X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=7f77cc664bec67025f62df51070adcbda2db25c2;hp=720fb9c732daef58311ac1b46d296246c2ce8288;hb=7e7beee2c946694130a484c923f6af8391867495;hpb=c378e979c7a9b9807941b27adbac690699abe70c diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 720fb9c7..7f77cc66 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) 1999-2002 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 @@ -21,6 +21,7 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include #include "pseries.h" @@ -34,7 +35,6 @@ #include "print.h" #include "archive.h" #include "utils.h" -#include "debugmsg.h" namespace GiNaC { @@ -45,10 +45,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(pseries, basic) * Default ctor, dtor, copy ctor, assignment operator and helpers */ -pseries::pseries() : basic(TINFO_pseries) -{ - debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT); -} +pseries::pseries() : inherited(TINFO_pseries) { } void pseries::copy(const pseries &other) { @@ -68,7 +65,7 @@ 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) @@ -76,11 +73,10 @@ 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_exactly_a(rel_)); + GINAC_ASSERT(is_exactly_a(rel_.lhs())); point = rel_.rhs(); - var = *static_cast(rel_.lhs().bp); + var = rel_.lhs(); } @@ -90,7 +86,6 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), s pseries::pseries(const archive_node &n, const 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; @@ -124,8 +119,6 @@ DEFAULT_UNARCHIVE(pseries) void pseries::print(const print_context & c, unsigned level) const { - debugmsg("pseries print", LOGLEVEL_PRINT); - if (is_a(c)) { c.s << std::string(level, ' ') << class_name() @@ -141,6 +134,23 @@ void pseries::print(const print_context & c, unsigned level) const var.print(c, level + delta_indent); point.print(c, level + delta_indent); + } else if (is_a(c)) { + c.s << class_name() << "(relational("; + var.print(c); + c.s << ','; + point.print(c); + c.s << "),["; + unsigned num = seq.size(); + for (unsigned i=0; icoeff.compare(_ex1())) { - c.s << '^'; + if (i->coeff.compare(_ex1)) { + if (is_a(c)) + c.s << "**"; + else + c.s << '^'; if (i->coeff.info(info_flags::negative)) { c.s << par_open; i->coeff.print(c); @@ -208,7 +221,7 @@ void pseries::print(const print_context & c, unsigned level) const int pseries::compare_same_type(const basic & other) const { - GINAC_ASSERT(is_of_type(other, pseries)); + GINAC_ASSERT(is_a(other)); const pseries &o = static_cast(other); // first compare the lengths of the series... @@ -266,7 +279,7 @@ 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(); + return ex_to((seq.end()-1)->coeff).to_int(); else return 0; } else { @@ -294,7 +307,7 @@ 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(); + return ex_to((seq.begin())->coeff).to_int(); else return 0; } else { @@ -323,14 +336,14 @@ ex pseries::coeff(const ex &s, int n) const { if (var.is_equal(s)) { if (seq.empty()) - return _ex0(); + 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)); + GINAC_ASSERT(is_exactly_a(seq[mid].coeff)); int cmp = ex_to(seq[mid].coeff).compare(looking_for); switch (cmp) { case -1: @@ -345,7 +358,7 @@ 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); } @@ -432,14 +445,14 @@ ex pseries::expand(unsigned options) const ->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) { @@ -452,10 +465,22 @@ 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); } ex pseries::convert_to_poly(bool no_order) const @@ -489,31 +514,33 @@ 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); + const symbol &s = ex_to(r.lhs()); if (!coeff.is_zero()) - seq.push_back(expair(coeff, _ex0())); + seq.push_back(expair(coeff, _ex0)); int n; for (n=1; nis_equal(*s.bp)) { + GINAC_ASSERT(is_exactly_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); } @@ -551,7 +577,7 @@ 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); } @@ -599,7 +625,7 @@ 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; @@ -633,7 +659,7 @@ ex add::series(const relational & r, int order, unsigned options) const op = it->rest; else op = it->rest.series(r, order, options); - if (!it->coeff.is_equal(_ex1())) + if (!it->coeff.is_equal(_ex1)) op = ex_to(op).mul_const(ex_to(it->coeff)); // Series addition @@ -676,13 +702,12 @@ 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); @@ -701,7 +726,7 @@ 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); @@ -713,7 +738,7 @@ 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); } @@ -723,30 +748,21 @@ 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(acc).mul_const(ex_to(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(op).power_const(ex_to(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(acc).mul_series(ex_to(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)); } @@ -778,17 +794,23 @@ ex pseries::power_const(const numeric &p, int deg) const // then of course x^(p*m) but the recurrence formula still holds. if (seq.empty()) { - // as a spacial case, handle the empty (zero) series honoring the + // 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; @@ -796,18 +818,18 @@ 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; i(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); + } 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).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 + + // No, expand basis into series + ex e = basis.series(r, order, options); return ex_to(e).power_const(ex_to(exponent), order); } @@ -879,8 +907,8 @@ 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_exactly_a(r.lhs())); + const symbol &s = ex_to(r.lhs()); if (var.is_equal(s) && point.is_equal(p)) { if (order > degree(s)) @@ -891,7 +919,7 @@ ex pseries::series(const relational & r, int order, unsigned options) const while (it != itend) { 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); @@ -922,7 +950,7 @@ ex ex::series(const ex & r, int order, unsigned options) const if (is_ex_exactly_of_type(r,relational)) rel_ = ex_to(r); else if (is_ex_exactly_of_type(r,symbol)) - rel_ = relational(r,_ex0()); + rel_ = relational(r,_ex0); else throw (std::logic_error("ex::series(): expansion point has unknown type"));