X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=a99725e56e98e93b61ad0ce2d73580ab0de1d974;hp=7264d933c068bb03a9b3659a318218e43cbb510c;hb=ffad02322624ab79fdad1a23a3aa83cd67376151;hpb=a40b470aeccc76b9a6055dc5191805e0bb6f7df2;ds=sidebyside diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 7264d933..a99725e5 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * 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 @@ -21,43 +21,36 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include #include "pseries.h" #include "add.h" -#include "inifcns.h" +#include "inifcns.h" // for Order function #include "lst.h" #include "mul.h" #include "power.h" #include "relational.h" +#include "operators.h" #include "symbol.h" #include "archive.h" #include "utils.h" -#include "debugmsg.h" namespace GiNaC { -GINAC_IMPLEMENT_REGISTERED_CLASS(pseries, basic) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, + print_func(&pseries::do_print). + print_func(&pseries::do_print_latex). + print_func(&pseries::do_print_tree). + print_func(&pseries::do_print_python). + print_func(&pseries::do_print_python_repr)) /* - * Default ctor, dtor, copy ctor, assignment operator and helpers + * Default constructor */ -pseries::pseries() : basic(TINFO_pseries) -{ - debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT); -} - -void pseries::copy(const pseries &other) -{ - inherited::copy(other); - seq = other.seq; - var = other.var; - point = other.point; -} - -DEFAULT_DESTROY(pseries) +pseries::pseries() : inherited(TINFO_pseries) { } /* @@ -67,7 +60,7 @@ DEFAULT_DESTROY(pseries) /** Construct pseries from a vector of coefficients and powers. * expair.rest holds the coefficient, expair.coeff holds the power. * The powers must be integers (positive or negative) and in ascending order; - * the last coefficient can be Order(_ex1()) to represent a truncated, + * the last coefficient can be Order(_ex1) to represent a truncated, * non-terminating series. * * @param rel_ expansion variable and point (must hold a relational) @@ -75,11 +68,10 @@ DEFAULT_DESTROY(pseries) * @return newly constructed pseries */ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_) { - debugmsg("pseries ctor from ex,epvector", LOGLEVEL_CONSTRUCT); - GINAC_ASSERT(is_ex_exactly_of_type(rel_, relational)); - GINAC_ASSERT(is_ex_exactly_of_type(rel_.lhs(),symbol)); + GINAC_ASSERT(is_a(rel_)); + GINAC_ASSERT(is_a(rel_.lhs())); point = rel_.rhs(); - var = *static_cast(rel_.lhs().bp); + var = rel_.lhs(); } @@ -87,9 +79,8 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), s * Archiving */ -pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("pseries ctor from archive_node", LOGLEVEL_CONSTRUCT); for (unsigned int i=0; true; ++i) { ex rest; ex coeff; @@ -118,81 +109,121 @@ void pseries::archive(archive_node &n) const DEFAULT_UNARCHIVE(pseries) ////////// -// functions overriding virtual functions from bases classes +// functions overriding virtual functions from base classes ////////// -void pseries::print(std::ostream &os, unsigned upper_precedence) const +void pseries::print_series(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, const char *pow_sym, unsigned level) const { - debugmsg("pseries print", LOGLEVEL_PRINT); - if (precedence<=upper_precedence) os << "("; + if (precedence() <= level) + c.s << '('; + // objects of type pseries must not have any zero entries, so the // trivial (zero) pseries needs a special treatment here: - if (seq.size()==0) - os << '0'; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + if (seq.empty()) + c.s << '0'; + + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + // print a sign, if needed - if (i!