return 0; - int min_pow = std::numeric_limits::max(); - while (it != itend) { - int pow = it->rest.ldegree(s); - if (pow < min_pow) - min_pow = pow; - ++it; - } - return min_pow; - } + if (seq.empty()) + return 0; + + if (var.is_equal(s)) + // Return first/smallest exponent + return ex_to((seq.begin())->coeff).to_int(); + + int min_pow = std::numeric_limits::max(); + for (auto & it : seq) + min_pow = std::min(min_pow, it.rest.degree(s)); + return min_pow; } /** Return coefficient of degree n in power series if s is the expansion @@ -377,43 +392,31 @@ ex pseries::collect(const ex &s, bool distributed) const } /** Perform coefficient-wise automatic term rewriting rules in this class. */ -ex pseries::eval(int level) const +ex pseries::eval() const { - if (level == 1) - return this->hold(); - - if (level == -max_recursion_level) - throw (std::runtime_error("pseries::eval(): recursion limit exceeded")); - + if (flags & status_flags::evaluated) { + return *this; + } + // Construct a new series with evaluated coefficients epvector new_seq; new_seq.reserve(seq.size()); - epvector::const_iterator it = seq.begin(), itend = seq.end(); - while (it != itend) { - new_seq.push_back(expair(it->rest.eval(level-1), it->coeff)); - ++it; - } - return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); + for (auto & it : seq) + new_seq.emplace_back(expair(it.rest, it.coeff)); + + return dynallocate(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated); } /** Evaluate coefficients numerically. */ -ex pseries::evalf(int level) const +ex pseries::evalf() const { - if (level == 1) - return *this; - - if (level == -max_recursion_level) - throw (std::runtime_error("pseries::evalf(): recursion limit exceeded")); - // Construct a new series with evaluated coefficients epvector new_seq; new_seq.reserve(seq.size()); - epvector::const_iterator it = seq.begin(), itend = seq.end(); - while (it != itend) { - new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff)); - ++it; - } - return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); + for (auto & it : seq) + new_seq.emplace_back(expair(it.rest.evalf(), it.coeff)); + + return dynallocate(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated); } ex pseries::conjugate() const @@ -421,18 +424,14 @@ ex pseries::conjugate() const if(!var.info(info_flags::real)) return conjugate_function(*this).hold(); - epvector * newseq = conjugateepvector(seq); + std::unique_ptr newseq(conjugateepvector(seq)); ex newpoint = point.conjugate(); - if (!newseq && are_ex_trivially_equal(point, newpoint)) { + if (!newseq && are_ex_trivially_equal(point, newpoint)) { return *this; } - ex result = (new pseries(var==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated); - if (newseq) { - delete newseq; - } - return result; + return dynallocate(var==newpoint, newseq ? std::move(*newseq) : seq); } ex pseries::real_part() const @@ -445,9 +444,9 @@ ex pseries::real_part() const epvector v; v.reserve(seq.size()); - for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) - v.push_back(expair((i->rest).real_part(), i->coeff)); - return (new pseries(var==point, v))->setflag(status_flags::dynallocated); + for (auto & it : seq) + v.emplace_back(expair(it.rest.real_part(), it.coeff)); + return dynallocate(var==point, std::move(v)); } ex pseries::imag_part() const @@ -460,33 +459,32 @@ ex pseries::imag_part() const epvector v; v.reserve(seq.size()); - for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) - v.push_back(expair((i->rest).imag_part(), i->coeff)); - return (new pseries(var==point, v))->setflag(status_flags::dynallocated); + for (auto & it : seq) + v.emplace_back(expair(it.rest.imag_part(), it.coeff)); + return dynallocate(var==point, std::move(v)); } ex pseries::eval_integ() const { - epvector *newseq = NULL; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + std::unique_ptr newseq(nullptr); + for (auto i=seq.begin(); i!