X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=063722b10dd90e34e0b7afec1eb0365db0202b5c;hp=bcad8c1960df67a445832d0eb9fcbd24a4c83857;hb=05d274b894f2f84217d308bf4d4f2202b9627c63;hpb=bb76e4b38b330365934e1b14d2feb2bad416f455 diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index bcad8c19..063722b1 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * GiNaC Copyright (C) 1999-2004 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 @@ -18,12 +18,9 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include -#include - #include "pseries.h" #include "add.h" #include "inifcns.h" // for Order function @@ -33,9 +30,14 @@ #include "relational.h" #include "operators.h" #include "symbol.h" +#include "integral.h" #include "archive.h" #include "utils.h" +#include +#include +#include + namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, @@ -50,7 +52,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, * Default constructor */ -pseries::pseries() : inherited(TINFO_pseries) { } +pseries::pseries() { } /* @@ -66,8 +68,43 @@ pseries::pseries() : inherited(TINFO_pseries) { } * @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(TINFO_pseries), 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(); @@ -79,16 +116,20 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), 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) { - for (unsigned int i=0; true; ++i) { + inherited::read_archive(n, sym_lst); + auto range = n.find_property_range("coeff", "power"); + seq.reserve((range.end-range.begin)/2); + + for (auto loc = range.begin; loc < range.end;) { ex rest; ex coeff; - if (n.find_ex("coeff", rest, sym_lst, i) && n.find_ex("power", coeff, sym_lst, i)) - seq.push_back(expair(rest, coeff)); - else - break; + n.find_ex_by_loc(loc++, rest, sym_lst); + n.find_ex_by_loc(loc++, coeff, sym_lst); + seq.emplace_back(expair(rest, coeff)); } + n.find_ex("var", var, sym_lst); n.find_ex("point", point, sym_lst); } @@ -96,17 +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 @@ -122,7 +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 @@ -163,7 +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; } @@ -241,7 +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) @@ -266,7 +304,9 @@ ex pseries::op(size_t i) const if (i >= seq.size()) throw (std::out_of_range("op() out of range")); - return seq[i].rest * power(var - point, seq[i].coeff); + if (is_order_function(seq[i].rest)) + 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 @@ -274,25 +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 = INT_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 @@ -302,25 +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 = INT_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 @@ -368,60 +392,127 @@ 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 { - epvector * newseq = conjugateepvector(seq); - ex newvar = var.conjugate(); + if(!var.info(info_flags::real)) + return conjugate_function(*this).hold(); + + std::unique_ptr newseq(conjugateepvector(seq)); ex newpoint = point.conjugate(); - if (!newseq && are_ex_trivially_equal(newvar, var) && are_ex_trivially_equal(point, newpoint)) { + if (!newseq && are_ex_trivially_equal(point, newpoint)) { return *this; } - ex result = (new pseries(newvar==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated); - if (newseq) { - delete newseq; + return dynallocate(var==newpoint, newseq ? std::move(*newseq) : seq); +} + +ex pseries::real_part() const +{ + if(!var.info(info_flags::real)) + return real_part_function(*this).hold(); + ex newpoint = point.real_part(); + if(newpoint != point) + return real_part_function(*this).hold(); + + epvector v; + v.reserve(seq.size()); + 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 +{ + if(!var.info(info_flags::real)) + return imag_part_function(*this).hold(); + ex newpoint = point.real_part(); + if(newpoint != point) + return imag_part_function(*this).hold(); + + epvector v; + v.reserve(seq.size()); + 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 +{ + std::unique_ptr newseq(nullptr); + for (auto i=seq.begin(); i!=seq.end(); ++i) { + if (newseq) { + 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.reset(new epvector); + newseq->reserve(seq.size()); + for (auto j=seq.begin(); j!=i; ++j) + newseq->push_back(*j); + newseq->emplace_back(expair(newterm, i->coeff)); + } } - return result; + + ex newpoint = point.eval_integ(); + if (newseq || !are_ex_trivially_equal(newpoint, point)) + return dynallocate(var==newpoint, std::move(*newseq)); + return *this; +} + +ex pseries::evalm() const +{ + // evalm each coefficient + epvector newseq; + bool something_changed = false; + for (auto i=seq.begin(); i!