X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=9a9045da6284e1fc591ff0c5f6fc273ccdac1374;hp=c35e2e47b3e6187d6f113c3a4d0faa6c448978a1;hb=f82099178e27212fdc6801bc609202c0f9c2193e;hpb=aeee6f84150b1c3dc2021232bade4c576b859987 diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index c35e2e47..9a9045da 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 @@ -21,11 +21,12 @@ * 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" @@ -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; @@ -119,20 +114,19 @@ 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(const print_context & c, unsigned level) const { - debugmsg("pseries print", LOGLEVEL_PRINT); - - if (is_of_type(c, print_tree)) { + if (is_a(c)) { c.s << std::string(level, ' ') << class_name() << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec << std::endl; unsigned delta_indent = static_cast(c).delta_indent; - for (unsigned i=0; i(c)) { + c.s << class_name() << "(relational("; + var.print(c); + c.s << ','; + point.print(c); + c.s << "),["; + unsigned num = seq.size(); + for (unsigned i=0; i(c) ? "{(" : "("; + std::string par_close = is_a(c) ? ")}" : ")"; // objects of type pseries must not have any zero entries, so the // trivial (zero) pseries needs a special treatment here: - if (seq.size() == 0) + if (seq.empty()) c.s << '0'; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { // print a sign, if needed if (i != seq.begin()) c.s << '+'; @@ -168,7 +180,7 @@ void pseries::print(const print_context & c, unsigned level) const } // print 'coeff', something like (x-1)^42 if (!i->coeff.is_zero()) { - if (is_of_type(c, print_latex)) + if (is_a(c)) c.s << ' '; else c.s << '*'; @@ -178,14 +190,17 @@ void pseries::print(const print_context & c, unsigned level) const c.s << par_close; } else var.print(c); - if (i->coeff.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); c.s << par_close; } else { - if (is_of_type(c, print_latex)) { + if (is_a(c)) { c.s << '{'; i->coeff.print(c); c.s << '}'; @@ -196,16 +211,17 @@ void pseries::print(const print_context & c, unsigned level) const } } else Order(power(var-point,i->coeff)).print(c); + ++i; } - if (precedence <= level) + if (precedence() <= level) c.s << ")"; } } 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... @@ -263,7 +279,7 @@ 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 { @@ -291,7 +307,7 @@ 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 { @@ -319,16 +335,16 @@ 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; @@ -342,18 +358,18 @@ 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) @@ -393,13 +409,13 @@ 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 lst & ls, const lst & lr, bool no_pattern) 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); + return convert_to_poly(true).subs(ls, lr, no_pattern); // Otherwise construct a new series with substituted coefficients and // expansion point @@ -407,10 +423,10 @@ 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(ls, lr, no_pattern), it->coeff)); ++it; } - return (new pseries(relational(var,point.subs(ls, lr)), newseq))->setflag(status_flags::dynallocated); + return (new pseries(relational(var,point.subs(ls, lr, no_pattern)), newseq))->setflag(status_flags::dynallocated); } /** Implementation of ex::expand() for a power series. It expands all the @@ -418,13 +434,15 @@ ex pseries::subs(const lst & ls, const lst & lr) const 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 @@ -471,7 +489,7 @@ ex pseries::convert_to_poly(bool no_order) const bool pseries::is_terminating(void) const { - return seq.size() == 0 || !is_order_function((seq.end()-1)->rest); + return seq.empty() || !is_order_function((seq.end()-1)->rest); } @@ -484,31 +502,33 @@ 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, numeric(0))); + 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); } @@ -546,7 +565,7 @@ 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); } @@ -566,7 +585,7 @@ 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) { @@ -576,7 +595,7 @@ 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) { @@ -594,7 +613,7 @@ 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; @@ -628,11 +647,11 @@ 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())) - 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; } @@ -671,13 +690,12 @@ 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); @@ -696,7 +714,7 @@ 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); @@ -708,7 +726,7 @@ 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); } @@ -718,30 +736,21 @@ 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)); } @@ -752,6 +761,7 @@ 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 + ... @@ -771,18 +781,24 @@ 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; @@ -790,18 +806,18 @@ 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); } @@ -836,33 +855,39 @@ 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_ex_exactly_of_type(basis, pseries)) + 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); + } 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 - 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); } @@ -870,8 +895,8 @@ 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)) @@ -880,9 +905,9 @@ 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); @@ -911,9 +936,9 @@ ex ex::series(const ex & r, int order, unsigned options) const relational rel_; if (is_ex_exactly_of_type(r,relational)) - rel_ = ex_to_relational(r); + 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")); @@ -925,12 +950,4 @@ 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