=seq.begin()) - os << '+'; + if (i != seq.begin()) + c.s << '+'; + if (!is_order_function(i->rest)) { + // print 'rest', i.e. the expansion coefficient if (i->rest.info(info_flags::numeric) && i->rest.info(info_flags::positive)) { - os << i->rest; - } else - os << "(" << i->rest << ')'; + i->rest.print(c); + } else { + c.s << openbrace << '('; + i->rest.print(c); + c.s << ')' << closebrace; + } + // print 'coeff', something like (x-1)^42 if (!i->coeff.is_zero()) { - os << '*'; - if (!point.is_zero()) - os << '(' << var-point << ')'; - else - os << var; - if (i->coeff.compare(_ex1())) { - os << '^'; - if (i->coeff.info(info_flags::negative)) - os << '(' << i->coeff << ')'; - else - os << i->coeff; + c.s << mul_sym; + if (!point.is_zero()) { + c.s << openbrace << '('; + (var-point).print(c); + c.s << ')' << closebrace; + } else + var.print(c); + if (i->coeff.compare(_ex1)) { + c.s << pow_sym; + c.s << openbrace; + if (i->coeff.info(info_flags::negative)) { + c.s << '('; + i->coeff.print(c); + c.s << ')'; + } else + i->coeff.print(c); + c.s << closebrace; } } - } else { - os << Order(power(var-point,i->coeff)); - } + } else + Order(power(var-point,i->coeff)).print(c); + ++i; } - if (precedence<=upper_precedence) os << ")"; + + if (precedence() <= level) + c.s << ')'; } +void pseries::do_print(const print_context & c, unsigned level) const +{ + print_series(c, "", "", "*", "^", level); +} -void pseries::printraw(std::ostream &os) const +void pseries::do_print_latex(const print_latex & c, unsigned level) const { - debugmsg("pseries printraw", LOGLEVEL_PRINT); - os << class_name() << "(" << var << ";" << point << ";"; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) - os << "(" << (*i).rest << "," << (*i).coeff << "),"; - os << ")"; + print_series(c, "{", "}", " ", "^", level); } +void pseries::do_print_python(const print_python & c, unsigned level) const +{ + print_series(c, "", "", "*", "**", level); +} -void pseries::printtree(std::ostream & os, unsigned indent) const +void pseries::do_print_tree(const print_tree & c, unsigned level) const { - debugmsg("pseries printtree",LOGLEVEL_PRINT); - os << std::string(indent,' ') << class_name() - << ", hash=" << hashvalue - << " (0x" << std::hex << hashvalue << std::dec << ")" - << ", flags=" << flags << std::endl; - for (unsigned i=0; i(other)); const pseries &o = static_cast(other); // first compare the lengths of the series... @@ -224,27 +255,20 @@ int pseries::compare_same_type(const basic & other) const } /** Return the number of operands including a possible order term. */ -unsigned pseries::nops(void) const +size_t pseries::nops() const { return seq.size(); } - /** Return the ith term in the series when represented as a sum. */ -ex pseries::op(int i) const +ex pseries::op(size_t i) const { - if (i < 0 || unsigned(i) >= seq.size()) + if (i >= seq.size()) throw (std::out_of_range("op() out of range")); - return seq[i].rest * power(var - point, seq[i].coeff); -} - -ex &pseries::let_op(int i) -{ - throw (std::logic_error("let_op not defined for pseries")); + return seq[i].rest * power(var - point, seq[i].coeff); } - /** Return degree of highest power of the series. This is usually the exponent * of the Order term. If s is not the expansion variable of the series, the * series is examined termwise. */ @@ -253,7 +277,7 @@ int pseries::degree(const ex &s) const if (var.is_equal(s)) { // Return last exponent if (seq.size()) - return ex_to_numeric((*(seq.end() - 1)).coeff).to_int(); + return ex_to((seq.end()-1)->coeff).to_int(); else return 0; } else { @@ -281,7 +305,7 @@ int pseries::ldegree(const ex &s) const if (var.is_equal(s)) { // Return first exponent if (seq.size()) - return ex_to_numeric((*(seq.begin())).coeff).to_int(); + return