=seq.end(); ++i) { + if (something_changed) { + ex newcoeff = i->rest.evalm(); + if (!newcoeff.is_zero()) + 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.emplace_back(expair(newcoeff, i->coeff)); + } + } + } + if (something_changed) + return dynallocate(var==point, std::move(newseq)); + else + return *this; } ex pseries::subs(const exmap & m, unsigned options) const @@ -436,12 +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 @@ -449,15 +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. @@ -465,51 +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; } @@ -519,6 +598,20 @@ bool pseries::is_terminating() const return seq.empty() || !is_order_function((seq.end()-1)->rest); } +ex pseries::coeffop(size_t i) const +{ + if (i >= nops()) + throw (std::out_of_range("coeffop() out of range")); + return seq[i].rest; +} + +ex pseries::exponop(size_t i) const +{ + if (i >= nops()) + throw (std::out_of_range("exponop() out of range")); + return seq[i].coeff; +} + /* * Implementations of series expansion @@ -533,8 +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 @@ -543,29 +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)); } @@ -600,18 +693,15 @@ 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(); - int pow_a = INT_MAX, pow_b = INT_MAX; + 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 if (a == a_end) { @@ -649,18 +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)); } @@ -675,16 +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)); @@ -703,15 +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)); } @@ -725,45 +811,60 @@ 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 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 = INT_MAX; - int higher_order_b = INT_MAX; + int higher_order_a = std::numeric_limits::max(); + int higher_order_b = std::numeric_limits::max(); if (is_order_function(coeff(var, a_max))) 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 < INT_MAX) - new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c))); - return pseries(relational(var, point), new_seq); + if (higher_order_c < std::numeric_limits::max()) + new_seq.emplace_back(expair(Order(_ex1), numeric(higher_order_c))); + return pseries(relational(var, point), std::move(new_seq)); } @@ -779,56 +880,96 @@ ex mul::series(const relational & r, int order, unsigned options) const // holds ldegrees of the series of individual factors std::vector ldegrees; + std::vector ldegree_redo; // find minimal degrees - const epvector::const_iterator itbeg = seq.begin(); - const epvector::const_iterator itend = seq.end(); - for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + // first round: obtain a bound up to which minimal degrees have to be + // considered + 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; + bool flag_redo = false; try { real_ldegree = buf.expand().ldegree(sym-r.rhs()); - } - catch (std::runtime_error) {} + } catch (std::runtime_error) {} if (real_ldegree == 0) { + if ( factor < 0 ) { + // This case must terminate, otherwise we would have division by + // zero. + int orderloop = 0; + do { + orderloop++; + real_ldegree = buf.series(r, orderloop, options).ldegree(sym); + } while (real_ldegree == orderloop); + } else { + // Here it is possible that buf does not have a ldegree, therefore + // check only if ldegree is negative, otherwise reconsider the case + // in the second round. + real_ldegree = buf.series(r, 0, options).ldegree(sym); + if (real_ldegree == 0) + flag_redo = true; + } + } + + ldegrees.push_back(factor * real_ldegree); + ldegree_redo.push_back(flag_redo); + } + + int degbound = order-std::accumulate(ldegrees.begin(), ldegrees.end(), 0); + // Second round: determine the remaining positive ldegrees by the series + // method. + // here we can ignore ldegrees larger than degbound + size_t j = 0; + for (auto & it : seq) { + if ( ldegree_redo[j] ) { + ex expon = it.coeff; + int factor = 1; + ex buf; + if (expon.info(info_flags::integer)) { + buf = it.rest; + factor = ex_to(expon).to_int(); + } else { + buf = recombine_pair_to_ex(it); + } + int real_ldegree = 0; int orderloop = 0; do { orderloop++; real_ldegree = buf.series(r, orderloop, options).ldegree(sym); - } while (real_ldegree == orderloop); + } while ((real_ldegree == orderloop) + && (factor*real_ldegree < degbound)); + ldegrees[j] = factor * real_ldegree; + degbound -= factor * real_ldegree; } - - ldegrees.push_back(factor * real_ldegree); + j++; } 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))); @@ -881,7 +1022,11 @@ ex pseries::power_const(const numeric &p, int deg) const throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series"); // adjust