=seq.end(); ++i) { if (newseq) { - newseq->push_back(expair(i->rest.eval_integ(), i->coeff)); + newseq->emplace_back(expair(i->rest.eval_integ(), i->coeff)); continue; } ex newterm = i->rest.eval_integ(); if (!are_ex_trivially_equal(newterm, i->rest)) { - newseq = new epvector; + newseq.reset(new epvector); newseq->reserve(seq.size()); - for (epvector::const_iterator j=seq.begin(); j!=i; ++j) + for (auto j=seq.begin(); j!=i; ++j) newseq->push_back(*j); - newseq->push_back(expair(newterm, i->coeff)); + newseq->emplace_back(expair(newterm, i->coeff)); } } ex newpoint = point.eval_integ(); if (newseq || !are_ex_trivially_equal(newpoint, point)) - return (new pseries(var==newpoint, *newseq)) - ->setflag(status_flags::dynallocated); + return dynallocate(var==newpoint, std::move(*newseq)); return *this; } @@ -495,25 +493,24 @@ ex pseries::evalm() const // evalm each coefficient epvector newseq; bool something_changed = false; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + for (auto i=seq.begin(); i!=seq.end(); ++i) { if (something_changed) { ex newcoeff = i->rest.evalm(); if (!newcoeff.is_zero()) - newseq.push_back(expair(newcoeff, i->coeff)); - } - else { + newseq.emplace_back(expair(newcoeff, i->coeff)); + } else { ex newcoeff = i->rest.evalm(); if (!are_ex_trivially_equal(newcoeff, i->rest)) { something_changed = true; newseq.reserve(seq.size()); std::copy(seq.begin(), i, std::back_inserter(newseq)); if (!newcoeff.is_zero()) - newseq.push_back(expair(newcoeff, i->coeff)); + newseq.emplace_back(expair(newcoeff, i->coeff)); } } } if (something_changed) - return (new pseries(var==point, newseq))->setflag(status_flags::dynallocated); + return dynallocate(var==point, std::move(newseq)); else return *this; } @@ -530,12 +527,9 @@ ex pseries::subs(const exmap & m, unsigned options) const // expansion point epvector newseq; newseq.reserve(seq.size()); - epvector::const_iterator it = seq.begin(), itend = seq.end(); - while (it != itend) { - newseq.push_back(expair(it->rest.subs(m, options), it->coeff)); - ++it; - } - return (new pseries(relational(var,point.subs(m, options)), newseq))->setflag(status_flags::dynallocated); + for (auto & it : seq) + newseq.emplace_back(expair(it.rest.subs(m, options), it.coeff)); + return dynallocate(relational(var,point.subs(m, options)), std::move(newseq)); } /** Implementation of ex::expand() for a power series. It expands all the @@ -543,15 +537,12 @@ ex pseries::subs(const exmap & m, unsigned options) const ex pseries::expand(unsigned options) const { epvector newseq; - epvector::const_iterator i = seq.begin(), end = seq.end(); - while (i != end) { - ex restexp = i->rest.expand(); + for (auto & it : seq) { + ex restexp = it.rest.expand(); if (!restexp.is_zero()) - newseq.push_back(expair(restexp, i->coeff)); - ++i; + newseq.emplace_back(expair(restexp, it.coeff)); } - return (new pseries(relational(var,point), newseq)) - ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)); + return dynallocate(relational(var,point), std::move(newseq)).setflag(options == 0 ? status_flags::expanded : 0); } /** Implementation of ex::diff() for a power series. @@ -559,51 +550,45 @@ ex pseries::expand(unsigned options) const ex pseries::derivative(const symbol & s) const { epvector new_seq; - epvector::const_iterator it = seq.begin(), itend = seq.end(); if (s == var) { // FIXME: coeff might depend on var - while (it != itend) { - if (is_order_function(it->rest)) { - new_seq.push_back(expair(it->rest, it->coeff - 1)); + for (auto & it : seq) { + if (is_order_function(it.rest)) { + new_seq.emplace_back(expair(it.rest, it.coeff - 1)); } else { - ex c = it->rest * it->coeff; + ex c = it.rest * it.coeff; if (!c.is_zero()) - new_seq.push_back(expair(c, it->coeff - 1)); + new_seq.emplace_back(expair(c, it.coeff - 1)); } - ++it; } } else { - while (it != itend) { - if (is_order_function(it->rest)) { - new_seq.push_back(*it); + for (auto & it : seq) { + if (is_order_function(it.rest)) { + new_seq.push_back(it); } else { - ex c = it->rest.diff(s); + ex c = it.rest.diff(s); if (!c.is_zero()) - new_seq.push_back(expair(c, it->coeff)); + new_seq.emplace_back(expair(c, it.coeff)); } - ++it; } } - return pseries(relational(var,point), new_seq); + return pseries(relational(var,point), std::move(new_seq)); } ex pseries::convert_to_poly(bool no_order) const { ex e; - epvector::const_iterator it = seq.begin(), itend = seq.end(); - - while (it != itend) { - if (is_order_function(it->rest)) { + for (auto & it : seq) { + if (is_order_function(it.rest)) { if (!no_order) - e += Order(power(var - point, it->coeff)); + e += Order(pow(var - point, it.coeff)); } else - e += it->rest * power(var - point, it->coeff); - ++it; + e += it.rest * pow(var - point, it.coeff); } return e; } @@ -615,7 +600,7 @@ bool pseries::is_terminating() const ex pseries::coeffop(size_t i) const { - if (i >=nops()) + if (i >= nops()) throw (std::out_of_range("coeffop() out of range")); return seq[i].rest; } @@ -641,8 +626,8 @@ ex basic::series(const relational & r, int order, unsigned options) const // default for order-values that make no sense for Taylor expansion if ((order <= 0) && this->has(s)) { - seq.push_back(expair(Order(_ex1), order)); - return pseries(r, seq); + seq.emplace_back(expair(Order(_ex1), order)); + return pseries(r, std::move(seq)); } // do Taylor expansion @@ -651,29 +636,29 @@ ex basic::series(const relational & r, int order, unsigned options) const ex coeff = deriv.subs(r, subs_options::no_pattern); if (!coeff.is_zero()) { - seq.push_back(expair(coeff, _ex0)); + seq.emplace_back(expair(coeff, _ex0)); } int n; for (n=1; nis_equal_same_type(ex_to(r.lhs()))) { if (order > 0 && !point.is_zero()) - seq.push_back(expair(point, _ex0)); + seq.emplace_back(expair(point, _ex0)); if (order > 1) - seq.push_back(expair(_ex1, _ex1)); + seq.emplace_back(expair(_ex1, _ex1)); else - seq.push_back(expair(Order(_ex1), numeric(order))); + seq.emplace_back(expair(Order(_ex1), numeric(order))); } else - seq.push_back(expair(*this, _ex0)); - return pseries(r, seq); + seq.emplace_back(expair(*this, _ex0)); + return pseries(r, std::move(seq)); } @@ -708,17 +693,14 @@ ex pseries::add_series(const pseries &other) const // Adding two series with different variables or expansion points // results in an empty (constant) series if (!is_compatible_to(other)) { - epvector nul; - nul.push_back(expair(Order(_ex1), _ex0)); - return pseries(relational(var,point), nul); + epvector nul { expair(Order(_ex1), _ex0) }; + return pseries(relational(var,point), std::move(nul)); } // Series addition epvector new_seq; - epvector::const_iterator a = seq.begin(); - epvector::const_iterator b = other.seq.begin(); - epvector::const_iterator a_end = seq.end(); - epvector::const_iterator b_end = other.seq.end(); + auto a = seq.begin(), a_end = seq.end(); + auto b = other.seq.begin(), b_end = other.seq.end(); int pow_a = std::numeric_limits::max(), pow_b = std::numeric_limits::max(); for (;;) { // If a is empty, fill up with elements from b and stop @@ -757,18 +739,18 @@ ex pseries::add_series(const pseries &other) const } else { // Add coefficient of a and b if (is_order_function((*a).rest) || is_order_function((*b).rest)) { - new_seq.push_back(expair(Order(_ex1), (*a).coeff)); + new_seq.emplace_back(expair(Order(_ex1), (*a).coeff)); break; // Order term ends the sequence } else { ex sum = (*a).rest + (*b).rest; if (!