ex_to((seq.begin())->coeff).to_int(); else return 0; } else { @@ -309,16 +333,16 @@ int pseries::ldegree(const ex &s) const ex pseries::coeff(const ex &s, int n) const { if (var.is_equal(s)) { - if (seq.size() == 0) - return _ex0(); + if (seq.empty()) + return _ex0; // Binary search in sequence for given power numeric looking_for = numeric(n); int lo = 0, hi = seq.size() - 1; while (lo <= hi) { int mid = (lo + hi) / 2; - GINAC_ASSERT(is_ex_exactly_of_type(seq[mid].coeff, numeric)); - int cmp = ex_to_numeric(seq[mid].coeff).compare(looking_for); + GINAC_ASSERT(is_exactly_a(seq[mid].coeff)); + int cmp = ex_to(seq[mid].coeff).compare(looking_for); switch (cmp) { case -1: lo = mid + 1; @@ -332,19 +356,18 @@ ex pseries::coeff(const ex &s, int n) const throw(std::logic_error("pseries::coeff: compare() didn't return -1, 0 or 1")); } } - return _ex0(); + return _ex0; } else return convert_to_poly().coeff(s, n); } /** Does nothing. */ -ex pseries::collect(const ex &s) const +ex pseries::collect(const ex &s, bool distributed) const { return *this; } - -/** Evaluate coefficients. */ +/** Perform coefficient-wise automatic term rewriting rules in this class. */ ex pseries::eval(int level) const { if (level == 1) @@ -364,7 +387,6 @@ ex pseries::eval(int level) const return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); } - /** Evaluate coefficients numerically. */ ex pseries::evalf(int level) const { @@ -385,14 +407,13 @@ ex pseries::evalf(int level) const return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); } - -ex pseries::subs(const lst & ls, const lst & lr) const +ex pseries::subs(const exmap & m, unsigned options) const { // If expansion variable is being substituted, convert the series to a // polynomial and do the substitution there because the result might // no longer be a power series - if (ls.has(var)) - return convert_to_poly(true).subs(ls, lr); + if (m.find(var) != m.end()) + return convert_to_poly(true).subs(m, options); // Otherwise construct a new series with substituted coefficients and // expansion point @@ -400,36 +421,36 @@ ex pseries::subs(const lst & ls, const lst & lr) const newseq.reserve(seq.size()); epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - newseq.push_back(expair(it->rest.subs(ls, lr), it->coeff)); + newseq.push_back(expair(it->rest.subs(m, options), it->coeff)); ++it; } - return (new pseries(relational(var,point.subs(ls, lr)), newseq))->setflag(status_flags::dynallocated); + return (new pseries(relational(var,point.subs(m, options)), newseq))->setflag(status_flags::dynallocated); } - /** Implementation of ex::expand() for a power series. It expands all the * terms individually and returns the resulting series as a new pseries. */ ex pseries::expand(unsigned options) const { epvector newseq; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { ex restexp = i->rest.expand(); if (!restexp.is_zero()) newseq.push_back(expair(restexp, i->coeff)); + ++i; } return (new pseries(relational(var,point), newseq)) - ->setflag(status_flags::dynallocated | status_flags::expanded); + ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)); } - -/** Implementation of ex::diff() for a power series. It treats the series as a - * polynomial. +/** Implementation of ex::diff() for a power series. * @see ex::diff */ ex pseries::derivative(const symbol & s) const { + epvector new_seq; + epvector::const_iterator it = seq.begin(), itend = seq.end(); + if (s == var) { - epvector new_seq; - epvector::const_iterator it = seq.begin(), itend = seq.end(); // FIXME: coeff might depend on var while (it != itend) { @@ -442,16 +463,24 @@ ex pseries::derivative(const symbol & s) const } ++it; } - return pseries(relational(var,point), new_seq); + } else { - return *this; + + while (it != itend) { + if (is_order_function(it->rest)) { + new_seq.push_back(*it); + } else { + ex c = it->rest.diff(s); + if (!c.is_zero()) + new_seq.push_back(expair(c, it->coeff)); + } + ++it; + } } -} + return pseries(relational(var,point), new_seq); +} -/** Convert a pseries object to an ordinary polynomial. - * - * @param no_order flag: discard higher order terms */ ex pseries::convert_to_poly(bool no_order) const { ex e; @@ -468,12 +497,9 @@ ex pseries::convert_to_poly(bool no_order) const return e; } - -/** Returns true if there is no order term, i.e. the series terminates and - * false otherwise. */ -bool pseries::is_terminating(void) const +bool pseries::is_terminating() const { - return seq.size() == 0 || !is_order_function((seq.end()-1)->rest); + return seq.empty() || !is_order_function((seq.end()-1)->rest); } @@ -486,31 +512,33 @@ bool pseries::is_terminating(void) const ex basic::series(const relational & r, int order, unsigned options) const { epvector seq; - numeric fac(1); + numeric fac = 1; ex deriv = *this; - ex coeff = deriv.subs(r); - const symbol &s = static_cast(*r.lhs().bp); + ex coeff = deriv.subs(r, subs_options::no_pattern); + const symbol &s = ex_to(r.lhs()); if (!coeff.is_zero()) - seq.push_back(expair(coeff, numeric(0))); + seq.push_back(expair(coeff, _ex0)); int n; for (n=1; nis_equal(*s.bp)) { + GINAC_ASSERT(is_a(r.lhs())); + + if (this->is_equal_same_type(ex_to(r.lhs()))) { if (order > 0 && !point.is_zero()) - seq.push_back(expair(point, _ex0())); + seq.push_back(expair(point, _ex0)); if (order > 1) - seq.push_back(expair(_ex1(), _ex1())); + seq.push_back(expair(_ex1, _ex1)); else - seq.push_back(expair(Order(_ex1()), numeric(order))); + seq.push_back(expair(Order(_ex1), numeric(order))); } else - seq.push_back(expair(*this, _ex0())); + seq.push_back(expair(*this, _ex0)); return pseries(r, seq); } @@ -548,7 +575,7 @@ ex pseries::add_series(const pseries &other) const // results in an empty (constant) series if (!is_compatible_to(other)) { epvector nul; - nul.push_back(expair(Order(_ex1()), _ex0())); + nul.push_back(expair(Order(_ex1), _ex0)); return pseries(relational(var,point), nul); } @@ -568,7 +595,7 @@ ex pseries::add_series(const pseries &other) const } break; } else - pow_a = ex_to_numeric((*a).coeff).to_int(); + pow_a = ex_to((*a).coeff).to_int(); // If b is empty, fill up with elements from a and stop if (b == b_end) { @@ -578,7 +605,7 @@ ex pseries::add_series(const pseries &other) const } break; } else - pow_b = ex_to_numeric((*b).coeff).to_int(); + pow_b = ex_to((*b).coeff).to_int(); // a and b are non-empty, compare powers if (pow_a < pow_b) { @@ -596,7 +623,7 @@ 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.push_back(expair(Order(_ex1), (*a).coeff)); break; // Order term ends the sequence } else { ex sum = (*a).rest + (*b).rest; @@ -626,15 +653,15 @@ ex add::series(const relational & r, int order, unsigned options) const epvector::const_iterator itend = seq.end(); for (; it!=itend; ++it) { ex op; - if (is_ex_exactly_of_type(it->rest, pseries)) + 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_pseries(op).mul_const(ex_to_numeric(it->coeff)); + if (!it->coeff.is_equal(_ex1)) + op = ex_to(op).mul_const(ex_to(it->coeff)); // Series addition - acc = ex_to_pseries(acc).add_series(ex_to_pseries(op)); + acc = ex_to(acc).add_series(ex_to(op)); } return acc; } @@ -673,13 +700,12 @@ ex pseries::mul_series(const pseries &other) const // results in an empty (constant) series if (!is_compatible_to(other)) { epvector nul; - nul.push_back(expair(Order(_ex1()), _ex0())); + nul.push_back(expair(Order(_ex1), _ex0)); return pseries(relational(var,point), nul); } // Series