number of coefficients - deg = deg - p.to_int()*ldeg; + int numcoeff = deg - (p*ldeg).to_int(); + if (numcoeff <= 0) { + epvector epv { expair(Order(_ex1), deg) }; + return dynallocate(relational(var,point), std::move(epv)); + } // O(x^n)^(-m) is undefined if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative()) @@ -889,9 +1034,9 @@ ex pseries::power_const(const numeric &p, int deg) const // Compute coefficients of the powered series exvector co; - co.reserve(deg); - co.push_back(power(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)); } @@ -952,30 +1094,63 @@ 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)) + if (!must_expand_basis && !exponent.info(info_flags::negint) + && (!is_a(basis) || !is_a(exponent))) return basic::series(r, order, options); // Is the expression of type 0^something? - if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero()) + if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero() + && (!is_a(basis) || !is_a(exponent))) return basic::series(r, order, options); // Singularity encountered, is the basis equal to (var - point)? 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 - int intexp = ex_to(exponent).to_int(); + numeric numexp; + if (is_a(exponent)) { + numexp = ex_to(exponent); + } else { + numexp = 0; + } const ex& sym = r.lhs(); // find existing minimal degree - int real_ldegree = basis.expand().ldegree(sym-r.rhs()); + ex eb = basis.expand(); + int real_ldegree = 0; + if (eb.info(info_flags::rational_function)) + real_ldegree = eb.ldegree(sym-r.rhs()); if (real_ldegree == 0) { int orderloop = 0; do { @@ -984,16 +1159,16 @@ ex power::series(const relational & r, int order, unsigned options) const } while (real_ldegree == orderloop); } - ex e = basis.series(r, order + real_ldegree*(1-intexp), options); + if (!(real_ldegree*numexp).is_integer()) + throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series"); + ex e = basis.series(r, (order + real_ldegree*(1-numexp)).to_int(), options); ex result; try { - result = ex_to(e).power_const(intexp, order); - } - catch (pole_error) { - epvector ser; - ser.push_back(expair(Order(_ex1), order)); - result = pseries(r, ser); + result = ex_to(e).power_const(numexp, order); + } catch (pole_error) { + epvector ser { expair(Order(_ex1), order) }; + result = pseries(r, std::move(ser)); } return result; @@ -1012,22 +1187,75 @@ 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); } +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 integrand with r substituted taken in boundaries. + ex fseries = f.series(r, order, options); + epvector fexpansion; + fexpansion.reserve(fseries.nops()); + for (size_t i=0; i(fseries).coeffop(i); + currcoeff = (currcoeff == Order(_ex1)) + ? currcoeff + : integral(x, a.subs(r), b.subs(r), currcoeff); + if (currcoeff != 0) + fexpansion.emplace_back( + expair(currcoeff, ex_to(fseries).exponop(i))); + } + + // Expanding lower boundary + 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(fseries).coeffop(i); + if (is_order_function(currcoeff)) + break; + ex currexpon = ex_to(fseries).exponop(i); + int orderforf = order-ex_to(currexpon).to_int()-1; + currcoeff = currcoeff.series(r, orderforf); + ex term = ex_to(aseries).power_const(ex_to(currexpon+1),order); + term = ex_to(term).mul_const(ex_to(-1/(currexpon+1))); + term = ex_to(term).mul_series(ex_to(currcoeff)); + result = ex_to(result).add_series(ex_to(term)); + } + + // Expanding upper boundary + ex bseries = (b-b.subs(r)).series(r, order, options); + fseries = f.series(x == (b.subs(r)), order, options); + for (size_t i=0; i(fseries).coeffop(i); + if (is_order_function(currcoeff)) + break; + ex currexpon = ex_to(fseries).exponop(i); + int orderforf = order-ex_to(currexpon).to_int()-1; + currcoeff = currcoeff.series(r, orderforf); + ex term = ex_to(bseries).power_const(ex_to(currexpon+1),order); + term = ex_to(term).mul_const(ex_to(1/(currexpon+1))); + term = ex_to(term).mul_series(ex_to(currcoeff)); + result = ex_to(result).add_series(ex_to(term)); + } + + return result; +} + /** Compute the truncated series expansion of an expression. * This function returns an expression containing an object of class pseries @@ -1050,12 +1278,10 @@ ex ex::series(const ex & r, int order, unsigned options) const else throw (std::logic_error("ex::series(): expansion point has unknown type")); - try { - e = bp->series(rel_, order, options); - } catch (std::exception &x) { - throw (std::logic_error(std::string("unable to compute series (") + x.what() + ")")); - } + e = bp->series(rel_, order, options); return e; } +GINAC_BIND_UNARCHIVER(pseries); + } // namespace GiNaC