(sum.is_zero())) - new_seq.push_back(expair(sum, numeric(pow_a))); + new_seq.emplace_back(expair(sum, numeric(pow_a))); ++a; ++b; } } } - return pseries(relational(var,point), new_seq); + return pseries(relational(var,point), std::move(new_seq)); } @@ -783,16 +765,14 @@ ex add::series(const relational & r, int order, unsigned options) const acc = overall_coeff.series(r, order, options); // Add remaining terms - epvector::const_iterator it = seq.begin(); - epvector::const_iterator itend = seq.end(); - for (; it!=itend; ++it) { + for (auto & it : seq) { ex op; - if (is_exactly_a(it->rest)) - op = it->rest; + if (is_exactly_a(it.rest)) + op = it.rest; else - op = it->rest.series(r, order, options); - if (!it->coeff.is_equal(_ex1)) - op = ex_to(op).mul_const(ex_to(it->coeff)); + op = it.rest.series(r, order, options); + if (!it.coeff.is_equal(_ex1)) + op = ex_to(op).mul_const(ex_to(it.coeff)); // Series addition acc = ex_to(acc).add_series(ex_to(op)); @@ -811,15 +791,13 @@ ex pseries::mul_const(const numeric &other) const epvector new_seq; new_seq.reserve(seq.size()); - epvector::const_iterator it = seq.begin(), itend = seq.end(); - while (it != itend) { - if (!is_order_function(it->rest)) - new_seq.push_back(expair(it->rest * other, it->coeff)); + for (auto & it : seq) { + if (!is_order_function(it.rest)) + new_seq.emplace_back(expair(it.rest * other, it.coeff)); else - new_seq.push_back(*it); - ++it; + new_seq.push_back(it); } - return pseries(relational(var,point), new_seq); + return pseries(relational(var,point), std::move(new_seq)); } @@ -833,23 +811,21 @@ ex pseries::mul_series(const pseries &other) const // Multiplying two series with different variables or expansion points // results in an empty (constant) series if (!is_compatible_to(other)) { - epvector nul; - nul.push_back(expair(Order(_ex1), _ex0)); - return pseries(relational(var,point), nul); + epvector nul { expair(Order(_ex1), _ex0) }; + return pseries(relational(var,point), std::move(nul)); } if (seq.empty() || other.seq.empty()) { - return (new pseries(var==point, epvector())) - ->setflag(status_flags::dynallocated); + return dynallocate(var==point, epvector()); } // Series multiplication epvector new_seq; - int a_max = degree(var); - int b_max = other.degree(var); - int a_min = ldegree(var); - int b_min = other.ldegree(var); - int cdeg_min = a_min + b_min; + const int a_max = degree(var); + const int b_max = other.degree(var); + const int a_min = ldegree(var); + const int b_min = other.ldegree(var); + const int cdeg_min = a_min + b_min; int cdeg_max = a_max + b_max; int higher_order_a = std::numeric_limits::max(); @@ -858,25 +834,37 @@ ex pseries::mul_series(const pseries &other) const higher_order_a = a_max + b_min; if (is_order_function(other.coeff(var, b_max))) higher_order_b = b_max + a_min; - int higher_order_c = std::min(higher_order_a, higher_order_b); + const int higher_order_c = std::min(higher_order_a, higher_order_b); if (cdeg_max >= higher_order_c) cdeg_max = higher_order_c - 1; - + + std::map rest_map_a, rest_map_b; + for (const auto& it : seq) + rest_map_a[ex_to(it.coeff).to_int()] = it.rest; + + if (other.var.is_equal(var)) + for (const auto& it : other.seq) + rest_map_b[ex_to(it.coeff).to_int()] = it.rest; + for (int cdeg=cdeg_min; cdeg<=cdeg_max; ++cdeg) { ex co = _ex0; // c(i)=a(0)b(i)+...