multiplication epvector new_seq; - int a_max = degree(var); int b_max = other.degree(var); int a_min = ldegree(var); @@ -698,7 +724,7 @@ ex pseries::mul_series(const pseries &other) const cdeg_max = higher_order_c - 1; for (int cdeg=cdeg_min; cdeg<=cdeg_max; ++cdeg) { - ex co = _ex0(); + 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); @@ -710,7 +736,7 @@ ex pseries::mul_series(const pseries &other) const new_seq.push_back(expair(co, numeric(cdeg))); } if (higher_order_c < INT_MAX) - new_seq.push_back(expair(Order(_ex1()), numeric(higher_order_c))); + new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c))); return pseries(relational(var, point), new_seq); } @@ -720,30 +746,21 @@ ex pseries::mul_series(const pseries &other) const * @see ex::series */ ex mul::series(const relational & r, int order, unsigned options) const { - ex acc; // Series accumulator - - // Get first term from overall_coeff - acc = overall_coeff.series(r, order, options); - + pseries acc; // Series accumulator + // Multiply with remaining terms - epvector::const_iterator it = seq.begin(); - epvector::const_iterator itend = seq.end(); - for (; it!=itend; ++it) { - ex op = it->rest; - if (op.info(info_flags::numeric)) { - // series * const (special case, faster) - ex f = power(op, it->coeff); - acc = ex_to_pseries(acc).mul_const(ex_to_numeric(f)); - continue; - } else if (!is_ex_exactly_of_type(op, pseries)) - op = op.series(r, order, options); - if (!it->coeff.is_equal(_ex1())) - op = ex_to_pseries(op).power_const(ex_to_numeric(it->coeff), order); + const epvector::const_iterator itbeg = seq.begin(); + const epvector::const_iterator itend = seq.end(); + for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + ex op = recombine_pair_to_ex(*it).series(r, order, options); // Series multiplication - acc = ex_to_pseries(acc).mul_series(ex_to_pseries(op)); + if (it==itbeg) + acc = ex_to(op); + else + acc = ex_to(acc.mul_series(ex_to(op))); } - return acc; + return acc.mul_const(ex_to(overall_coeff)); } @@ -754,6 +771,7 @@ ex mul::series(const relational & r, int order, unsigned options) const ex pseries::power_const(const numeric &p, int deg) const { // method: + // (due to Leonhard Euler) // let A(x) be this series and for the time being let it start with a // constant (later we'll generalize): // A(x) = a_0 + a_1*x + a_2*x^2 + ... @@ -773,18 +791,24 @@ ex pseries::power_const(const numeric &p, int deg) const // repeat the above derivation. The leading power of C2(x) = A2(x)^2 is // then of course x^(p*m) but the recurrence formula still holds. - if (seq.size()==0) { - // as a spacial case, handle the empty (zero) series honoring the + if (seq.empty()) { + // as a special case, handle the empty (zero) series honoring the // usual power laws such as implemented in power::eval() if (p.real().is_zero()) - throw (std::domain_error("pseries::power_const(): pow(0,I) is undefined")); + throw std::domain_error("pseries::power_const(): pow(0,I) is undefined"); else if (p.real().is_negative()) - throw (pole_error("pseries::power_const(): division by zero",1)); + throw pole_error("pseries::power_const(): division by zero",1); else return *this; } - int ldeg = ldegree(var); + const int ldeg = ldegree(var); + if (!(p*ldeg).is_integer()) + throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series"); + + // O(x^n)^(-m) is undefined + if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative()) + throw pole_error("pseries::power_const(): division by zero",1); // Compute coefficients of the powered series exvector co; @@ -792,18 +816,18 @@ ex pseries::power_const(const numeric &p, int deg) const co.push_back(power(coeff(var, ldeg), p)); bool all_sums_zero = true; for (int i=1; icoeff = i->coeff + deg; + epvector newseq = seq; + epvector::iterator i = newseq.begin(), end = newseq.end(); + while (i != end) { + i->coeff += deg; + ++i; + } return pseries(relational(var, point), newseq); } @@ -838,33 +865,39 @@ pseries pseries::shift_exponents(int deg) const * @see ex::series */ ex power::series(const relational & r, int order, unsigned options) const { - ex e; - if (!is_ex_exactly_of_type(basis, pseries)) { - // Basis is not a series, may there be a singularity? - bool must_expand_basis = false; - try { - basis.subs(r); - } catch (pole_error) { - must_expand_basis = true; - } - - // Is the expression of type something^(-int)? - if (!must_expand_basis && !exponent.info(info_flags::negint)) - return basic::series(r, order, options); + // If basis is already a series, just power it + if (is_exactly_a(basis)) + return ex_to(basis).power_const(ex_to(exponent), order); + + // Basis is not a series, may there be a singularity? + bool must_expand_basis = false; + try { + basis.subs(r, subs_options::no_pattern); + } catch (pole_error) { + must_expand_basis = true; + } - // Is the expression of type 0^something? - if (!must_expand_basis && !basis.subs(r).is_zero()) - return basic::series(r, order, options); + // Is the expression of type something^(-int)? + if (!must_expand_basis && !exponent.info(info_flags::negint)) + return basic::series(r, order, options); - // Singularity encountered, expand basis into series - e = basis.series(r, order, options); - } else { - // Basis is a series - e = basis; + // Is the expression of type 0^something? + if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero()) + 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)); + else + new_seq.push_back(expair(Order(_ex1), exponent)); + return pseries(r, new_seq); } - - // Power e - return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order); + + // No, expand basis into series + ex e = basis.series(r, order, options); + return ex_to(e).power_const(ex_to(exponent), order); } @@ -872,8 +905,8 @@ ex power::series(const relational & r, int order, unsigned options) const ex pseries::series(const relational & r, int order, unsigned options) const { const ex p = r.rhs(); - GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol)); - const symbol &s = static_cast(*r.lhs().bp); + GINAC_ASSERT(is_a(r.lhs())); + const symbol &s = ex_to(r.lhs()); if (var.is_equal(s) && point.is_equal(p)) { if (order > degree(s)) @@ -882,9 +915,9 @@ ex pseries::series(const relational & r, int order, unsigned options) const epvector new_seq; epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - int o = ex_to_numeric(it->coeff).to_int(); + int o = ex_to(it->coeff).to_int(); if (o >= order) { - new_seq.push_back(expair(Order(_ex1()), o)); + new_seq.push_back(expair(Order(_ex1), o)); break; } new_seq.push_back(*it); @@ -908,14 +941,13 @@ ex pseries::series(const relational & r, int order, unsigned options) const * @return an expression holding a pseries object */ ex ex::series(const ex & r, int order, unsigned options) const { - GINAC_ASSERT(bp!=0); ex e; relational rel_; - if (is_ex_exactly_of_type(r,relational)) - rel_ = ex_to_relational(r); - else if (is_ex_exactly_of_type(r,symbol)) - rel_ = relational(r,_ex0()); + if (is_a(r)) + rel_ = ex_to(r); + else if (is_a(r)) + rel_ = relational(r,_ex0); else throw (std::logic_error("ex::series(): expansion point has unknown type")); @@ -927,12 +959,4 @@ ex ex::series(const ex & r, int order, unsigned options) const return e; } -////////// -// static member variables -////////// - -// protected - -unsigned pseries::precedence = 38; // for clarity just below add::precedence - } // namespace GiNaC