+a(i)b(0) for (int i=a_min; cdeg-i>=b_min; ++i) { - ex a_coeff = coeff(var, i); - ex b_coeff = other.coeff(var, cdeg-i); - if (!is_order_function(a_coeff) && !is_order_function(b_coeff)) - co += a_coeff * b_coeff; + const auto& ita = rest_map_a.find(i); + if (ita == rest_map_a.end()) + continue; + const auto& itb = rest_map_b.find(cdeg-i); + if (itb == rest_map_b.end()) + continue; + if (!is_order_function(ita->second) && !is_order_function(itb->second)) + co += ita->second * itb->second; } if (!co.is_zero()) - new_seq.push_back(expair(co, numeric(cdeg))); + new_seq.emplace_back(expair(co, numeric(cdeg))); } if (higher_order_c < std::numeric_limits::max()) - new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c))); - return pseries(relational(var, point), new_seq); + new_seq.emplace_back(expair(Order(_ex1), numeric(higher_order_c))); + return pseries(relational(var, point), std::move(new_seq)); } @@ -895,20 +883,18 @@ ex mul::series(const relational & r, int order, unsigned options) const std::vector ldegree_redo; // find minimal degrees - const epvector::const_iterator itbeg = seq.begin(); - const epvector::const_iterator itend = seq.end(); // first round: obtain a bound up to which minimal degrees have to be // considered - for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + for (auto & it : seq) { - ex expon = it->coeff; + ex expon = it.coeff; int factor = 1; ex buf; if (expon.info(info_flags::integer)) { - buf = it->rest; + buf = it.rest; factor = ex_to(expon).to_int(); } else { - buf = recombine_pair_to_ex(*it); + buf = recombine_pair_to_ex(it); } int real_ldegree = 0; @@ -945,16 +931,16 @@ ex mul::series(const relational & r, int order, unsigned options) const // method. // here we can ignore ldegrees larger than degbound size_t j = 0; - for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + for (auto & it : seq) { if ( ldegree_redo[j] ) { - ex expon = it->coeff; + ex expon = it.coeff; int factor = 1; ex buf; if (expon.info(info_flags::integer)) { - buf = it->rest; + buf = it.rest; factor = ex_to(expon).to_int(); } else { - buf = recombine_pair_to_ex(*it); + buf = recombine_pair_to_ex(it); } int real_ldegree = 0; int orderloop = 0; @@ -962,7 +948,7 @@ ex mul::series(const relational & r, int order, unsigned options) const orderloop++; real_ldegree = buf.series(r, orderloop, options).ldegree(sym); } while ((real_ldegree == orderloop) - && ( factor*real_ldegree < degbound)); + && (factor*real_ldegree < degbound)); ldegrees[j] = factor * real_ldegree; degbound -= factor * real_ldegree; } @@ -971,21 +957,19 @@ ex mul::series(const relational & r, int order, unsigned options) const int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0); - if (degsum >= order) { - epvector epv; - epv.push_back(expair(Order(_ex1), order)); - return (new pseries(r, epv))->setflag(status_flags::dynallocated); + if (degsum > order) { + return dynallocate(r, epvector{{Order(_ex1), order}}); } // Multiply with remaining terms - std::vector::const_iterator itd = ldegrees.begin(); - for (epvector::const_iterator it=itbeg; it!=itend; ++it, ++itd) { + auto itd = ldegrees.begin(); + for (auto it=seq.begin(), itend=seq.end(); it!=itend; ++it, ++itd) { // do series expansion with adjusted order ex op = recombine_pair_to_ex(*it).series(r, order-degsum+(*itd), options); // Series multiplication - if (it == itbeg) + if (it == seq.begin()) acc = ex_to(op); else acc = ex_to(acc.mul_series(ex_to(op))); @@ -1040,11 +1024,8 @@ ex pseries::power_const(const numeric &p, int deg) const // adjust number of coefficients int numcoeff = deg - (p*ldeg).to_int(); if (numcoeff <= 0) { - epvector epv; - epv.reserve(1); - epv.push_back(expair(Order(_ex1), deg)); - return (new pseries(relational(var,point), epv)) - ->setflag(status_flags::dynallocated); + epvector epv { expair(Order(_ex1), deg) }; + return dynallocate(relational(var,point), std::move(epv)); } // O(x^n)^(-m) is undefined @@ -1054,7 +1035,7 @@ ex pseries::power_const(const numeric &p, int deg) const // Compute coefficients of the powered series exvector co; co.reserve(numcoeff); - co.push_back(power(coeff(var, ldeg), p)); + co.push_back(pow(coeff(var, ldeg), p)); for (int i=1; icoeff += deg; - ++i; - } - return pseries(relational(var, point), newseq); + for (auto & it : newseq) + it.coeff += deg; + return pseries(relational(var, point), std::move(newseq)); } @@ -1116,6 +1094,29 @@ ex power::series(const relational & r, int order, unsigned options) const must_expand_basis = true; } + bool exponent_is_regular = true; + try { + exponent.subs(r, subs_options::no_pattern); + } catch (pole_error) { + exponent_is_regular = false; + } + + if (!exponent_is_regular) { + ex l = exponent*log(basis); + // this == exp(l); + ex le = l.series(r, order, options); + // Note: expanding exp(l) won't help, since that will attempt + // Taylor expansion, and fail (because exponent is "singular") + // Still l itself might be expanded in Taylor series. + // Examples: + // sin(x)/x*log(cos(x)) + // 1/x*log(1 + x) + return exp(le).series(r, order, options); + // Note: if l happens to have a Laurent expansion (with + // negative powers of (var - point)), expanding exp(le) + // will barf (which is The Right Thing). + } + // Is the expression of type something^(-int)? if (!must_expand_basis && !exponent.info(info_flags::negint) && (!is_a(basis) || !is_a(exponent))) @@ -1130,10 +1131,10 @@ ex power::series(const relational & r, int order, unsigned options) const if (basis.is_equal(r.lhs() - r.rhs())) { epvector new_seq; if (ex_to(exponent).to_int() < order) - new_seq.push_back(expair(_ex1, exponent)); + new_seq.emplace_back(expair(_ex1, exponent)); else - new_seq.push_back(expair(Order(_ex1), exponent)); - return pseries(r, new_seq); + new_seq.emplace_back(expair(Order(_ex1), exponent)); + return pseries(r, std::move(new_seq)); } // No, expand basis into series @@ -1166,9 +1167,8 @@ ex power::series(const relational & r, int order, unsigned options) const try { result = ex_to(e).power_const(numexp, order); } catch (pole_error) { - epvector ser; - ser.push_back(expair(Order(_ex1), order)); - result = pseries(r, ser); + epvector ser { expair(Order(_ex1), order) }; + result = pseries(r, std::move(ser)); } return result; @@ -1187,17 +1187,15 @@ ex pseries::series(const relational & r, int order, unsigned options) const return *this; else { epvector new_seq; - epvector::const_iterator it = seq.begin(), itend = seq.end(); - while (it != itend) { - int o = ex_to(it->coeff).to_int(); + for (auto & it : seq) { + int o = ex_to(it.coeff).to_int(); if (o >= order) { - new_seq.push_back(expair(Order(_ex1), o)); + new_seq.emplace_back(expair(Order(_ex1), o)); break; } - new_seq.push_back(*it); - ++it; + new_seq.push_back(it); } - return pseries(r, new_seq); + return pseries(r, std::move(new_seq)); } } else return convert_to_poly().series(r, order, options); @@ -1208,7 +1206,7 @@ ex integral::series(const relational & r, int order, unsigned options) const if (x.subs(r) != x) throw std::logic_error("Cannot series expand wrt dummy variable"); - // Expanding integrant with r substituted taken in boundaries. + // Expanding integrand with r substituted taken in boundaries. ex fseries = f.series(r, order, options); epvector fexpansion; fexpansion.reserve(fseries.nops()); @@ -1218,12 +1216,12 @@ ex integral::series(const relational & r, int order, unsigned options) const ? currcoeff : integral(x, a.subs(r), b.subs(r), currcoeff); if (currcoeff != 0) - fexpansion.push_back( + fexpansion.emplace_back( expair(currcoeff, ex_to(fseries).exponop(i))); } // Expanding lower boundary - ex result = (new pseries(r, fexpansion))->setflag(status_flags::dynallocated); + ex result = dynallocate(r, std::move(fexpansion)); ex aseries = (a-a.subs(r)).series(r, order, options); fseries = f.series(x == (a.subs(r)), order, options); for (size_t i=0; i